Question

When two carts collide, we know that the total momentum of the system should be conserved, as long as there are no external forces acting on the system. That is, Pi = Pf, where Pi and Pf are the total momenta before and after the collision, respectively.

TOTALLY INELASTIC COLLISIONS

A. Carts with Equal Mass

Orient the carts so their Velcro bumpers face each other. In the collisions they MUST stick together.

1. Place one cart at rest in the middle of the track. Give the other cart an initial velocity toward the cart at rest.

Prediction

Observation

2. Start with both carts at opposite ends of the track and push them toward each other with about the same speed.

Prediction

Observation

3. Start with both carts at the same end. Give the first cart a slow initial speed, and the second a faster speed so it catches the first about half way down the track.

Prediction

Observation

B. Carts with Unequal Mass

4. Place two mass bars on one of the carts. Now its mass is about 3 times the mass of the other cart. Put the 3M cart at rest in the middle of the track and push the other toward it.

Prediction

Observation

5. Put the 1M cart in the middle and push the 3M cart toward it.

Prediction

Observation

6. Start the carts at different ends of the track. Give them about the same speed toward each other.

Prediction

Observation

7. Start both carts at the same end of the track. Give the 1M a slow speed, and the 3M a faster speed so that it collides with the first.

Prediction

Observation

8. Start both carts at the same end of the track. Now give the 3M a slow speed, and the 1M a faster speed so that it collides with the first.

Prediction

Observation

ELASTIC COLLISIONS

A. Carts with Equal Mass

Orient the carts so their magnetic bumpers face each other. The carts MUST bounce without hitting.

1. Place one cart at rest in the middle of the track. Give the other cart an initial velocity toward the cart at rest.

Prediction

Observation

2. Start with both carts at opposite ends of the track and push them toward each other with about the same speed.

Prediction

Observation

3. Start with both carts at the same end. Give the first cart a slow initial speed, and the second a faster speed so it catches the first about half way down the track.

Prediction

Observation

B. Carts with Unequal Mass

4. Place two mass bars on one of the carts. Now its mass is about 3 times the mass of the other cart. Put the 3M cart at rest in the middle of the track and push the other toward it.

Prediction

Observation

5. Put the 1M cart in the middle and push the other toward it.

Prediction

Observation

6. Start the carts at opposite ends of the track. Give them about the same speed toward each other.

Prediction

Observation

7. Start both carts at the same end of the track. Give the 1M a slow speed, and the 3M a faster speed so that it collides with the first.

Prediction

Observation

8. Start both carts at the same end of the track. Now give the 3M a slow speed, and the 1M a faster speed so that it collides with the first.

Prediction

Observation

Answer 1

1)In inelastic collision momentum before collision and after collision is conserved but kinetic energy is not conserved. So when one cart is at rest then its kinetic energy is k.e=1/2mv²=0

The other is moving so kinetic energy is k.e=1/2mv²

For a perfectly inelastic collision, the two bodies stick together, so that m1v1+m2v2=(m1+m2)vf

Since mass is same that is m1=m2=m and v1=0 then

mv2=2mvf, therefore v2=1/2vf.

So both the cart move with half the velocity of second cart.

2)when both cart starts with same velocity and same mass m then by conservation of momentum

mv1+mv2=(m+m)vf

Here both velocity is same that is v1=v2=v, then

mv+mv=(m+m)vf

2mv=2mvf, that is v =vf

that is after collision they move with same initial velocity with sticking together

B)4)as the mass of two cart is m&3m and since 3m is at rest its velocity v1=0

Therefore by conservation of momentum

3mv1+mv2=(3m+m)vf

That is 0+ mv2=4mvf

So v2=4vf

That is both the cart after collision move with 1/4 velocity of second carts initial velocity.

5)now 1m cart is in rest that is v2=0 and 3m is moving toward it

So 3mv1+mv2=(3m+m)vf

3mv1=4mvf

vf=3/4v1

So the final velocity will be 3/4 of intial velocity of heavier mass