Question

A 70 kg train cart is rolling at 36 m/s when it collides with a 120 kg train car rolling at 20 m/s. After the train carts collide they stick together and roll away. What is the final velocity of the stuck together train carts?

Answer 1

To find the final velocity of the stuck together train carts, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision. Plugging in the values, we find that the final velocity of the stuck together train carts is approximately 25.9 m/s.

Step-by-step explanation:

In order to find the final velocity of the stuck together train carts, we can use the principle of conservation of momentum. The principle states that the total momentum before the collision is equal to the total momentum after the collision.

The formula for momentum is:

P = mv

Where P is the momentum, m is the mass, and v is the velocity.

Using this formula, we can calculate the momentum of the first train car and the second train car:

P1 = m1v1

= 70 kg × 36 m/s

= 2520 kg·m/s

P2 = m2v2

= 120 kg × 20 m/s

= 2400 kg·m/s

Since momentum is conserved, the total momentum after the collision is equal to the total momentum before the collision:

P1 + P2 = (m1 + m2)vf

Where vf is the final velocity of the stuck together train carts.

Plugging in the values, we get:

2520 kg·m/s + 2400 kg·m/s = (70 kg + 120 kg)vf

Simplifying the equation, we find:

4920 kg·m/s = 190 kg·vf

Dividing both sides by 190 kg, we get:

vf = 4920 kg·m/s / 190 kg

≈ 25.9 m/s

Therefore, the final velocity of the stuck together train carts is approximately 25.9 m/s.