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in Physics by (70.7k points)

A block of mass m is pulled along a rough horizontal surface by a constant applied force of magnitude F1 that acts at an angle θ to the horizontal, as indicated. The acceleration of the block is a1. Express all algebraic answers in terms of m, F1, θ , a1, and fundamental constants.

a. On the figure below, draw and label a free-body diagram showing all the forces on the block.

b. Derive an expression for the normal force exerted by the surface on the block. 

c. Derive an expression for the coefficient of kinetic friction μ between the block and the surface. 

d. On the axes below, sketch graphs of the speed v and displacement x of the block as functions of time t if the block started from rest at x = 0 and t = 0.

e. If the applied force is large enough, the block will lose contact with the surface. Derive an expression for the magnitude of the greatest acceleration amax that the block can have and still maintain contact with the ground.

1 Answer

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e. The condition for the block losing contact is when the normal force goes to zero, which means friction is zero as well. ΣFx = Fmax cos θ = mamax and ΣFy = Fmax sinθ – mg = 0 giving Fmax = mg/(sinθ) and amax = (Fmaxcosθ)/m which results in amax = gcotθ.

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