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A model train with a mass of #4 kg# is moving along a track at #6 (cm)/s#. If the curvature of the track changes from a radius of #36 cm# to #48 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

Elena Albarran

The change in centripetal force is #=0.01N#

The centripetal force is

#vecF_C=(mv^2)/r*vecr#

The mass is of the train #m=4kg#

The velocity of the train is #v=0.06ms^-1#

The radii of the tracks are

#r_1=0.36m#

and

#r_2=0.48m#

The variation in the centripetal force is

#DeltaF=F_2-F_1#

The centripetal forces are

#||F_1||=4*0.06^2/0.36=0.04N#

#||F_2||=4*0.06^2/0.48=0.03N#

#DeltaF=F_1-F_2=0.04-0.03=0.01N#

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Answer 2

Amelia Adams

To calculate the change in centripetal force, you can use the formula:

ΔF = mv^2/Δr

Where:

ΔF is the change in centripetal force
m is the mass of the train
v is the velocity of the train
Δr is the change in radius of the track

Plug in the given values and solve for ΔF to find the change in centripetal force.

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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.