# Solving an Elastic Collision Problem

• jezelee
In summary, the problem involves two spheres of different masses hanging from strings attached to the same point on the ceiling. The lighter sphere is initially pulled aside at a 60 degree angle and released, causing both spheres to collide elastically. The question is asking for the maximum angle that the string holding the lighter sphere makes after the collision. To solve this problem, you will need to use the conservation of momentum and energy, as well as the relationship between change in height and angle in a pendulum swing.
jezelee
Other than finding the intial xy coordinates and knowing gravity as a factor I am not sure where to go with this problem as the formulas I have deal with final angles and not initial. The problem follows:

Two spheres of mass 1kg & 1.5Kg hang @ rest at the ends of strings that are both 1.5m long and attached at the same point on the ceiling. The lighter sphere is pulled aside so that it makes an angle of 60 degrees w/ vertical. The lighter sphere is then released and the two spheres collide elastically. When they rebound, what is the largest angle with respect to the vertical that the string holding the lighter sphere makes?

Help would be greatly appreciated. Thanks.

Remember both momentum and energy is conserved. So initial (total) momentum = final (total) momentum. Likewise, initial (total) energy = final (total) energy.

A good tip is that the change in height in a pendulum swing is L-Lcos(theta). Draw out a picture so you can see this relationship and then store it in your memory, it comes in handy a lot

As for this question, find the initial velocity before the collision and use that to calculate the final velocity after the collision (KE conserved). Once you know how much kinetic energy it has afterward, find the new maximum height

## 1. What is an elastic collision?

An elastic collision is a type of collision between two objects in which both kinetic energy and momentum are conserved. This means that the total energy and momentum before and after the collision is equal.

## 2. How is an elastic collision problem solved?

To solve an elastic collision problem, you must use the conservation of momentum and conservation of kinetic energy equations. These equations involve the mass, velocity, and direction of the objects before and after the collision.

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

In an elastic collision, both kinetic energy and momentum are conserved. In an inelastic collision, only momentum is conserved while some kinetic energy is lost. This means that the objects involved in an inelastic collision will experience a change in speed or direction.

## 4. What factors affect the outcome of an elastic collision?

The outcome of an elastic collision is affected by the masses and velocities of the objects involved. Objects with higher masses will have a greater effect on the collision, while objects with higher velocities will have a greater change in momentum.

## 5. Can an elastic collision occur in real life?

Yes, elastic collisions can occur in real life. Examples include collisions between billiard balls on a pool table or collisions between molecules in a gas. These collisions are not perfectly elastic, but they are close enough to be considered elastic for practical purposes.

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