Question:

A 500 kg car is initially at rest on a frictionless track. A 200 kg cart, initially moving with a velocity of 5 m/s in the positive x-direction, collides with the car. After the collision, the car and the cart stick together and move off together with a common velocity. Calculate the final velocity of the car and cart system after the collision. Assume the positive direction as the direction in which the cart was moving initially.

Answer:

To solve this problem, we can apply the principle of conservation of linear momentum. According to this principle, the total linear momentum of an isolated system remains constant before and after a collision.

We know that the linear momentum (p) of an object can be calculated by multiplying its mass (m) with its velocity (v).

Before the collision: Car (mass, m1 = 500 kg, velocity, v1 = 0 m/s) Cart (mass, m2 = 200 kg, velocity, v2 = 5 m/s)

The initial momentum of the system can be calculated by summing the individual momenta of the car and the cart.

Initial momentum (p_initial) = m1 * v1 + m2 * v2

Let's calculate the initial momentum:

After the collision, the car and the cart stick together and move off with a common velocity (v_final).

Final momentum (p_final) = (m1 + m2) * v_final

According to the conservation of momentum principle:

p_initial = p_final

1000 kg m/s = (500 kg + 200 kg) * v_final

Let's calculate the final velocity:

Therefore, the final velocity of the car and cart system after the collision is approximately 1.43 m/s in the positive x-direction.