A runner taking part in the 200 m dash must run around the end of a track that has a circular arc with a radius of curvature of 30 m. If he completes the 200 m dash in 23.2 s and runs at constant speed throughout the race, what is the magnitude of his centripetal acceleration as he runs the curved portion of the track?

Solution to 11PE

Step 1 of 3</p>

We are asked to calculate the magnitude centripetal acceleration of a runner who is running a 200m distance on a circular track of radius 30m in 23.2s. His speed is constant throughout the race. Thus, the speed of the runner will remain constant in the circular track as well.

We have to use the concept of circular motion to find the acceleration.

Step 2 of 3</p>

We know that the centripetal force is directly proportional to the product of mass and square of velocity and inversely proportional to the radius.

............................. (1)

According to the Newton’s second law of motion,

......................................................... (2)

is the force on a body

is the mass of the body

is the acceleration of the body.

Equating both the equations,

........................................(3)