Impact and Motion Figure 2.68 illustrates a carriage with mass M that has an oblique surface. The carriage can move frictionless on the ground. We drop a small ball of mass m on the surface when the carriage is at rest.
(a) Assume the ball falls from a height h above the impact point on the oblique surface. Determine the velocity of M as a function of θ if the restitution coefficient is e.
(b) Is there any optimal value for θ to provide a maximum speed of M?
(c) Assume h > > l and the first ball hits at the top point of the surface. If we drop balls every t1 seconds, then what would be the maximum speed of M when the final ball hits the carriage? How many balls will hit the carriage?
(d) Assume h and l are comparable and the first ball hits at the top point of the surface. If we drop balls every t1 seconds, then what would be the maximum speed of M when the final ball hits the carriage? How many balls will hit the carriage?
