Question

A 49 g marble moving at 1.9 m/s strikes a 28 g marble at rest. Assume the collision is perfectly elastic and the marbles collide head-on.

Part A:
What is the speed of the first marble immediately after the collision?

Part B:
What is the speed of the second marble immediately after the collision?

Answer 1

Concepts and reason

The concept used to solve this problem is perfectly elastic head-on collision.

In the case of perfectly elastic collision, both momentum and kinetic energy are conserved quantities. Because of the collision, there is no net loss in kinetic energy in the system

Use conservation of momentum and conservation of kinetic energy to deduce the equations for before and after collision.

Finally use these equations to find speed of the first marble and second marble immediately after the collision.

Fundamentals

A marble moving with an initial speed strikes another marble at rest. Assuming the collision is perfectly elastic and the marble collide head-on.

From the conservation of momentum,

Here, is the mass of the first marble, is the mass of second marble, is the initial speed of the first marble, is the initial speed of the second marble, is the final speed of the first marble, and is the final speed of the second marble.

Substitute for in the conservation of momentum equation, because second marble initial at rest.

…… (1)

From conservation of energy,

Substitute for .

Substitute algebraic identity for .

…… (2)

Divide the equation (2) by (1).

…… (3)

Substitute equation (3) in (1).

Rearrange the above equation to get final speed of the first marble,

Substitute equation for in equation (1).

Rearrange the above equation to get final speed of the second marble,

(A)

Expression for the final speed of the first marble immediately after collision is,

Substitute for , for , and for .

Therefore, the final speed of the first marble immediately after collision is.

(B)

Expression for the final speed of the second marble immediately after collision is,

Substitute for , for , and for .

Ans: Part A

The final speed of the first marble immediately after collision is .

Part B

The final speed of the second marble immediately after collision is .