Question

Uniform Circular Motion

1. A car whose speed is 40 km/h rounds a curve whose radius is 100 m. What is its acceleration?

2. Determine the centripetal force acting upon a 40-kg child who makes 10 revolutions around the Cliffhanger in 29.3 seconds. The radius of the barrel is 2.90 meters

Answer 1

1) Convert km/h to m/s:

$$v=40·1000/3600=11.11\text{ m/s}.$$

The centripetal (radial) acceleration:

$$a=\frac{v^2}R=1.23\text{ m/s}^2.$$

2) Find the angular velocity of the kid:

$$\omega=2\pi n=2\pi\frac Nt.$$

Find the centripetal acceleration:

$$a=\omega^2r=4\pi^2n^2r.$$

By Newton's second law, find the force:

$$F=ma=4\pi^2n^2rm=533\text{ N}.$$