a 142 kg crate is placed on an inclined ramp. When the angle the ramp makes with

Question

a 142 kg crate is placed on an inclined ramp. When the angle the ramp makes with the horizantal is increased to ALPHA, the crate begins to slide downward.

a) draw a free body diagram showing the forces acting on the crate.

b) calculate equations representing the compontents of foces acting on the crate.

c. If the coefficient of static friction between the crate and the ramp is 0.65, what is the angle alpha when the crate just begins to slide downward.

(also just a side question i have...) Does acceleration not count on a free body diagram because its not a force?

Explanation / Answer

Normal Force acting :

N = 142*9.8*cos(ALPHA)

Downward force along slope :

D= =142*9.8*sin(ALPHA)

Balancing forces :

142*9.8*sin(ALPHA)=0.65*142*9.8*cos(ALPHA)

tan(ALPHA) =0.65*142*9.8/(142*9.8)

=0.65

ALPHA = 33.024 degree

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