Question

. A motorcycle of mass 100 kilograms travels around a flat, circular track of radius  10 meters with a constant speed of 20 meters per second. What force is required  to keep the motorcycle moving in a circular path at this speed?

Answer 1

The centripetal acceleration is given by

$a_{c}=\dfrac{V^{2}}{r}$

Wherein.

$V=20\;m/s$ is the speed.

$r=10\;m$ Is the acceleration.

Evaluating numerically

$a_{c}=\dfrac{V^{2}}{r}\\ a_{c}=\dfrac{(20\;m/s)^{2}}{10\;m}\\ a_{c}=40\;m/s^{2}$

The centripetal force is given by

$F_{C}=m\;a_{c}$

In where.

$a_{c}=40\;m/s^{2}$ Is the centripetal acceleration.

$m=100\;kg$ Is the mass.

Evaluating numerically.

$F_{C}=m\;a_{c}\\ F_{C}=100\;Kg\times 40\;m/s^{2}\\ F_{c}=4000\;N$

 The force required to keep the motorcycle moving in a circular path at this speed is

$F_{c}=4000\;N$