1. A car is driving around a bank curve such that it can safely go around a circular curve at a given velocity, v_o, even when on ice (zero friction). Any slower and the car would slide down towards the center of the circle, any faster and the car would slide up the hill and away from the center of the circle. If a static frictional coefficient, μ_s, is introduced then the car can safely navigate around the curve at any speed between a minimum speed of v_min and a maximum speed of v_max. Can you find expressions for vmin and vmax as a function of v_o, and the radius of the road, R.

2. In the system shown three masses are connected via string and a series of pulleys to one another.

Find the acceleration of all blocks.

Do not assume the slope to be frictionless, but assume that block A is in motion.

3. In a cardiac stress test the patient is required to walk on an inclined treadmill. Imagine that the patients mass is 80 kg and that the inclined treadmill is at a slope of 15^o. The efficiency of the human body can be taken to be 25%.

a) Obtain an expression for the power required by the patient to maintain a velocity of 3ms^-1.

b) How long would the patient have to walk on the treadmill to burn the energy contained in a bottle of beer, a slice of pizza and a jelly doughnut?