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For this problem, you are allowed to consult with other members of the class, but not with faculty and not with anyone outside the course. Simplify all your expressions.

A car of mass, 2m, is going around a turn at a constant radius, R, with velocity, v0. The turn is not banked – it is a flat surface. Assume the car and the road are on Earth’s surface.

a) Is the friction that holds the car on the road around the turn static or kinetic? Explain your answer.

b) Find the minimum coefficient of friction needed for the car to make the turn in terms of v0, R, g, and any other variables or constants that are necessary for the expression.

c) Find the kinetic energy of the car in terms of m, v0, and any constants.


d) The car hits an icy patch and careens off the turn in a straight line. It maintains its velocity, v0, until it hits a block of mass, m, attached to a massless spring with spring constant, k. The car has a perfectly inelastic collision with the block attached to the spring. Find the velocity, v2, of the combined car and block immediately after the collision takes place in terms of m, v0, and any needed constants.

e) Determine the distance that the spring compresses after the collision in terms of m, k, v0, and any necessary constants.

f) Find the time for the spring to return to its original position the first time after it compresses and starts to stretch in terms of m, k, and any other necessary variables or constants.

What happens to your answer in part f if the car has a mass of 11m instead?

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