Question

2) A 35.0 kg crate is being push across a horizontal floor with a force F = 150 N that makes an angle θ = 29.0° with the horizontal as illustrated in the figure below. Find the magnitude of the acceleration of the crate, given that the coefficient of kinetic friction between the crate and the floor is 0.20.

↑ F L.

3) A 7.00 kg block is pressed against a vertical wall by a force (→F), as shown in the figure below. The coefficient of static friction between the block and the wall is 0.31 and the directional angle θ for the force is 48°. Determine the magnitude of the force (→F) when the block is about to slide up the wall.

answer both questions please.

Answer 1

2)

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N = Normal force f = frictional force sigma F_y = m times a N - F sin theta - mg = m times 0 (as there is no vertical acceleration) N = F sin theta + mg = 150 times sin 29 degree + 35 times 9.8 = (150 times 0.484) + (35 times 9.8) = 72.6 + 343 = 415.6 N sigma = m times a F cos theta - f = m times a F cos theta - mu N = m times a (150 times 0.874) - (0.2 times 415.6) = 35 times a 131.1 - 83.12 = 35 times a 47.98 = 35 times a a = 1.37 m/s^2 \r\n N: Normal force f_s: State frictional force sigma F_x = m times a N - F sin theta = m times 0 N = F sin theta sigma F_y = m times a F cos theta - mg - f_s

3)