A stationary 3.0-m board of mass 5.5 kg is hinged at one end. A force F vector i

Question

A stationary 3.0-m board of mass 5.5 kg is hinged at one end. A force F vector is applied vertically at the other end, and the board makes a 30 degree angle with the horizontal. A 65-kg block rests on the board 80 cm from the hinge as shown in the figure below. (a) Find the magnitude of the force F vector. (b) Find the force exerted by the hinge. (c) Find the magnitude of the force F vector as well as the force exerted by the hinge (F vector_H), if F vector is exerted, instead, at right angles to the board. F vector N F vector_H N

Explanation / Answer

b] The net vertical force on the system is zero.

so, F + FH = (m + M)g

=> FH = (5.5 + 65)(9.8) - 196.82 = 494.08 N

c] Take moments about the point of contact of the board and the ground. Then, for the system to remain in equilibrium, the net torque is zero.

so,

mgcos30 (1.5) + Mgcos30 (0.8) - 3F = 0

=> F = 170.45 N

And the net vertical force is zero on the system. So,

Fcos30 + FH = (m + M)g

=> FH = (5.5 + 65)(9.8) - 170.45cos30 = 543.285 N.

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