A model train with a mass of #7 kg# is moving along a track at #15 (cm)/s#. If the curvature of the track changes from a radius of #24 cm# to #45 cm#, by how much must the centripetal force applied by the tracks change?

Question

A model train with a mass of #7  kg# is moving along a track at #15 (cm)/s#.  If the curvature of the track changes from a radius of #24 cm# to #45 cm#, by how much must the centripetal force applied by the tracks change?

Lily Adams · Accepted Answer

0.31N

Determine the Centripetal Force for one of the scenarios first; in this example, I'll determine the force needed for the 24 cm track. Your quantities should now be converted to standard units, such as meters and meters per second. Thus, 24 cm = 0.24 m, 45 cm = 0.45 m, and 15 cm/s = 0.15 m/s. Then use the formula: #F_c = (mv^2)/r# And substitute the given values: #F_c = ((7 kg)(0.15m s^-1)^2)/(0.24 m) = 0.656 N# #F_c = ((7 kg)(0.15m s^-1)^2)/(0.45 m) = 0.350 N# Now find the difference between the two forces: #0.656N - 0.350N = 0.31N#

Julia Aguilar · Answer

undefined To calculate the change in centripetal force applied by the tracks when the curvature of the track changes, we can use the formula for centripetal force: $ F_c = \frac{mv^2}{r} $, where $ m $ is the mass of the object, $ v $ is the velocity, and $ r $ is the radius of the curvature.

Initially, the radius of curvature is $ r_1 = 24 $ cm and the velocity $ v = 15 $ cm/s.
Finally, the radius of curvature changes to $ r_2 = 45 $ cm.

Using the initial conditions:
$ F_{c1} = \frac{7 \times (15)^2}{24} $

Using the final conditions:
$ F_{c2} = \frac{7 \times (15)^2}{45} $

To find the change in centripetal force, subtract $ F_{c1} $ from $ F_{c2} $.