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Question

A motorcycle and a bus are moving with the same momentum which of them has greater kinetic energy?


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Solution

Step 1: Given data.

It is given that, the momentum of motorcycle and bus is equal.

Step 2: Formula to be used.

  1. The formula of momentum p of an object having mass m and velocity v is defined as p=mv.
  2. The formula of the kinetic energy K.E of an object having mass m and velocity v is defined as K.E=12mv2.

Step 3: Find the relation between the kinetic energy of the motorcar and the bus.

Assume that, mc be the mass of the motorcycle and vc be the velocity of the motorcycle.

Also, mb be the mass of the bus and vb be the velocity of the bus.

We know that the mass of the bus is always greater than the mass of the motocycle.

That is, mc<mb.

Since, mcvc=mbvb...1.

which implies that, vc>vb.

Divide both sides by 2.

12vc>12vb

Now, multiply both sides by mcvc.

12mcvc2>12mcvcvb

From equation 1.

12mcvc2>12mcvb2

This implies that the kinetic energy of the motorcycle is greater than the kinetic energy of the bus.

Therefore, the motorcycle has greater kinetic energy.


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