A model train with a mass of #2 kg# is moving along a track at #9 (cm)/s#. If the curvature of the track changes from a radius of #5 cm# to #25 cm#, by how much must the centripetal force applied by the tracks change?

Question

A model train with a mass of #2  kg# is moving along a track at #9 (cm)/s#.  If the curvature of the track changes from a radius of #5 cm# to #25 cm#, by how much must the centripetal force applied by the tracks change?

Benjamin Asiedu · Accepted Answer

The change in centripetal force is #=0.277N#

Centripetal force is what

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

The mass is of the train #m=2kg#

The velocity of the train is #v=0.09ms^-1#

The tracks' respective radii are

#r_1=0.05m#

additionally

#r_2=0.25m#

The centripetal force's variance is

#DeltaF=F_2-F_1#

What are the centripetal forces?

#||F_1||=2*0.09^2/0.05=0.324N#

#||F_2||=2*0.09^2/0.25=0.0648N#

#DeltaF=F_1-F_2=0.342-0.0648=0.277N#

Charlotte Aaron · Answer

undefined The centripetal force required for circular motion is given by the formula:

$$ F_c = \frac{mv^2}{r} $$

Where:
- $ F_c $ is the centripetal force,
- $ m $ is the mass of the object (2 kg in this case),
- $ v $ is the velocity of the object (9 cm/s in this case), and
- $ r $ is the radius of the circular path.

Initially, when the radius $ r_1 = 5 $ cm, the centripetal force $ F_{c1} $ is calculated using the formula above.

Then, when the radius $ r_2 = 25 $ cm, the centripetal force $ F_{c2} $ is calculated using the same formula.

Finally, the change in centripetal force $ \Delta F_c $ is found by subtracting $ F_{c1} $ from $ F_{c2} $.