Question

A curve of radius 20 m is banked so that a 1000 kg car traveling at 60 km/h can round it even if the road is so icy that the coefficient of static friction is approximately zero. The acceleration of gravity is 9.81 m/s 2 . ? Find the minimum speed at which a car can travel around this curve without skidding if the coefficient of static friction between the road and the tires is 0.2. Answer in units of m/s.

A ferris wheel rotates 2 times each minute and has a diameter of 17 m. The acceleration of gravity is 9.8 m/s 2 .What force does the seat exert on a 53 kg rider at the lowest point of the ride? Answer in units of N.

Answer 1

And

Centripetal force = (tangential velocity)^2 ÷ radius
Centripetal acceleration = (tangential velocity)^2 ÷ radius

As the Ferris wheel rotates 1 time, the rider moves the distance equal to the circumference of the circle = (2 * ? * 8.5) meters.
In one minute the rider moves 4 * (2 * ? * 8.5) = 68 * ? meters

Tangential velocity = total distance (in meters) ÷ total time (in seconds)
Tangential velocity = 68 * ? meters ÷ 60 seconds = 1.13 * ? m/s
This is the velocity of a rider on the Ferris wheel.

Centripetal force = 53 * (1.13 * ?)^2 ÷ 8.5 =79.04 N
Weight = 53 * 9.8 = 519.4 N  
At the lowest point of the ride, the direction of the weight is away from center of the Ferris wheel.
Force = Weight + centripetal force
Force = 519.4+79.04 = 598.44 N