The question
Name: ______________________ Date: ____________ A car over a hill (12 points)
Diagram
A car over a hill
A car of mass m drives over the crest of a hill at a constant speed v. Near the crest the road follows a vertical circle of radius R. Air resistance and the friction along the direction of motion balance, so the speed stays constant.
(a) Draw a free-body diagram of the car at the top of the crest, showing only the vertical forces. Represent each force with a distinct arrow starting on the dot, labeled with its type and agent, with lengths that show their relative sizes. [3 points]
(b) Derive an expression for the normal force on the car at the crest in terms of m, v, R and physical constants, consistent with your free-body diagram. [3 points]
(c) Sketch a graph of the normal force on the car at the crest against v², for speeds from zero up to the speed at which the normal force becomes zero. Label the intercepts in terms of m, g and R. [3 points]
(d) The driver goes over the crest faster than √(gR). Predict what happens to the car at the crest, and explain how your free-body diagram, your equation and your graph each support the prediction. [3 points]