A model train, with a mass of #2 kg#, is moving on a circular track with a radius of #4 m#. If the train's kinetic energy changes from #2 j# to #16 j#, by how much will the centripetal force applied by the tracks change by?

Question

A model train, with a mass of #2 kg#, is moving on a circular track with a radius of #4 m#.  If the train's kinetic energy changes from #2 j# to #16 j#, by how much will the centripetal force applied by the tracks change by?

Isabella Alvarez · Accepted Answer

It will increase #8# times, which in this case corresponds to an increase of #8N#.

Since the kinetic energy is #E_k=1/2mv^2# and increased from #2J to 16J#, ie increased #8# times, it implies that the #v^2# must have increased #8# times, and hence #v# increased #sqrt8# times. (Assuming mass remains constant.) Now the centripetal force is given my #F_c=(mv^2)/r# and directed towards the centre of the circle. So assuming the mass and radius stays the same, if #v^2# increases #8# times, then #F_c# also increases #8 times#. Now the initial velocity was #sqrt(E_k/(1/2m))=sqrt(2/(1/2xx2))=sqrt2 m//s# So initial centripetal force was #Fc=(2xx2)/4=1N#. Therefore the new centripetal force will be #8# times more, ie #8N#.

Charles Aeschliman · Answer

undefined Use the formula $KE = \frac{1}{2}mv^2$ to find the initial and final velocities of the train. Then, use the centripetal force formula $F_c = \frac{mv^2}{r}$ to calculate the initial and final centripetal forces. The change in centripetal force is the difference between the final and initial values.