Question

Cart 1, with m1= 5.8 kg, is moving on a frictionless linear air track at an initial speed of 1.8 m/s. It undergoes an elastic collision with an initially stationary cart 2, with m2, an unknown mass. After the collision, cart 1 continues in its original direction at 0.7 m/s. 1) The horizontal component of the momentum is conserved for cart 1. cart 2. the system of cart 1 and cart 2. Momentum is not conserved for any of these systems. 2) The mechanical energy is conserved for cart 1. cart 2. the system of cart 1 and cart 2. Mechanical energy is not conserved in any of these systems. 3) What is the magnitude of the momentum of cart 1 before the collision? kg m/s 4) What is the magnitude of the momentum of cart 2 before the collision? kg m/s 5) What is the magnitude of the momentum of cart 1 after the collision? kg m/s 6) What is the magnitude of the momentum of cart 2 after the collision? kg m/s 7) What is the kinetic energy of cart 1 before the collision? J 8) What is the kinetic energy of cart 2 before the collision? J 9) What is the kinetic energy of cart 1 after the collision? J 10) What is the kinetic energy of cart 2 after the collision? J 11) Using your energy and momentum for cart 2 after the collision, find the mass of cart 2. (Hint: Remember that kinetic energy can be written in terms of momentum KE=p22m)

Answer 1

Collision is elastic.

Mass of first cart

Velocity of first cart before collision,

Velocity of first cart after collision,

Second cart is at rest before collision.

1)

Since the net horizontal force is zero on the system of carts and , horizontal momentum of carts and is conserved.

2)

Since the collision is elastic, mechnical energy of the system of carts and is conserved.

3)

Magnitude of momentum of cart 1 before collision

4)

Magnitude of momentum of cart 2 before collision

5)

Magnitude of momentum of cart 1 after collision

6)

Conserving momentum    

Magnitude of momentum of cart 2 after collision

7)

Kinetic energy of cart 1 before collision

8)

Kinetic energy of cart 2 before collision

9)

Kinetic energy of cart 1 after collision

10)

Since the collision is elastic, kinetic energy is conserved.  

11)

Mass of second cart