Question

A particle of mass m moves with constant speed v on a circular path of radius r . Find magnitude of average force on it in half revolution.

Answer 1

Answer on Question #45266, Physics, Mechanics | Kinematics | Dynamics

Question:

A particle of mass m moves with constant speed v on a circular path of radius r. Find magnitude of average force on it in half revolution.

Answer:

From Newton's second law, force is related to momentum p by:

$$F = \frac {\Delta p}{\Delta t}$$

where $\Delta t$ is time, $\Delta p$ is change of momentum, $F$ is average force.

Change of momentum in half revolution equals:

$$\Delta p = 2 m v$$

And time of the half revolution equals:

$$\Delta t = \frac {\pi r}{v}$$

Therefore:

$$F = \frac {2 m v}{\frac {\pi r}{v}} = \frac {2}{\pi} \frac {m v ^ {2}}{r}$$

Answer: $\frac{2}{\pi} \frac{m v^2}{r}$

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