A model train, with a mass of #8 kg#, is moving on a circular track with a radius of #2 m#. If the train's kinetic energy changes from #36 j# to #48 j#, by how much will the centripetal force applied by the tracks change by?

Question

A model train, with a mass of #8 kg#, is moving on a circular track with a radius of #2 m#.  If the train's kinetic energy changes from #36 j# to #48 j#, by how much will the centripetal force applied by the tracks change by?

Elena Albarran · Accepted Answer

The change in centripetal force is #=12N#

The centripetal force is

#F=(mv^2)/r#

The kinetic energy is

#KE=1/2mv^2#

The variation of kinetic energy is

#Delta KE=1/2mv^2-1/2m u^2#

#=1/2m(v^2-u^2)#

The mass is #m=8kg#

The radius is #r=2m#

The variation of centripetal force is

#DeltaF=m/r(v^2-u^2)#

#DeltaF=2m/r1/2(v^2-u^2)#

#=(2)/r*1/2m(v^2-u^2)#

#=(2)/r*Delta KE#

#=2/2*(48-36)N#

#=12N#

Axel Acevedo · Answer

undefined The centripetal force acting on an object moving in a circular path is given by the formula:

$ F_c = \frac{mv^2}{r} $

where $ m $ is the mass of the object, $ v $ is the velocity, and $ r $ is the radius of the circular path.

To find the change in centripetal force, we first calculate the initial centripetal force using the initial kinetic energy:

$ KE_{\text{initial}} = \frac{1}{2}mv^2 $

Then, we use the formula for centripetal force to find the initial centripetal force. Next, we calculate the final centripetal force using the final kinetic energy, and finally, we find the difference between the initial and final centripetal forces.