1) A cyclist with a mass of 80kg approaches a corner with a radius of curvature of 12m. What is the maximum speed that the car can turn the corner, if:

a) there is a constant friction force of 720N:

b) on a wet day, the coefficient of friction is 0.3

2) A ball with a mass of 20g is swung around in uniform circular motion at an angle to the vertical as shown below. The length of the string is 1.2m and the radius of curvature is 60cm.

Calculate:

a) the angle between the string and the vertical

b) the tension in the string

c) the centripetal force acting on the ball

d) the magnitude of the velocity of the ball

3) A 1250kg car travels around a curved section of a highway with a radius of 100m in uniform circular motion. The road is banked at 5° as shown below.

Calculate:

a) The maximum speed the car can travel around the corner, ignoring friction

b) The maximum speed the car can travel around the corner when there is a frictional force between the car and the road of 5000N: