Home > Physics > Circular Motion

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 #140 cm#, by how much must the centripetal force applied by the tracks change?

Answer 1

Leo Abeyta

The change in centripetal force is #=0.294N#

The centripetal force is

#F=(mv^2)/r#

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

The velocity of the train is #v=0.21ms^-1#

The radii are

#r_1=0.42m#

and

#r_2=1.40m#

The variation in the 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*0.21^2/1.40=0.126N#

#DeltaF=F_1-F_2=0.42-0.126=0.294N#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Elena Albarran

The change in centripetal force applied by the tracks can be determined using the formula:

[ \Delta F_c = m \cdot \left(\frac{v_f^2}{r_f} - \frac{v_i^2}{r_i}\right) ]

where:

( \Delta F_c ) is the change in centripetal force,
( m ) is the mass of the train (4 kg),
( v_i ) is the initial velocity (21 cm/s),
( r_i ) is the initial radius (42 cm),
( v_f ) is the final velocity (21 cm/s, as no change in speed is mentioned),
( r_f ) is the final radius (140 cm).

By signing up, you agree to our Terms of Service and Privacy Policy

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.