# Velocity after collision and Kinetic Energy.

1. Feb 17, 2016

### Meezus

1. The problem statement, all variables and given/known data
A trolley of mass 0.5 kg rolls along a level, frictionless ramp at a velocity of 6.0 m s-1. It collides with a second trolley of mass 1.0 kg which is initially at rest. The first trolley rebounds with a speed of 2.0 m s-1 .
a) Stating clearly any principles involved, find the velocity of the second trolley after the collision.
b) Compare the kinetic energy before and after the collision. Is the collision elastic?

2. Relevant equations
p = m x v
E=1/2*m*v^2

3. The attempt at a solution
Momentum before collusion for carriage A: 0.5 x 6 = 3
Momentum before collusion for carriage B: 1 x 0 = 0
Total Momentum before : 3 + 0 = 3.
Total Mass = 1 + 0.5 = 1.5.
p = m x v
v = p / m
3 / 1.5 = 2.
The principles involved are that as long as no external forces are acting on the object the total momentum stays the same in a collisions.
Is this correct for the first one?

part b:

0.5 x 1.5 x 62 = 27
0.5 x 1.5 x 22 = 3

The collision is inelastic as kinetic energy is lost?

2. Feb 17, 2016

### Staff: Mentor

What is meant by "rebounds"?

3. Feb 17, 2016

### Meezus

Like when you throw a ball at a wall and it comes back. It "rebounds" off wall.

4. Feb 17, 2016

### Staff: Mentor

So the two bodies do not stick together.

Then try to complete this table, too:

5. Feb 17, 2016

### Meezus

I thought because momentum is conserved the total momentum is the same after?

6. Feb 17, 2016

### Staff: Mentor

It should be. Can you fill in the blanks?

7. Feb 17, 2016

### Meezus

Momentum after collision for carriage A: 0.5 x 2 = 1
Momentum after collision for carriage B:1 x ? = ?
Total Momentum after collision: 3

If the total momentum stays the same the velocity for carriage B must be 2.

8. Feb 17, 2016

### Staff: Mentor

If a body rebounds, its velocity changes direction.

9. Feb 17, 2016

### Meezus

Ok. Is what I have done correct? I don't see where the rebound part comes into play?

10. Feb 17, 2016

### haruspex

Velocity and momentum are vectors. Direction matters. If a ball hits a wall square on at velocity v and rebounds with the same speed, what is its new velocity?

11. Feb 17, 2016

### ajaykrishna1990

total momentum is conserved.
total momentum before collision = total momentum after collision
(if there is no external unbalanced force is acting there! )

12. Feb 17, 2016

### Staff: Mentor

The correct answer is 0.5 x -2 because rebound velocity is in the opposite direction. Momentum is a vector quantity.