physics

A book of mass 7 kg rests on a plank. You tilt one end of the plank and slowly increase the angle of the tilt. The coefficient of static friction between the book and the plank is 0.40. What is the maximum angle of tilt for which the book will remain stationary and not slide down the plank?

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1. m*g = 7 * 9.8 = 68.6 N. = Wt. of book.

Fp = 68.6*sin A = Force parallel to the
plank.

Fn = 68.6*Cos A = Force perpendicular to
the plank.

Fs = u*Fn = 0.4*68.6*Cos A

Fp-Fs = m*a
68.6*sin A - 0.4*68.6*Cos A = m*0 = 0
68.6*Sin A = 0.4*68.6*Cos A
Sin A = 0.4*Cos A
Divide both sides by Cos A:
Sin A/Cos A = 0.4
Replace Sin A/Cos A with Tan A:
Tan A = 0.4
A = 21.8o, Max.

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