A ball of mass 0.3 kg is initially moving with velocity v = (2 m/s)i + (1 m/s)j. The ball is hit (very hard!) and breaks into two pieces. The first piece has mass m1 = 0.2 kg and velocity v1 = (-1 m/s)i and the second piece has mass m2 = 0.1 kg and velocity

v2 = (4 m/s)j. What impulse was delivered to the ball when it was hit?

 

First note the relation between impulse and change of momentum:

I = D p = pf - pi

Before

 

After

px

py

 

px

py

 0.6 kg· m/s

  0.3 kg· m/s

Particle 1

 - 0.2 kg· m/s

  0

 

 

Particle 2

  0

  0.4 kg· m/s

 

 

Total

  - 0.2 kg· m/s

0.4 kg· m/s

Now use the results in the table to calculate the impulse delivered to the ball.

Make a sketch showing the two momenta and the impulse.

Ix = - 0.2 kg· m/s - 0.6 kg· m/s = -0.8 N· s

Iy = 0.4 kg· m/s - 0.3 kg· m/s = 0.1 N· s