Pulling a Crate: Static and Kinetic Forces of Friction (a) In Fig. below, if the

Question

Pulling a Crate: Static and Kinetic Forces of Friction (a) In Fig. below, if the coefficient of static friction between the 40.0-kg crate and the floor is 0.650, what is the magnitude of the minimum horizontal force the worker must pull to get the crate moving? (b) If the worker maintains that force once the crate starts to move and the coefficient of kinetic friction between the surfaces is 0.500, what is the magnitude of the acceleration of the crate? Pulling at an Angle: A Closer Look at the Normal Force A worker pulling a crate applies a force at an angle of 30° to the horizontal, as shown in Fig. below. What is the magnitude of the minimum force he must apply to move the crate?

Explanation / Answer

Using force balance

in vertical direction

N + Fy = mg

N = mg - Fy = mg - F*sin A

in horizontal direction

Fx = F*cos A

Ff = friction force = us*N = us*(mg - F*sin A)

Fnet = 0 = Fx - Ff

Fx = Ff

F*cos 30 deg = 0.650*(40*9.81 - F*sin 30 deg)

F*(cos 30 deg + 0.650*sin 30 deg) = 0.650*40*9.81

F = 0.650*40*9.81/(cos 30 deg -+0.650*sin 30 deg)

F = 214.15 N

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