2. A hollow ring (red) of radius R and mass M is initially stationary at the bottom of a ramp. It is struck by a horizontally moving particle (blue) of mass m at speed vo as seen below: Vo ↑ O Suppose the collision is elastic and that the ring begins to roll smoothly afterwards. (a) How much larger must M be compared to m so that the projectile is travelling to the left after the collision? (b) How high does the ring roll smoothly up the ramp? (c) Would your answer in (b) be larger or smaller if the ring were instead a solid disk of mass M and radius R? Explain.

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter8: Central-force Motion
Section: Chapter Questions
Problem 8.16P
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2. A hollow ring (red) of radius R and mass M is initially stationary at the
bottom of a ramp. It is struck by a horizontally moving particle (blue) of
mass m at speed vo as seen below:
Vo
Suppose the collision is elastic and that the ring begins to roll smoothly
afterwards.
(a) How much larger must M be compared to m so that the projectile
is travelling to the left after the collision?
(b) How high does the ring roll smoothly up the ramp?
(c) Would your answer in (b) be larger or smaller if the ring were instead
a solid disk of mass M and radius R? Explain.
Transcribed Image Text:2. A hollow ring (red) of radius R and mass M is initially stationary at the bottom of a ramp. It is struck by a horizontally moving particle (blue) of mass m at speed vo as seen below: Vo Suppose the collision is elastic and that the ring begins to roll smoothly afterwards. (a) How much larger must M be compared to m so that the projectile is travelling to the left after the collision? (b) How high does the ring roll smoothly up the ramp? (c) Would your answer in (b) be larger or smaller if the ring were instead a solid disk of mass M and radius R? Explain.
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