The force P is applied to the 59-kg block when it is at rest. Determine the magnitude and direction of the friction force exerted by the surface on the block if (a) P = 0, (b) P = 198 N, and (c) P = 288 N. (d) What value of P is required to initiate motion up the incline? The static and kinetic coefficients of friction between the block and the incline are μs = 0.20 and μk = 0.16, respectively. The friction force is positive if up the incline, negative if down the incline.

Explanation:

Coefficient of static friction(μs) = 0.20 Coefficient of kinetic friction (μk) = 0.16

Mass of block (m) = 59kg

acceleration due to gravity (g) = 9.8m/s^2

Normal force = weight of block = mg

Weight of block(W) = 59kg × 9.8m/s^2 = 578.2N

N = 578.2 N

Maximum force of static friction Fs(max) is given by ;

Coefficient of static friction (μs) × N

0.20 × 578.2N = 115.64

As long as P is < 115.64, then the block will remain stationary and thus static frictional force = P (Fs = P)

magnitude and direction of the friction force exerted by the surface on the block if;

(A.) P = 0, Fs = 0

B.) P = 198N;

Fk = μk × N = 0.16 × 578.2 = 92.512N

Fs =

C.) P = 288;

Fk = μk × N = 0.16 × 578.2 =

D.) P value required to initiate motion;

0.2 × 59kg × 9.8m/s^2 = 115.64N

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