a homeowner wants to raise one end of an upright piano in order to place coaster

Question

a homeowner wants to raise one end of an upright piano in order to place coasters under the wheels. It takes 1.6 x 10*3 N to raise one end of the piano, but the maximum force the homeowner can apply is 4.0 x 10*2 N. to accomplish the task, she places a fulcrum 0.30 m from the piano and uses a strong board as a first-class lever to raise the piano.


Calculate the minimum length of the effort arm requires to lift the piano?
Find the total length of the board?
If she applied her effort further from the fulcrum, would the effort increase or decrease?

Explanation / Answer

This is a form of a torque problem Torque is Force times distance. And considering a fulcrum and board, a force downward on one end equals a force upwards on the other. The piano lies .3 meters away from the fulcrum, and the force to lift it is 1.6 x 10^3 N. F * d = (1.6 x 10^3 N) (.3 m) = 480 Nm This must equal the torque the homeowner places on her end of the lever. Additionally, she can apply a force of 4 x 10^2 N. Just solve for distance. d = 480Nm / F = 480 Nm / (4 x 10^2 N) = 1.2 m Minimum length of effort arm is 1.2 meters. If she increased the length of her effort arm, the homeowner would exert less effort for the same effect. Since the torque equals force times distance, increasing distance will decrease force for the same torque. So if she doubled the length of her effort arm, she would only need to apply half the force she would originally need.

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