A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #6 m#. If the train's kinetic energy changes from #24 j# to #96 j#, by how much will the centripetal force applied by the tracks change by?

Question

A model train, with a mass of #4 kg#, is moving on a circular track with a radius of #6 m#.  If the train's kinetic energy changes from #24 j# to #96 j#, by how much will the centripetal force applied by the tracks change by?

Nathan Ashcroft · Accepted Answer

Mass of the train m= 4kg
The radius of circular path (r)=6m
Initial velocity,#v_1#
final velocity,#v_2#
Initial KE,#=1/2mv_1^2#
final KE,#1/2mv_2^2#
Change in KE =#1/2mv_2^2-1/2mv_1^2=96-24=72J#
Dividing both sides of this equation by radius (r)of circular path and multiplying both sides by 2 we have
#mv_2^2/r-mv_1^2/r=2*72/r#
We see that left side of the equation is the change in centripetal force
So The change in centripetal force is #=2*72/r=2.72/6(N.m)/m=24N#

Layla Ahmed · Answer

undefined To calculate the change in centripetal force applied by the tracks, we first need to find the initial and final velocities of the train. We can use the formula for kinetic energy:

Initial kinetic energy (KE_initial) = 1/2 * mass * initial velocity^2
Final kinetic energy (KE_final) = 1/2 * mass * final velocity^2

Given that the initial kinetic energy (KE_initial) is 24 J and the final kinetic energy (KE_final) is 96 J, we can rearrange the formulas to solve for the initial and final velocities:

Initial velocity^2 = (2 * KE_initial) / mass
Final velocity^2 = (2 * KE_final) / mass

Next, we need to find the difference in velocities (Δv) by subtracting the initial velocity from the final velocity:

Δv = final velocity - initial velocity

Now, we can use the formula for centripetal force to calculate the initial and final centripetal forces applied by the tracks:

Initial centripetal force (F_initial) = mass * initial velocity^2 / radius
Final centripetal force (F_final) = mass * final velocity^2 / radius

Finally, we can find the change in centripetal force by subtracting the initial centripetal force from the final centripetal force:

Change in centripetal force (ΔF) = F_final - F_initial