The person pulls upward with force 100N. The plank is 3 m long and weight 50 N.

Question

The person pulls upward with force 100N. The plank is 3 m long and weight 50 N. The box is 0.5 m from the left end. Your task is to compute the unknown weight of the box. To compute torque, you may use any point for axis of rotation, as long as the plank isn't rotating. Why for this problem will you choose the location of the fulcrum as the axis of rotation? Compute the torque exerted by the person's applied force. State whether it's cw or ccw. Compute the torque exerted by the weight of the plank. State whether it's cw or ccw. Compute the weight of the box. Compute the upward force exerted by the fulcrum.

Explanation / Answer

a) We pick the fulcrum as the pivot point because both the normal force there and the box is unknown. By picking this point whatever the unknown normal force is does not produce torque and get's canceled out. This eliminates and unknown. b) Torque = Force*distance (as long as the forces and distances are perpendicular, which they are). (100)(3) = 300 Nm This is ccw. c) (50)(1.5) = 75 Nm This is cw. d) All the torques that will produce ccw motion must equal all the torques producing cw motion since no rotation is occurring. (100)(3) = (50)(1.5) + (0.5)(w) , where w is the weight of the box. 300 = 75 +.5w 225 = .5w w = 450N e) There is no translational motion either so all forces must equal each other. The only directions forces are acting is up and down... so all the downward forces must equal all the upward forces. 50 +450 = 100 +n , where n is the normal force exerted by the fulcrum. n = 400N

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