A pirate demands that his 75 kg prisoner “walk the plank”. The prisoner walks out on an 8.0 m long, 50 kg horizontal board that juts out from the side of the pirate ship. If he walks out and stands 7.5 m from the place where the board is connected to the ship’s side, what is the net torque applied to the board?
Question
A pirate demands that his 75 kg prisoner “walk the plank”. The prisoner walks out on an 8.0 m long, 50 kg horizontal board that juts out from the side of the pirate ship. If he walks out and stands 7.5 m from the place where the board is connected to the ship’s side, what is the net torque applied to the board?
Solution
To solve this problem, we need to understand the concept of torque. Torque is the rotational equivalent of linear force. The direction of the torque is along the axis of rotation. Torque is calculated by multiplying the force applied by the distance from the pivot point at which the force is applied.
In this case, the pivot point is where the plank connects to the ship. The forces acting on the plank are the weight of the plank, the weight of the prisoner, and the upward force exerted by the ship. The weight of an object is calculated by multiplying its mass by the acceleration due to gravity, which is approximately 9.8 m/s^2.
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Calculate the weight of the plank: Weight of plank = mass of plank * gravity Weight of plank = 50 kg * 9.8 m/s^2 = 490 N
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Calculate the weight of the prisoner: Weight of prisoner = mass of prisoner * gravity Weight of prisoner = 75 kg * 9.8 m/s^2 = 735 N
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Calculate the torque due to the weight of the plank: The weight of the plank acts at its center of mass, which is halfway along the plank, or 4.0 m from the pivot point. Torque due to plank = force due to plank * distance from pivot Torque due to plank = 490 N * 4.0 m = 1960 N*m
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Calculate the torque due to the weight of the prisoner: The prisoner is standing 7.5 m from the pivot point. Torque due to prisoner = force due to prisoner * distance from pivot Torque due to prisoner = 735 N * 7.5 m = 5512.5 N*m
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Calculate the net torque: The net torque is the sum of the torques due to the plank and the prisoner. Both torques are acting in the same direction, so we add them. Net torque = torque due to plank + torque due to prisoner Net torque = 1960 Nm + 5512.5 Nm = 7472.5 N*m
So, the net torque applied to the board is 7472.5 N*m.
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