A model train with a mass of #4 kg# is moving along a track at #18 (cm)/s#. If the curvature of the track changes from a radius of #25 cm# to #42 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

The centripetal force changes in a factor of #25/42#, i.e. approximately #0.6# times greater.

The centripetal force acting on a moving mass #m# traveling a circular path with radius #r# at a constant speed #v# is given by the formula:
#F_c = m v^2/r#
If the path's radius is modified from a #r_1# value to a #r_2# one, the initial centripetal force #F_{c1}# changes to a new value #F_{c2}# which can be compared using the above formula:
#{F_{c2}}/{F_{c1}} = {m v^2/r_2}/{m v^2/r_1} = {1/r_2}/{1/r_1}=r_1 / r_2#

Thus:

#{F_{c2}}/{F_{c1}} = r_1 / r_2 = {25 cm} / {42 cm} ~~0.595... rArr F_{c2} ~~0.595 F_{c1}#
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Answer 2

To find the change in centripetal force, first calculate the initial and final centripetal forces using the formulas:

Initial centripetal force: F_initial = (mv^2)/r_initial Final centripetal force: F_final = (mv^2)/r_final

Then, subtract the initial force from the final force to find the change:

Change in centripetal force: ΔF = F_final - F_initial

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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.

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