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The mass of 2 particles A and B are 4kg & 5 kg respectively. Their velocities are 5m/s & 10m/s respectively in +x direction. Find the heat generated if both the particles are brought to rest by friction.

In this question, I can think of 2 ways-

1. KE of A = 50 J & KE of B = 250 J => Total energy = 300 J. Hence heat released = 300 J

2. velocity and mass of Centre of mass are 70/9 m/s and 9 kg respectively. So, KEcom = 2450/9 & velocity of A & B relative to COM are -25/9 m/s and 20/9 m/s respectively. So KE of A and B relative to COM =3125/162 J & 1000/81 respectively. Hence, total energy = 49225/162 J. Hence energy released = 49225/162 J.

Both the methods seem right in their own way. Can anyone tell me which is actually right and why?

9 years ago

In first method your frame of reference is earth which is a inertial frame so only real forces are acting and in this case it is friction.So loss of kinetic energy will be equal to work done by frictional forces.

Whereas in second case your frame of reference is non-inertial i.e. pseudo force also come into picture.So loss in kinetic energy will be equal to total work done by all forces.i.e. friction and pseudo forces.

So to calculate work done by friction 1st approach is right.

9 years ago

One more thing, if there were no friction, what would be the energy of system - 1st one or 2nd one?

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