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2 DYNAMICS

P20 003.m

Two spheres, one sphere of mass m and the other of mass 3m approach each other along a straight line. Each sphere has a speed v as they approach each other. The two spheres have a head-on collision and they combine and move as a single object.

What is the velocity of the combined object after the collision?

What is the speed of the combined object after the collision?

What percentage of the initial kinetic energy of the moving spheres is dissipated as thermal energy as a result of the collision?

View solution below only after you have completed the answering the question.

Solution

Assume a [1D] collision along the X-axis (don’t need to worry about vector nature of the momentum).

Label the three objects as A, B and C.

Momentum is conserved in the collision.

momentum before collision = momentum after collision

The velocity of the combined spheres is -v / 2.

The combined spheres move in the – X direction with speed v /2.

75% of the original kinetic energy of the spheres is lost as thermal energy as a result of the collision.