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A model train with a mass of #4 kg# is moving along a track at #21 (cm)/s#. If the curvature of the track changes from a radius of #42 cm# to #90 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

Charles Aeschliman

The centripetal force changes by #=0.224N#

The centripetal force is

#F=(mv^2)/r#

The mass is #m=4kg#

The velocity is #v=0.21ms^-1#

The radii are

#r_1=0.42m#

and

#r_2=0.9m#

The variation in centripetal force is

#DeltaF=F_2-F_1#

The centripetal forces are

#F_1=4*0.21^2/0.42=0.42N#

#F_2=4*0.21^2/0.9=0.196N#

#DeltaF=0.42-0.196=0.224N#

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Answer 2

Olivia Askew

The centripetal force ((F_c)) acting on an object moving in a circle is given by the formula:

[ F_c = \frac{m \cdot v^2}{r} ]

Given:

Mass of the train ((m)): 4 kg
Velocity of the train ((v)): 21 cm/s
Initial radius ((r_1)): 42 cm
Final radius ((r_2)): 90 cm

Calculate the initial centripetal force ((F_{c1})) using the initial radius, and then calculate the final centripetal force ((F_{c2})) using the final radius. The change in centripetal force is given by:

[ \Delta F_c = F_{c2} - F_{c1} ]

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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.