Question

A small, 300 g cart is moving at 1.90 m/s on an air track when it collides with a larger, 5.00 kg cart at rest. After the collision, the small cart recoils at 0.890 m/s.

Part A:
What is the speed of the large cart after the collision?

Answer 1

Concepts and reason

The concepts used to solve this problem are conservation of momentum.

Find the expression for the final speed after collision by equating before collision and after collision.

Finally find the final speed by substituting the mass, initial velocity in before collision and after collision.

Fundamentals

Conservation of momentum states,

In an isolated system if collision occurs between the two objects,the total momentum of the two objects before collision is equal to the total momentum of the two objects after collision.

Here, is the momentum before collision and is the momentum after collision.

The principle of conservation of momentum is to measure characteristics of motion.

The small mass of a cart is moving in a air track with initial momentum before hitting the large cart which is at rest.

The expression for momentum is,

Here, is the momentum, is the mass, and is the velocity.

The expression for the Initial momentum of a small cart before collision is,

Here, is the initial momentum, is the mass of small cart, and is the initial velocity.

The expression for the final momentum of a small cart after collision is,

Here, is the final momentum, is the mass of the large cart, and is the final velocity.

(A)

When the small cart moves on an air track, the motion occurs in one dimension.

The Total momentum before collision is equal to total momentum after collision.

The total momentum of two objects before collision is equal to the moment of the object in motion and plus the momentum of object at rest.

The expression for the total momentum before collision is,

Here, is the velocity of small cart and is the velocity of large cart.

For the large cart the initial velocity is zero because, the object is at rest. Since the expression rearranges as,

The total momentum of two objects after collision is equal to the momentum of the object in motion and plus the momentum of object at rest.

The expression for the total momentum after collision is,

Here, is the velocity of small cart and is the velocity of large cart.

By conservation of momentum principle,

By rearranging the above equation,

The expression for final speed is,

The expression for the final speed of the large cart after collision is,

Substitute for , for , for and for .

Ans: Part A

The final speed of the large cart after collision is .