Question

A giant "egg" explodes as part of a fireworks display. The eggis at rest before the explosion, and after the explosion, it breaksinto two pieces, with the masses indicated in the diagram,traveling in opposite directions.

Part A

What is the momentum $p_A,i$ of piece A before the explosion?

Express your answer numerically inkilogram meters per second.

Part B

During the explosion, is the force of piece Aon piece B greater than, less than, or equal to the force of pieceB on piece A?

Part C

The momentum of piece B is measured to be500 $\rm kg \cdot m/s$ after the explosion. Find the momentum $p_A,f$ of piece A after the explosion.

Enter your answer numerically inkilogram meters per second.

Answer 1

Concepts and reason

The concepts used to solve this problem are momentum, force and law of conservation of momentum.

Determine the momentum of piece A before the explosion. Write the expression for the momentum in terms of mass and velocity of piece A. Use law of conservation of momentum to show that the momentum is same for both pieces after the explosion. Hence, show that the forces are also the same. Use law of conservation of momentum and express the momentum of A in terms of B after the explosion. Substitute the value of momentum of B after the explosion to find the momentum of A.

Fundamentals

Momentum is mathematically defines as,

Here, m is the mass of the body and v is its velocity.

Law of conservation of momentum states that “total momentum before collision is equal to the total momentum after collision”.

From the law of conservation of momentum,

Here, and are the momentum of the piece A and B before explosion and , are the momentum of the piece A and B after explosion

The expression for the force acting on the egg is given by,

Here, dP is the change in momentum and dt is the change in time.

(A)

The expression for momentum of piece A before explosion is,

Here, is the mass of the piece A and is the velocity of the piece A before explosion.

The egg is at rest. So, the velocity of piece A before explosion is zero.

Substitute 0 for in .

(B)

During the explosion, the pieces move in opposite directions. This means, the momentum of the pieces are opposite in direction. The momenta of the pieces are also equal in magnitude.

Therefore, the force of piece A on piece B is equal and opposite to that of piece B on piece A.

(C)

From the law of conservation of momentum,

Since, the egg is at rest before explosion, the momentum of pieces A and B are zero before the explosion.

Substitute 0 for ,

Substitute for,

The momentum of piece A after explosion is,

Ans: Part A

Momentum of piece A before explosion is zero.

Part B

The force of piece A on piece B is equal and opposite to that of piece B on piece A.

Part C

The momentum of piece A after explosion is.