Set 4 Problem number 11

• Problem

• Solution

• Generalized Solution

• Explanation in terms of Figure(s), Extension

• Figure(s)

Problem

Two objects collide, one  of mass 24 kg and moving in the positive direction at 9 m/s and the other of mass 7 kg moving at 26 m/s in the negative direction.

• Assuming that the two objects stick together when they collide, what then is the total mass and velocity immediately after collision?

Solution

The momentum of the first is ( 9 m/s)( 24 kg)= 216 kg m/s, and that of the second is ( - 26 m/s)( 7 kg) = -182 kg m/s.

• The total momentum is therefore 216 kg m/s + -182 kg m/s =  34 kg m/s.
• The total mass is easily found to be 31 kg. Since the total momentum after collision is the same as that before collision, we see that after collision we have a mass of 31 kg with momentum 34 kg m/s.
• Dividing we obtain velocity ( 34 kg m/s)/( 31 kg) = 1.096774 m/s.

Generalized Solution

The total momentum of a mass m1 moving at velocity v1 and a mass m2 moving at velocity v2 is

• pTot = m1 v1 + m2 v2.

By Newton's Third Law and the Impulse-Momentum Theorem this momentum will remain unchanged during collision.

After collision we wil have one object of mass m1 + m2 and momentum m1 v1 + m2 v2. The object will therefore have velocity

velocity = momentum / mass = (m1 v1 + m2 v2) / (m1 + m2).