(III) A block of mass M 10kg is in motion downhill on a frictionless plane incli

Question

(III) A block of mass M 10kg is in motion downhill on a frictionless plane inclined at = 20° from the horizontal. (a) Compute the coefficient of static friction which would correspond to an angle of repose equal to 20 (b) Determine the accleration of the block down the incline. (e) Determine the normal force of contact acting between the block and the incline. (d) (i) Suppose that kinetic friction acts between the incline and the block, with 0.2. Compute the acceleration of the block down the incline in this case. (ii) Suppose that the coefficient of kinetic friction is-04, and compute the accelera- tion of the block in this case. (e) Instead suppose that the mass of the block is 20kg. Choose the factor by which the results for (b) (d) (i-i) change. (b) acceleration 1/4 1/2 1 2 4other (c) normal force1/4 1/2 1 2 4 other (d) (i) acceleration 1/4 1/2 1 2 4 other (d) (ii) acceleration1/4 1/2 1 2 4 other Page 3 of 4

Explanation / Answer

(III) (a) us = tan(20) = 0.364

(B) along the incline, Fnet = m a

m g sin20 = m a

a = 9.8 sin20 = 3.35 m/s^2

(C) N = m g cos20 = 10 x 9.8 x cos20

N = 92 N

(D) (i) fnet = m g sin20 - f = m a

m g sin20 - 0.2 m g cos20 = m a

a = g ( sin20 - 0.2 cos20)

a = 1.51 m/s^2

(ii) a = 9.8 ( sin20 - 0.4 cos20)

a = -0.33 m/s^2

(e) b -> 1

C -> 2

d(i) -> 1

(ii) -> 1

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