Question

ЧТ 2. You are trying to build a better moose trap. The design is shown in the figure below. A large uniform platform of mass 80 kg and length 10 m is attached by a hinge to a vertical wall. A cable from the wall to the platform holds the platform horizontal The cable is designed to break when a 400 kg moose gets all four feet onto the platform. (Don't worry about damage to the moose, the moose will fall gently into a shalow lake of maple syrup). The cable attaches 4 m from the wall and makes an angle of 0 40 with the horizontal as shown. Assume that when the moose is fly on the platform its center of mass is at 9 m from the hinge. cable M 400 kg m-80 kg hinge 4 m 9 m 10 m (a) Consider the forces and torques on the platform. Without a moose on the platform, what is the tension in the cable? (b) without a moose what is the horizontal and vertical forces at the hingge? (c) what breaking tension should the cable have in order to break just when the moose gets into trapping position?

Answer 1

a Let tension in Cable is good as Balancing torque about hinge h aare a Ixsin 40°x 4 - 80x 9.8 x 10 = 0 g T= 1524.6 N the tension in cable is 1524.GN (b at hinge s prinelos 15 horizontal force = I Cos 40' = 1524,6 Cos 40 vertical force = 80x9.8 – 1524.6 Sin 40% 5-196 N av the vertical force is 196 N upwards © Let tension is T Tx Sin 40°x 4 – 80x 9.8 x 10 – 400x9.8 X 9 = 0 T= 15246. IN The tension in the rope is 15246.1N