a mover pushes a heavy chair up an inclined plane into a truck. The inclined plane is 2m long, and it lifts the chair to a height of one metre. The chair's weight is 360 Newtons. The mover has to...

a mover pushes a heavy chair up an inclined plane into a truck. The inclined plane is 2m long, and it lifts the chair to a height of one metre. The chair's weight is 360 Newtons. The mover has to exert 220N of force to slide the chair up the ramp. What is the mechanical efficiency?

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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Hello!

An inclined plane allows us to use less force to lift things. The ratio between the weight and the force required to lift an object via an inclined plane is called mechanical advantage. In our case it is `360/220 approx 1.64.`

But nothing comes free of charge. In the case of an inclined plane the cost is the increase of path length. Also, in real life, some friction is involved. To compute this cost, one must use the notion of work.

In a situation when the direction of movement and the direction of the force exerted coincide, work is defined as a product of the displacement and the force. Work is measured in N*m's called Joules (J).

Denote the work required to make an action without the machine as `A_0` and the work with the use of the machine as `A_1.` The mechanical efficiency is defined as `A_0/A_1.`

 

In our case it is simple to find both works:

`A_0` = (the height)*(the weight) = 1*360 = 360 (J),

`A_1` = (the length)*(the force) = 2*220 = 440 (J).

So efficiency is `360/440 approx 0.82.` This is the answer.

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