Question

When a very light object such as a ping-pong ball hits head-on a very heavy object that is at rest, such as a bowling ball, and the collision is elastic, the light object bounces back with a speed that is only very slightly less than the initial speed. It's like bouncing off a wall. The heavy object recoils with a speed that is very small compared to the speed of the light object. By solving exactly the equations for momentum and energy conservation (and assuming an elastic collsion), it can be shown that the following results are true, without making approximations, and these exact results can be used to explore how good the approximate results are. The light object has a mass m, initial speed v₁, and final speed us. The heavy object has a mass M and a final speed V US = V = M-m - V¡, M + m 2m M + m Part 1 US Suppose m = 1 kg and its initial speed u, so U v, if M > > m.-U₁, so V is nearly zero if M > > m. = = 90 m/s. Suppose M 100 kg and this heavy object is initially at rest). The final speed us of th

Answer 1

The student's question inquires about the outcome of an elastic collision where a light object bounces off a heavier object initially at rest. Conservation laws confirm the light object will rebound with almost the same speed, while the heavier object moves with a much lower speed.

Step-by-step explanation:

The student's question concerns the behavior of two objects of significantly different masses during an elastic collision, a concept from Physics.

Specifically, it looks at the scenario where a light object (e.g., a ping-pong ball) collides head-on with a heavier object (e.g., a bowling ball) that is initially at rest, and how their speeds compare after the collision.

The question indicates that the light object (mass m) has an initial speed v1, and after the collision, it has a final speed us.

The heavier object (mass M) is initially at rest, and after the collision, it has a final speed V.

By using the conservation of momentum and kinetic energy (which is conserved in an elastic collision), we can confirm that the light object rebounds with a velocity almost equal to its initial velocity if M is much larger than m, and the heavier object moves forward with a very small speed in comparison to the light object.