אלבום פתרונות אנרגיה 23423 מעודכן

נערוך תרשים כוחות לכוחות הפועלים על הגוף כאשר זווית נטיית החוט היא 30 מעלות:

כוח המתיחות פועל בכיוון רדיאלי, כדי לכתוב את משוואת התנועה המעגלית נבצע הפרדה ישרת זווית לכוח הכובד.

נתייחס למערכת צירים שבה ציר X משיק למסלול , וציר Y הוא ציר רדיאלי.

נכתוב את משוואות התנועה לכיוון המשיקי ולכיוון הרדיאלי:

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נבטא את כוח המתיחות ממשוואת התנועה הרדיאלית:

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כדי לחשב את המתיחות בנקודה D נמצא את המהירות בנקודה D בעזרת שימור האנרגיה.

כוח המתיחות פועל בניצב לתנועה לכן הוא לא מבצע עבודה , רק כוח הכובד מבצע עבודה לכן האנרגיה המכנית נשמרת.

נשווה בין האנרגיה המכנית בנקודה D לאנרגיה המכנית בנקודה A:

נבחר מישור ייחוס בגובה הנקודה B.

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mathvariant=¨bold¨ mathcolor=¨#0000FF¨»L«/mi»«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¨»30«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«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¨»L«/mi»«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¨»60«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨»«/mspace»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»D«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msqrt mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»L«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mstyle mathvariant=¨bold¨»«mrow»«mo»[«/mo»«mi»cos«/mi»«mo»(«/mo»«mn»30«/mn»«mo»)«/mo»«mo»-«/mo»«mi»cos«/mi»«mo»(«/mo»«mn»60«/mn»«mo»)«/mo»«mo»]«/mo»«/mrow»«/mstyle»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msqrt mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»7«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»32«/mn»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»7«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨»«/mspace»«mspace 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נציב את VD ואת שאר הנתונים , בביטוי המתיחות TD:

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נמצא גיאומטרית את כיוון כוח המתיחות:

לכן גודלו של כוח המתיחות הוא 1.6 ניוטון , וכיוונו 60 מעלות מעל האופק.