Two carts on an air track have the same mass and speed and are traveling towards each other. If they collide and stick together, find (a) the total momentum and (b) total kinetic energy of the system. (c) Describe a different colliding system with this same final momentum and kinetic energy

a)

Let m be the mass of the first cart

Let v be the initial speed of the first cart.

Since the carts have the same mass and speed, then

the mass of the second cart is m

the initial speed of the second cart is v

Momentum = mass * volume

Therefore,

Momentum of the first cart before collision is mv

Momentum of the first car before collision is mv

Total momentum before collision is

mv + mv = 2mv

Let v1 be the combined volume after they stuck together. Momentum after collision is (m + m) V = 2mv1

From the law of conservation of momentum, momentum before collision = momentum after collision.

Therefore,

2mv = 2mv1

b) kinetic energy = 1/2mv²

Total Kinetic energy before collision = 1/2 * mv² + 1/2 * mv²

= mv²

Total kinetic energy after collision

= 1/2 * 2 * m * V1²

= mV1²

c)

A different colliding system would involve two carts moving in opposite direction.