פתרונות פרקטיקות-3- דינמיקה שני גופים

גוף 1 נע בצורה אנכית בעוד גוף 2 נע לאורך המישור המשופע.

משום שהגופים מחוברים בחוט אידיאלי מתוח, תאוצותיהם שוות בגודלן.

על מנת שתאוצותיהם יהיו שוות בסימנן, נגדיר את הצירים כך:

עבור גוף 1: נגדיר את ציר ה-Y כלפי מטה.

עבור גוף 2: נגדיר את ציר ה-X במעלה המישור ואת ציר ה-Y במאונך למישור כלפי מעלה.

על גוף 1 פועלים שני כוחות: כוח הכובד W₁ וכוח המתיחות T.

נערוך תרשים כוחות על גוף 1:

נרשום משוואת תנועה בכיוון אנכי:

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על גוף 2 פועלים ארבעה כוחות: כוח הכובד W₂, כוח הנורמל N, כוח המתיחות T וכוח החיכוך f_k.

נערוך תרשים כוחות על גוף 2:

נערוך הפרדה ישרת זווית ל-W₂:

גוף 2 נמצא במנוחה בכיוון ציר ה-Y ובתאוצה בכיוון ציר ה-X.

גוף 1 נמצא בתאוצה בכיוון ציר ה-Y.

נכתוב את משוואות התנועה עבור גוף 2 בכיוון מאונך למישור:

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נציב את הנורמל בביטוי החיכוך הקינטי:

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נחבר בין שתי המשוואות המסומנות האחרונות ונבטא את התאוצה:

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