3 min readβ’november 17, 2021
(a) Draw a free body diagram for the box on the top dot and a free body diagram with components on the bottom dot. The dotted line represents the incline. (3pts)
(b) In the space provided below, derive an equation for the coefficient of friction, π, when the box is moving up the hill at constant velocity. Express your answer in terms of m, g, Fapp, trig identities, and π.
(c) If the mass of the box is 25 kg, the applied force is 250 N, and the angle π is 22o, calculate the coefficient of friction using your equation from part b) as the person is pushing the box up the hill. Show all work. (1pt)
(d) The ramp is now chilled until the coefficient of friction equals 0.02 and the box begins to accelerate down the incline. In addition, the person is no longer pushing the box. In the space provided below, draw a free body diagram for the box on the top dot and a free body diagram with components on the bottom dot. The dotted line represents the incline. (3pts)
(e) Derive an equation for the acceleration of the box as it slides down the hill. Express your answer in terms of m, g, π, trig identities, and π. (4pts)
(f) Calculate the acceleration of the box down the hill using the information given in parts (a) through (e). Show all work. (2pts)
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