Set 4 Problem number 8

• Problem

• Solution

• Generalized Solution

Problem

Find the total momentum of a system consisting of

• an object of mass 6 kg moving in the positive x direction at 16 m/s,  and
• another object of mass 11 kg moving at 28 m/s in the negative x direction. 

Solution

The magnitude of the momentum of the first is ( 16 m/s)( 6 kg)= 96 kg m/s, and that of the second is ( 28 m/s)( 11 kg) = 308 kg m/s.

• Note:  This gives the second object the greater influence in the collision; if the two objects were to become embedded in one another in the collision the final velocity of the system would be in the direction of the second.

The velocity of the second is in the negative direction so its momentum is - 308 kg m/s.

• The total momentum is therefore 96 kg m/s + - 308 kg m/s = - 212 kg m/s.

We see that the total momentum is in the direction (negative) of the more influential object.

Generalized Solution

The total momenum of two masses is the sum of their individual momenta.

Thus the total momentum of masses m1 and m2, moving with respective velocities v1 and v2, is the total

• pTotal = m1 v1 + m2 v2

of their individual momenta m1 v1 and m2 v2.