A 4.35-kg wooden block slides 2.25 m down a wooden incline at constant velocity.

Question

A 4.35-kg wooden block slides 2.25 m down a wooden incline at constant velocity. (The coefficient of static friction is 0.410, and the coefficient of kinetic friction is 0.190.) (a) What is the angle of the incline? (a) degree with respect to the horizontal (b) When we are considering energy, why is it useful to include the surface of the incline in the system? The block pushes on the incline, so we need to consider the kinetic energy of the surface as well as the block. The kinetic friction causes thermal energy to build up in both the block and the surface. The thermal energy only builds up in the block, but we need the surface's friction to act on it. The kinetic friction comes from the incline, so all the thermal energy of the system builds up in the surface. (c) Calculate the increase in the system's thermal energy.

Explanation / Answer

m =4.35 kg , d =2.25 , us =0.4, uk =0.19

(a) tan(theta) = uk

(theta) = arctan(0.190)

theta = 10.76 degrees with respect to horizontal

(b) Work done by friction force is equal to increase in thermal energy

W =fk*d = uk*mg*cos(theta)*d

W = 0.19*4.35*9.8*cos(10.76)*2.25

W = 17.9 J

Increase in thermal energy = 17.9 J

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