Elastic Collisions - Part 3 - Blank PDF

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LEcturen notes for this class for the previous year...

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Imagine a cart (cart A) is involved in a head-on, elastic collision with a stationary cart (cart B). The collision is cushioned by a spring, that is on one of the carts:

1. Before the collision Cart B is at rest

Cart A is moving

The system’s EM is entirely in the form of Ek

B

2. First half of collision: Because , cart A is getting closer to cart B. This causes the spring in between A and B to be compressed. E k is being transferred into E s (caused by the restoring force of the spring) A

Ek of system is Es of system is

B

3. At the midpoint of the collision: The spring is at it most compressed. Thus the two carts are at the closest point to each other, that they will reach during the collision. Distance between these carts, at this point is called “minimum separation”.

A

E k of system is at E s of system is at

B

4. The second half of collision: Because , the distance in between the two carts is increasing. This causes the spring in to be extending back to its original length. Es is being transferred into Ek (caused by the restoring force of the spring) Ek of system is Es of system is

A

B

5. After the collision: The spring has now returned to its original shape. All of the elastic potential energy that was stored during the collision, has now been returned back into kinetic energy. The system’s EM is entirely in the form of Ek

A

B

At the midpoint of the collision, both objects have the same velocity. This is VERY similar to a completely inelastic collision. The maximum amount of kinetic energy that could have been transferred out of the system, during the collision, HAS BEEN. The only real difference is that in a completely inelastic collision, this energy was transferred to a form that cannot be returned to the system in the form of kinetic energy, whereas in an elastic collision, the energy was transferred into a form that could then be returned to the system as kinetic energy.

Using this: Two dynamics carts are involved in a head-on, elastic collision. Prior to the collision, cart A (which has a mass of 1.5 kg) is travelling at 2.1 m/s [S] and cart B (which has a mass of 1.2 kg) is travelling at 1.7 m/s [N]. Cart A has a 10.0 cm spring on one end of it, which is used to cushion the collision. The force constant of the spring is 1500 N/m. a) What is the velocity of the two carts when they are closest together? b) What is the minimum separation of the two carts? c) What is the velocity of the two carts, after the collision? A

B

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