A model train, with a mass of 4 kg, is moving on a circular track with a radius of 3 m. If the train's kinetic energy changes from 12 J to 48 J, by how much will the centripetal force applied by the tracks change by?

1 Answer

Centripetal force changes from 8N to 32N

Explanation:

Kinetic energy K of an object with mass m moving at a velocity of v is given by 12mv2. When Kinetic energy increases 4812=4 times, velocity is hence doubled.

The initial velocity will be given by v=2Km=2×124=6 and it will become 26 after increase in kinetic energy.

When an object moves in a circular path at a constant speed, it experiences a centripetal force is given by F=mv2r, where: F is centripetal force, m is mass, v is velocity and r is radius of circular path. As there is no change in mass and radius and centripetal force is also proportional to square of velocity,

Centripetal force at the beginning will be 4×(6)23 or 8N and this becomes 4×(26)23 or 32N.

Hence centripetal force changes from 8N to 32N