Elastic Collision - Symbolic Question

In summary, the conversation discusses a scenario where a small ball is dropped from the center of mass of a larger ball. The small ball rebounds with surprising speed due to elastic collisions with the larger ball and the floor. The problem asks for the velocities of the balls before and after the collision, as well as the ratio of the small ball's rebound distance to its initial fall distance. The equations for elastic collision and conservation of energy are provided as hints for solving the problem.
  • #1
kanavulator
2
0

Homework Statement



Suppose you hold a small ball of mass m1 in contact with, and directly over, the center of mass of a large ball of mass m2. If you then drop the small ball a short time after dropping the large ball, the small ball rebounds with surprising speed. If we ignore air resistance and assume the large ball makes an elastic collision with the floor and then makes an elastic collision with the still descending small ball and that large ball has much larger mass than the small ball then:

a) If the velocity of the small ball immediately before the collision is v, what is the velocity of the large ball? (in terms of v)

b) What is the velocity of the small ball immediately after its collision with the large ball? (in terms of v)

c) What is the ratio of the small ball's rebound distance to the distance it fell before the collision? (a number)

Homework Equations



1/2mv^2 + mgh = 1/2mv^2 + mgh
Elastic collision: V1 = -V2

The Attempt at a Solution



a. -V
b. ?
c. ?
 
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  • #2
Hint: Analyze the problem in the center of mass frame, then transform back to the lab frame. (Assume m2 >> m1.)
 
  • #3
That...doesn't make a bit of sense to me. Pardon my lack of knowledge, but I'm not really familiar with the terms you were using, Doc Al.
 
  • #4
kanavulator said:
That...doesn't make a bit of sense to me. Pardon my lack of knowledge, but I'm not really familiar with the terms you were using, Doc Al.
No problem. Sometimes problems are easier to solve in certain frames of reference--but let's forget that for the moment.

What do you know about elastic collision?

kanavulator said:
1/2mv^2 + mgh = 1/2mv^2 + mgh
You'll need this for part c.

Elastic collision: V1 = -V2
What does this mean? If you mean the relative velocity reverses: Great! Use it.

The Attempt at a Solution



a. -V
Assuming you meant -v (the same v as the small ball): Good!

Here's a hint for part b: If a ping pong ball hits a bowling ball, what happens to the velocity of the bowling ball? (To a good approximation.)
 

1. What is an elastic collision?

An elastic collision is a type of collision between two objects in which there is no loss of kinetic energy. In other words, the total kinetic energy of the system before and after the collision remains the same.

2. What is the difference between an elastic collision and an inelastic collision?

In an elastic collision, the total kinetic energy of the system is conserved. In an inelastic collision, some of the kinetic energy is lost due to the deformation of the objects involved or the generation of heat or sound.

3. What is the equation for calculating the final velocities in an elastic collision?

The equation for calculating the final velocities in an elastic collision is v1f = ((m1 - m2) * v1i + 2 * m2 * v2i) / (m1 + m2) and v2f = ((m2 - m1) * v2i + 2 * m1 * v1i) / (m1 + m2), where m1 and m2 are the masses of the two objects and v1i and v2i are their initial velocities.

4. Can an elastic collision occur between two objects of different masses?

Yes, an elastic collision can occur between two objects of different masses. In fact, the equation for calculating the final velocities in an elastic collision takes into account the masses of both objects.

5. What are some real-life examples of elastic collisions?

Some real-life examples of elastic collisions include billiard balls colliding on a pool table, two cars colliding without suffering any damage, and a tennis ball bouncing off a racquet.

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