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Question(s) / Instruction(s):

a) A box of mass m = 5.95 kg sits on a frictionless, horizontal table. A heavy rope is attached to the box, and it is pulled horizontally by a force of magnitude F = 64.2 N. (You can ignore any sag in the rope.) If the magnitude of the acceleration of the box is a = 10.03 m/s2: find the mass of the rope.

b) When mass M is hung on a vertical spring, the spring stretches distance x. When M is replaced by mass 1.67M on the same spring, the mass stretches an extra 2.21 cm. Find x, the original distance the spring stretched when mass M was hanging on it.

c) A sled of mass M = 384 kg is being pulled along a horizontal surface by a massless rope that makes an angle of θ = 19.1o up from the horizontal. The rope is pulled with a force of magnitude F = 2370 N, and the coefficient of kinetic friction between the ground and the sled is μk = 0.252. Find a, the magnitude of the acceleration of the sled.

d) A 40.3 kg block slides on a horizontal surface. It starts at speed vo = 4.01 m/s and comes to rest in distance s = 9.56 m. Find μk, the coefficient of kinetic friction between the surface and the block.

e) A block of ice of mass m slides down an incline that makes an angle θ = 28.6o with the horizontal. In trial 1 there is no friction; the block starts at rest and takes time t to reach the bottom of the incline. In trial 2 there is friction, and the block slides down the incline in time 3.59t. Find μk, the coefficient of kinetic friction between the ice and the incline in trial 2.

f) The handle of a floor mop makes an angle θ = 30.6o with the horizontal. Assume the handle is massless, and the mop has mass M = 7.34 kg. The coefficient of kinetic friction between the mop and the floor is μk = 0.331. Find F, the magnitude of the force, exerted downward along the handle, that will cause the mop to slide across the floor without acceleration.

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