פרקטיקות 2- עבודת כוח לא משמר.

שאלה 3

לצורך התרגול, לא נסתמך רק על ערך ההעתק המחושב בסעיף הקודם ונערוך חישוב מלא.

א. חישוב הגובה אליו הגיע הגוף בעזרת עקרונות הקינמטיקה דינמיקה:

נתוני השאלה:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»k«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»g«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»30«/mn»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msup»«/math»

נערוך תרשים כוחות ונבצע הפרדה ישרת זווית:

נכתוב את משוואות התנועה ביחס לציר X שכיוונו ככיוון התנועה, וציר Y שכיוונו ניצב לתנועה, ככיוון הנורמל:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#931;F«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Y«/mi»«/msub»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«mi mathvariant=¨bold¨»N«/mi»«mo mathvariant=¨bold¨»=«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/menclose»«mspace linebreak=¨newline¨/»«/math»                                    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#931;F«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»f«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»W«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»sin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»=«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»a«/mi»«/menclose»«mspace linebreak=¨newline¨/»«/math»

נבטא את התאוצה ממשוואת התנועה בכיוון ציר X:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»f«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«menclose mathcolor=¨#FF0000¨ notation=¨updiagonalstrike¨»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨updiagonalstrike¨»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨updiagonalstrike¨»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«/math»

נבטא את ההעתק בעזרת ביטוי ריבוע המהירויות:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msup»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»x«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msup»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msup»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»[«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»)«/mo»«mo mathvariant=¨bold¨»]«/mo»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msup»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»[«/mo»«msub»«mi mathvariant=¨bold¨»§#956;«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»sin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»]«/mo»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

 נבטא גיאומטרית את הגובה «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«/math» בו נעצר הגוף,  כתלות ב- Δx .

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»h«/mi»«mrow»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«/mstyle»«/math»

נציב  את ביטוי ההעתק:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#FF0000¨»«mrow»«msup»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»[«/mo»«msub»«mi mathvariant=¨bold¨»§#956;«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»sin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»]«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»h«/mi»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mi mathvariant=¨bold¨»sin«/mi»«mrow»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨»§#183;«/mo»«mrow»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«msup»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»[«/mo»«msub»«mi mathvariant=¨bold¨»§#956;«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»sin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»]«/mo»«/mrow»«/mfrac»«/menclose»«/mstyle»«/math»

נחשב את הגובה בו נעצר הגוף:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»sin«/mi»«mrow»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨»§#183;«/mo»«mstyle mathvariant=¨bold¨»«mo stretchy=¨true¨»(«/mo»«msup»«mi»V«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«msup»«msub»«mi»V«/mi»«mn»0«/mn»«/msub»«mn»2«/mn»«/msup»«mo stretchy=¨true¨»)«/mo»«/mstyle»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»[«/mo»«msub»«mi mathvariant=¨bold¨»§#956;«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»sin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»]«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»sin«/mi»«mrow»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mn mathvariant=¨bold¨»30«/mn»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨»§#183;«/mo»«mstyle mathvariant=¨bold¨»«mo stretchy=¨true¨»(«/mo»«msup»«mn»0«/mn»«mn»2«/mn»«/msup»«mo»-«/mo»«msup»«mn»20«/mn»«mn»2«/mn»«/msup»«mo stretchy=¨true¨»)«/mo»«/mstyle»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»[«/mo»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»8«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»10«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»30«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»10«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»sin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»30«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»]«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»400«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»6«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»92«/mn»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»200«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»23«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»84«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»38«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«/mstyle»«/math»

ב. חישוב הגובה אליו הגיע הגוף בעזרת משפט עבודה אנרגיה:

       כוח הנורמל פועל בניצב לתנועה, הוא לא מבצע עבודה.

      כוח החיכוך פועל בכיוון נגדי לתנועה. 

      הזווית בין כוח הכובד לכיוון התנועה היא 120 מעלות .

      נכתוב בהתאם את משפט העבודה אנרגיה:

                                    «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#931;W«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»w«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mg«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨updiagonalstrike¨»«msub»«mi mathvariant=¨bold¨»W«/mi»«mi mathvariant=¨bold¨»N«/mi»«/msub»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»w«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mg«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mv«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«msup»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«msub»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»180«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«mi mathvariant=¨bold¨»W«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»120«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mV«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«msup»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«/math»

בדומה לפעולות האלגבריות בסעיף הקודם, נבטא את העתק התנועה:

                                                                                                                               «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msup»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»[«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»120«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»§#956;«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»30«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»]«/mo»«/mrow»«/mfrac»«/math»

נבטא גאומטרית את הגובה אליו הגיע הגוף בעזרת פונקצית הסינוס:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mn mathvariant=¨bold¨»30«/mn»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#FF0000¨»«mrow»«msup»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»[«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»120«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»§#956;«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»30«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»]«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mn mathvariant=¨bold¨»30«/mn»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨»h«/mi»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mi mathvariant=¨bold¨»sin«/mi»«mrow»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mn mathvariant=¨bold¨»30«/mn»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨»§#183;«/mo»«mrow»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«msup»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«msub»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»[«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»120«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»§#956;«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mn mathvariant=¨bold¨»30«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»]«/mo»«/mrow»«/mfrac»«/menclose»«/mstyle»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨ mathsize=¨18px¨»sin«/mi»«mrow»«mo mathvariant=¨bold¨ mathsize=¨18px¨ stretchy=¨true¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»30«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mrow»«mo mathvariant=¨bold¨ mathsize=¨18px¨ stretchy=¨true¨»(«/mo»«msup»«mi mathvariant=¨bold¨ mathsize=¨18px¨»V«/mi»«mn mathvariant=¨bold¨ mathsize=¨18px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathsize=¨18px¨»-«/mo»«msup»«msub»«mi mathvariant=¨bold¨ mathsize=¨18px¨»V«/mi»«mn mathvariant=¨bold¨ mathsize=¨18px¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathsize=¨18px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathsize=¨18px¨ stretchy=¨true¨»)«/mo»«/mrow»«/mrow»«mrow»«mn mathvariant=¨bold¨ mathsize=¨18px¨»2«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathsize=¨18px¨»[«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»g«/mi»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»cos«/mi»«mo mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»120«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«mo mathvariant=¨bold¨ mathsize=¨18px¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathsize=¨18px¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathsize=¨18px¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»g«/mi»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»cos«/mi»«mo mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»30«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«mo mathvariant=¨bold¨ mathsize=¨18px¨»]«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨ mathsize=¨18px¨»sin«/mi»«mrow»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»30«/mn»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mrow»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«msup»«mn mathvariant=¨bold¨ mathsize=¨18px¨»0«/mn»«mn mathvariant=¨bold¨ mathsize=¨18px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathsize=¨18px¨»-«/mo»«msup»«mn mathvariant=¨bold¨ mathsize=¨18px¨»20«/mn»«mn mathvariant=¨bold¨ mathsize=¨18px¨»2«/mn»«/msup»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«/mrow»«/mrow»«mrow»«mn mathvariant=¨bold¨ mathsize=¨18px¨»2«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathsize=¨18px¨»[«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»10«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»cos«/mi»«mo mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»120«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«mo mathvariant=¨bold¨ mathsize=¨18px¨»-«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»0«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨».«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»8«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»10«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»0«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨».«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»866«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»]«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨ mathsize=¨18px¨»0«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨».«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»5«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mrow»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mo mathvariant=¨bold¨ mathsize=¨18px¨»-«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»400«/mn»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«/mrow»«/mrow»«mrow»«mn mathvariant=¨bold¨ mathsize=¨18px¨»2«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathsize=¨18px¨»[«/mo»«mo mathvariant=¨bold¨ mathsize=¨18px¨»-«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»5«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»-«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»6«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨».«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»928«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»]«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨ mathsize=¨18px¨»-«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»200«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨ mathsize=¨18px¨»-«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»23«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨».«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»856«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»38«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»m«/mi»«/math»

ג. חישוב הגובה אליו הגיע הגוף בעזרת משפט עבודה אנרגיה.

 כוח החיכוך הקינטי הוא הכוח הלא משמר היחיד שעושה עבודה:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder mathcolor=¨#0000FF¨»«munder»«mi mathvariant=¨bold¨»W«/mi»«mo mathvariant=¨bold¨»§#9183;«/mo»«/munder»«mrow»«mi mathvariant=¨bold¨»§#1502;§#1513;§#1502;§#1512;§#1497;§#1501;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»§#1500;§#1488;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»§#1499;§#1493;§#1495;§#1493;§#1514;«/mi»«/mrow»«/munder»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«munder mathcolor=¨#0000FF¨»«munder»«mrow»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»E«/mi»«/mrow»«mo mathvariant=¨bold¨»§#9183;«/mo»«/munder»«mrow»«mi mathvariant=¨bold¨»§#1499;§#1493;§#1500;§#1500;§#1514;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»§#1502;§#1499;§#1504;§#1497;§#1514;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»§#1489;§#1488;§#1504;§#1512;§#1490;§#1497;§#1492;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»§#1513;§#1497;§#1504;§#1493;§#1497;«/mi»«/mrow»«/munder»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«mspace linebreak=¨newline¨/»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«msub»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#952;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mspace linebreak=¨newline¨/»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«msub»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#952;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»[«/mo»«mrow»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«msub»«mi mathvariant=¨bold¨»E«/mi»«mi mathvariant=¨bold¨»K«/mi»«/msub»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»U«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨»-«/mo»«mrow»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«msub»«mi mathvariant=¨bold¨»E«/mi»«msub»«mi mathvariant=¨bold¨»K«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub»«mi mathvariant=¨bold¨»U«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ stretchy=¨true¨»]«/mo»«/mrow»«mspace linebreak=¨newline¨/»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«msub»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#952;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»K«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»K«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«/math»

כוח החיכוך הקינטי פועל בכיוון נגדי לתנועה, הזווית בין כיוון התנועה לכיוון כוח החיכוך שווה ל 180 מעלות.

בסיום התנועה הגוף נעצר, לכן האנרגיה הקינטית בסיום התנועה שווה ל אפס.

ביחס למישור תנועה הנמצא בנקודה בה הגוף התחיל את תנועתו, האנרגיה הפוטנציאלית כובדית ההתחלתית שווה לאפס.

נבטא במשוואה את כוח החיכוך הקינטי, בהתאם להגדרת הכוח ולמשוואת התנועה בכיוון ציר Y:

                                                                                                                         «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«msub»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»180«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»K«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»K«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mspace linebreak=¨newline¨/»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«msub»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨updiagonalstrike¨»«msub»«mi mathvariant=¨bold¨»E«/mi»«mi mathvariant=¨bold¨»K«/mi»«/msub»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»K«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨updiagonalstrike¨»«msub»«mi mathvariant=¨bold¨»U«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/menclose»«mspace linebreak=¨newline¨/»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»f«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»K«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/msub»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»K«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/msub»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»mg«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#FF0000¨»c«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#FF0000¨»o«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#FF0000¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»(«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#FF0000¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»K«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/msub»«/math»

נכתוב בצורה מפורשת את האנרגיה הפוטנציאלית בסוף התנועה ואת האנרגיה הקינטית בתחילת התנועה:

              «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mg«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»K«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«/msub»«mspace linebreak=¨newline¨/»«mo»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mg«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mg«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«/math»

נבטא גאומטרית את העתק התנועה בתלות בגובה אליו הגיע הגוף. 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»sin«/mi»«mrow mathcolor=¨#0000FF¨»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»30«/mn»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathsize=¨18px¨»h«/mi»«mrow»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»X«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»§#8658;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathsize=¨18px¨»h«/mi»«mrow»«mi mathvariant=¨bold¨ mathsize=¨18px¨»sin«/mi»«mrow»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»30«/mn»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«/mrow»«/mrow»«/mfrac»«/math»

נציב את ביטוי ההעתק במשוואה המתקבלת מביטוי עבודת הכוח הלא משמר:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mg«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#8710;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»X«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mg«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mg«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfrac mathcolor=¨#FF0000¨»«mi mathvariant=¨bold¨ mathsize=¨18px¨»h«/mi»«mrow»«mi mathvariant=¨bold¨ mathsize=¨18px¨»sin«/mi»«mrow»«mo mathvariant=¨bold¨ mathsize=¨18px¨ stretchy=¨true¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»30«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨ stretchy=¨true¨»)«/mo»«/mrow»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mg«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«/math»

נכתוב ביטוי ל h:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨downdiagonalstrike¨»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathsize=¨18px¨»h«/mi»«mrow»«mi mathvariant=¨bold¨ mathsize=¨18px¨»sin«/mi»«mrow»«mo mathvariant=¨bold¨ mathsize=¨18px¨ stretchy=¨true¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»30«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨ stretchy=¨true¨»)«/mo»«/mrow»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨downdiagonalstrike¨»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨downdiagonalstrike¨»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathsize=¨18px¨ mathvariant=¨bold¨»h«/mi»«mrow»«mi mathvariant=¨bold¨»ta«/mi»«mi mathsize=¨18px¨ mathvariant=¨bold¨»n«/mi»«mrow»«mo mathsize=¨18px¨ stretchy=¨true¨ mathvariant=¨bold¨»(«/mo»«mn mathsize=¨18px¨ mathvariant=¨bold¨»30«/mn»«mo mathsize=¨18px¨ stretchy=¨true¨ mathvariant=¨bold¨»)«/mo»«/mrow»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathsize=¨18px¨ mathvariant=¨bold¨»h«/mi»«mrow»«mi mathvariant=¨bold¨»ta«/mi»«mi mathsize=¨18px¨ mathvariant=¨bold¨»n«/mi»«mrow»«mo mathsize=¨18px¨ stretchy=¨true¨ mathvariant=¨bold¨»(«/mo»«mn mathsize=¨18px¨ mathvariant=¨bold¨»30«/mn»«mo mathsize=¨18px¨ stretchy=¨true¨ mathvariant=¨bold¨»)«/mo»«/mrow»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»V«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»h«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msub»«mi mathvariant=¨bold¨ mathsize=¨18px¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathsize=¨18px¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ 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mathsize=¨18px¨»2«/mn»«/mfrac»«/mstyle»«mstyle displaystyle=¨true¨»«mfrac»«mrow»«mi mathvariant=¨bold¨ mathsize=¨18px¨»g«/mi»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»tan«/mi»«mrow»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»30«/mn»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathsize=¨18px¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathsize=¨18px¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathsize=¨18px¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»g«/mi»«/mrow»«mrow»«mi mathvariant=¨bold¨ mathsize=¨18px¨»tan«/mi»«mrow»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»30«/mn»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«/mrow»«/mrow»«/mfrac»«/mstyle»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨18px¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msup»«msub»«mi mathvariant=¨bold¨ mathsize=¨18px¨»V«/mi»«mn mathvariant=¨bold¨ mathsize=¨18px¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathsize=¨18px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»tan«/mi»«mrow»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»30«/mn»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«/mrow»«/mrow»«mrow»«mn mathvariant=¨bold¨ mathsize=¨18px¨»2«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»g«/mi»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»tan«/mi»«mrow»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»30«/mn»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathsize=¨18px¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathsize=¨18px¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathsize=¨18px¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»g«/mi»«mo mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mi mathvariant=¨bold¨ mathsize=¨18px¨»h«/mi»«mo mathvariant=¨bold¨ mathsize=¨18px¨»=«/mo»«mfrac»«mrow»«msup»«msub»«mi mathvariant=¨bold¨ mathsize=¨18px¨»V«/mi»«mn mathvariant=¨bold¨ mathsize=¨18px¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathsize=¨18px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»tan«/mi»«mrow»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»30«/mn»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«/mrow»«/mrow»«mrow»«mn mathvariant=¨bold¨ mathsize=¨18px¨»2«/mn»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»g«/mi»«mo mathvariant=¨bold¨ mathsize=¨18px¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mi mathvariant=¨bold¨ mathsize=¨18px¨»tan«/mi»«mrow»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»(«/mo»«mn mathvariant=¨bold¨ mathsize=¨18px¨»30«/mn»«mo stretchy=¨true¨ mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathsize=¨18px¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathsize=¨18px¨»§#956;«/mi»«mi mathvariant=¨bold¨ mathsize=¨18px¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathsize=¨18px¨»)«/mo»«/mrow»«/mfrac»«/menclose»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

נציב את הנתונים ונמצא את ערכו של h:

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ד.  חישוב כמות האנרגיה המכנית שהלכה לאיבוד במהלך תנועת הגוף:

כמות האנרגיה המכנית שהלכה לאיבוד במהלך התנועה, שווה להפרש בין האנרגיה המכנית בסוף התנועה לאנרגיה המכנית בתחילת התנועה.

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בסיום התנועה  הגוף נעצר, האנרגיה הקינטית בסיום התנועה שווה לאפס.

נקבע את מישור הייחוס בנקודה ממנה הגוף התחיל לנוע , כך שהאנרגיה הפוטנצילית בתחילת התנועה שווה לאפס.

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ה. בהנחה שכמות כל האנרגיה המכנית שהלכה לאיבוד הומרה לחום, כמות החום היא : «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»580«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»85«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»J«/mi»«/math»

ו.  חישוב עבודת כוח החיכוך הקינטי

הכוח הלא משמר היחיד שמבצע עבודה על הגוף הוא כוח החיכוך. לכן, מביטוי עבודת הכוחות הלא משמרים, עבודת כוח החיכוך שווה לשינוי באנרגיה המכנית:

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דרך נוספת: נחשב את עבודת כוח החיכוך.

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בסעיף קודם מצאנו שהעתק התנועה הוא 16.76 מטר , נחשב בהתאם את עבודת כוח החיכוך:

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*מתקבלים ערכים מעט שונים, כתוצאה מחוסר דיוק בחישוב הפרש האנרגיות.