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A model train with a mass of #8 kg# is moving along a track at #16 (cm)/s#. If the curvature of the track changes from a radius of #48 cm# to #120 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

Nathan Ashcroft

The centripetal force would decrease from 0.427 N to 0.171 N, a change of 0.256 N

Centripetal force required for a circular path is found from

#F_c# = #(mv^2)/r#

First, we should get rid of the centimetres! Convert both to metres to avoid conversion factor errors.

When travelling at #0.16 m/s# on the track having #r = 0.48m#, the required force is

#F_c# = #(8 xx 0.16^2)/0.48# = #0.427 N#

On the track having the greater radius, less force is required (note the #r# in the denominator)

#F_c# = #(8 xx 0.16^2)/1.2# = #0.171 N#

So, the change is centripetal force is #0.256 N#

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Answer 2

Xavier Adame

The centripetal force applied by the tracks must decrease by 75.0 N.

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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.