Centripetal Acceleration (CIE A Level Physics)

Two runners are running around a circular track. One runner follows path X and the other follows path Y, as shown in Fig. 1.1.

The radius of path X is 36.50 m. Path Y is parallel to, and 1.2 m outside, path X. Both runners have mass 75 kg. The maximum lateral (sideways) friction force F that the runners can experience without sliding is 57 mN. 

Show that the maximum speed at which the runner on path Y can move is 0.17 m s^–1.

Compare the centripetal acceleration and maximum speed of the runner on path X compared to path Y.

Calculate the time taken for the runner in path X to complete 1 lap.

The runner on path Y has an ankle injury that has come back with a vengeance, so it takes them twice as long to complete 1 lap.

A bowl-shaped skating ramp can be modelled as a hollow sphere.

A skateboarder with a horizontal speed follows a circular path inside the bowl of radius 2.3 m, as shown in Fig 1.1.

Fig 1.1

The forces acting on the skateboarder are their weight W and the normal reaction force R of the ramp on the skateboarder. R is at an angle θ to the horizontal. 

Determine an equation for W in terms of θ and the resultant force, F on the skateboarder.

Explain why force F is significant to the motion of the skateboarder.

For the radius of the ramp in Fig 1.1, the skateboarder travels at a speed of 6.0 m s^–1. 

Show that the angle θ is 32°.