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A model train with a mass of #4 kg# is moving along a track at #9 (cm)/s#. If the curvature of the track changes from a radius of #180 cm# to #63 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

Amelia Adams

The centripetal force changes by #0.028N#

The centripetal force is

#F=(mv^2)/r#

The change in centripetal force is

#DeltaF=(mv^2)/(Delta r)#

So,

#DeltaF=(4*0.09^2)/(1.8-0.63)=0.0324/1.17N#

#=0.028N#

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Answer 2

William Audy

To find the change in centripetal force, we first calculate the initial and final centripetal forces.

Initial radius: ( R_1 = 180 , \text{cm} ) Final radius: ( R_2 = 63 , \text{cm} ) Initial velocity: ( v = 9 , \text{cm/s} ) Mass of the train: ( m = 4 , \text{kg} )

Initial centripetal force: [ F_{\text{initial}} = \frac{mv^2}{R_1} ]

Final centripetal force: [ F_{\text{final}} = \frac{mv^2}{R_2} ]

Change in centripetal force: [ \Delta F = F_{\text{final}} - F_{\text{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.