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A model train with a mass of #3 kg# is moving along a track at #8 (cm)/s#. If the curvature of the track changes from a radius of #21 cm# to #18 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

Adrian Ayala

The change in centripetal force is #=0.016N#

Centripetal force is what

#F=(mv^2)/r#

mass, #m=3kg#

speed, #v=0.08ms^-1#

radius, #=(r) m#

The centripetal force fluctuation is

#DeltaF=F_2-F_1#

#F_1=mv^2/r_1=3*0.08^2/0.21=0.091N#

#F_2=mv^2/r_2=3*0.08^2/0.18=0.107N#

#DeltaF=0.107-0.091=0.016N#

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Answer 2

Lily Adams

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

[ F_c = \frac{mv^2}{r} ]

where:

( F_c ) is the centripetal force,
( m ) is the mass of the train (3 kg),
( v ) is the velocity of the train (8 cm/s), and
( r ) is the radius of the curvature (21 cm for the initial radius and 18 cm for the final radius).

Substitute the values into the formula and calculate the initial and final centripetal forces. Then find the difference between the two forces to determine 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.