A model train, with a mass of #3 kg#, is moving on a circular track with a radius of #5 m#. If the train's kinetic energy changes from #9 j# to #45 j#, by how much will the centripetal force applied by the tracks change by?

Answer 1

The change in centripetal force is #=14.4N#

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=3kg#
The radius of the track is #r=5m#

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#
#=2/5*(45-9)N#
#=14.4N#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the change in centripetal force, we first need to calculate the initial and final velocities of the train using the kinetic energy formula:

Initial kinetic energy (KE1) = 9 J Final kinetic energy (KE2) = 45 J

KE1 = (1/2) * mass * initial velocity^2 9 = (1/2) * 3 * initial velocity^2 Initial velocity = √(9 * 2 / 3) = √6 m/s

KE2 = (1/2) * mass * final velocity^2 45 = (1/2) * 3 * final velocity^2 Final velocity = √(45 * 2 / 3) = √30 m/s

Now, we can use the centripetal force formula to find the initial and final centripetal forces:

Initial centripetal force (F1) = (mass * initial velocity^2) / radius F1 = (3 * (√6)^2) / 5 = (3 * 6) / 5 = 18/5 N

Final centripetal force (F2) = (mass * final velocity^2) / radius F2 = (3 * (√30)^2) / 5 = (3 * 30) / 5 = 90/5 N

The change in centripetal force is: ΔF = F2 - F1 ΔF = (90/5) - (18/5) = 72/5 N

So, the centripetal force applied by the tracks changes by 72/5 N.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7