What is the impulse exerted on objects A and B during their collision?

[Joe Jacobs]

Homework Statement

Two small steel balls A and B have mass 0.6 kg and 0.2 kg respectively. They are moving
towards each other in opposite directions on a smooth horizontal table when they collide
directly. Immediately before the collision, the speed of A is 8 m s^–1 and the speed of B is 2 m s^–1. Immediately after the collision, the direction of motion of A is unchanged and the speed of B is twice the speed of A. Find
(a) the speed of A immediately after the collision,
(b) the magnitude of the impulse exerted on B in the collision.

Homework Equations

total momentum before collision = total momentum after collision
p=mv
Impulse = Ft = m(v-u)

The Attempt at a Solution

I've got the correct answer for (a), 4.4 m s^-1 so I'll skip that bit. It's (b) that I don't get. It asks for the impulse exerted on B so that should be the impulse exerted by A

Ft = 0.6(4.4 - 8) = 0.6(-3.6) = -2.16 N s

since they ask for magnitude only

/therefore Impulse = 2.16 N s

But the answer given calculates the impulse exerted by B and still gets the same answer

Impulse = 0.2(2 + 8.8) = 2.16 N s

Why?

EDIT: Sorry don't know how to get the therefore symbol in LaTeX...my first time using it actually :D

 

[alphysicist]

Hi Joe Jacobs,

Homework Statement

Two small steel balls A and B have mass 0.6 kg and 0.2 kg respectively. They are moving
towards each other in opposite directions on a smooth horizontal table when they collide
directly. Immediately before the collision, the speed of A is 8 m s^–1 and the speed of B is 2 m s^–1. Immediately after the collision, the direction of motion of A is unchanged and the speed of B is twice the speed of A. Find
(a) the speed of A immediately after the collision,
(b) the magnitude of the impulse exerted on B in the collision.

Homework Equations

total momentum before collision = total momentum after collision
p=mv
Impulse = Ft = m(v-u)

The Attempt at a Solution

I've got the correct answer for (a), 4.4 m s^-1 so I'll skip that bit. It's (b) that I don't get. It asks for the impulse exerted on B so that should be the impulse exerted by A

Ft = 0.6(4.4 - 8) = 0.6(-3.6) = -2.16 N s

This is the impulse exerted on A. The impulse on an object is equal to its change in momentum. Notice that this impulse is negative, and it is the ball B that puts a negative force on ball A. (Ball A felt a negative force, because it had a positive velocity and then slowed down.)

since they ask for magnitude only

/therefore Impulse = 2.16 N s

But the answer given calculates the impulse exerted by B and still gets the same answer

Impulse = 0.2(2 + 8.8) = 2.16 N s

Why?

If you are asking why the magnitudes are the same, think about what Newton's third law says about this situation.

 

[Joe Jacobs]

This is the impulse exerted on A. The impulse on an object is equal to its change in momentum. Notice that this impulse is negative, and it is the ball B that puts a negative force on ball A. (Ball A felt a negative force, because it had a positive velocity and then slowed down.)

That was the answer I was looking for. Thx