A ball rolls without slipping down the track as shown in the figure below, start
ID: 2139112 • Letter: A
Question
A ball rolls without slipping down the track as shown in the figure below, starting from rest at a height h1 = 22 m as shown. The ball is traveling horizontally when it leaves the bottom of the track, which has a height h2 = 9.5 m. Find where the ball hits the ground; that is, find L.
A ball rolls without slipping down the track as shown in the figure below, starting from rest at a height h1 = 22 m as shown. The ball is traveling horizontally when it leaves the bottom of the track, which has a height h2 = 9.5 m. Find where the ball hits the ground; that is, find L.Explanation / Answer
m g (h1 - h2) = 0.5 m v^2 + 0.5 I w^2
m g (h1 - h2) = 0.5 m v^2 + 0.5 (2/5 m R^2) (v/R)^2
g (h1 - h2) = 0.5 v^2 + (1/5) v^2
v = sqrt(9.8*(22-9.5)/0.7)
v = 13.22875655532295 m/s
-9.5 = -0.5*9.8*t^2 ==> t = 1.392399192115566 s
L = v t = 13.2287 *1.392399192115566
= 18.41963119273919 m
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