Question

Two blocks of weights (W_1) and (W_2) are placed on an incline so that they are in contact. Assuming that the coefficient of static friction between block 1 and the surface of the incline is (mu_1), and between block 2 and the surface of the is (mu_2), calculate the maximum angle (alpha) for which the system will remain in equilibrium.

          Two blocks of weights (W_1) and (W_2) are placed on an incline so that they are in contact. Assuming that the coefficient of static friction between block 1 and the surface of the incline is (mu_1), and between block 2 and the surface of the is (mu_2), calculate the maximum angle (alpha) for which the system will remain in equilibrium.
        
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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Two blocks of weights (W_1) and (W_2) are placed on an incline so that they are in contact. Assuming that the coefficient of static friction between block 1 and the surface of the incline is (mu_1), and between block 2 and the surface of the is (mu_2), calculate the maximum angle (alpha) for which the system will remain in equilibrium.
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Transcript

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00:01 In this problem a block with a mass of 7 kg is placed on an incline and we have to find out the maximum angle the incline can be at before the block starts to slide down.
00:17 So the forces acting on the block are the normal force which is perpendicular to incline and gravitational force mg which is vertically downward and the friction force which is parallel to incline and up the incline.
00:40 Now the angle between the gravitational force and the direction perpendicular to incline is theta which is same as the angle of the incline.
00:53 So the component of gravitational force perpendicular to incline is mg cos theta and the component of gravitational force parallel to the incline will be mg sin theta.
01:15 Now in the direction perpendicular to incline the acceleration is zero so the forces along this line must balance which means the normal force will be equal to mg cos theta and the static friction force is coefficient of friction times normal force...
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