A model train, with a mass of #5 kg#, is moving on a circular track with a radius of #1 m#. If the train's kinetic energy changes from #25 j# to #40 j#, by how much will the centripetal force applied by the tracks change by?

Question

A model train, with a mass of #5 kg#, is moving on a circular track with a radius of #1 m#.  If the train's kinetic energy changes from #25 j# to #40 j#, by how much will the centripetal force applied by the tracks change by?

Benjamin Asiedu · Accepted Answer

The change in the centripetal force is #=15N#

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 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#

#=2/1*(40-25)N#

#=15N#

William Audy · Answer

undefined The change in kinetic energy of the model train can be calculated using the formula:

Change in kinetic energy = Final kinetic energy - Initial kinetic energy

Given:
Initial kinetic energy = 25 J
Final kinetic energy = 40 J

Change in kinetic energy = 40 J - 25 J = 15 J

The centripetal force applied by the tracks is responsible for providing the necessary centripetal acceleration to keep the train moving in a circular path. The centripetal force can be calculated using the formula:

Centripetal force = (mass × velocity^2) / radius

To find the change in centripetal force, we first need to determine the initial and final velocities of the train. Since kinetic energy is directly proportional to the square of velocity, we can use the relationship:

Kinetic energy = (1/2) × mass × velocity^2

Given:
Mass (m) = 5 kg
Radius (r) = 1 m

For the initial kinetic energy:
25 J = (1/2) × 5 kg × velocity_initial^2

Solving for velocity_initial:
velocity_initial = √(2 × 25 J / 5 kg)

Similarly, for the final kinetic energy:
40 J = (1/2) × 5 kg × velocity_final^2

Solving for velocity_final:
velocity_final = √(2 × 40 J / 5 kg)

Now that we have the initial and final velocities, we can calculate the initial and final centripetal forces using the formula:

Centripetal force = (mass × velocity^2) / radius

Then, the change in centripetal force is given by:

Change in centripetal force = Final centripetal force - Initial centripetal force