Dynamics of Rotational Motion Problem #14 - Comparison of Sliding Down a Ramp vs. Rails
Автор: Sine Theta Prime
Загружено: 2023-10-22
Просмотров: 129
Описание:
A uniform ball of radius R rolls without slipping between two rails such that the horizontal distance is d between the two contact points of the rails to the ball.
a.) In a sketch show that at any instant v_cm = ω*sqrt(R² - d²/4). Discuss this expression in the limits of d = 0 and d = 2R.
b.) For a uniform ball starting from rest and descending a vertical distance of h while rolling without slipping down a ramp, v_cm = sqrt(10gh/7).
Replacing the ramp with the two rails, show that v_cm = sqrt[10gh/(5 + 2/(1 - d²/4R²)]. In each case, the work done by friction has been ignored.
c.) Which speed in part (b) is smaller? Why? Answer in terms of how the loss of potential energy is shared between the gain in translational and rotational kinetic energies.
d.) For which value of the ratio d/R do the two expressions for the speed in part (b) differ by 5.0%? By 0.50%?
0:00 Problem Description
0:33 Setup + Part A
5:14 Part B
8:14 Part C
11:14 Part D
13:50 Solution Card
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