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Name: Brenda R.
Status: N/A
Age: 40s
Location: N/A
Country: N/A
Date: 11/2/2003

How does the efficiency of an inclined plane vary with the angle of inclination?

If by efficiency you mean how much work is needed to raise a block using the inclined plane, it depends on the coefficient of friction between the block and the plane.

If the plane is frictionless, the work done, W, to raise a block of mass m through a height h (g is the acceleration due to gravity = 9.8 m/s^2 = 32 ft/s^2) is

W = mgh

Notice that this is independent of the angle of the plane. The force, F, needed decreases as the angle of the plane decreases. F = mg sin(angle). However, as the angle decreases and the required force decreases, the distance the block must be pushed along the plane to raise the block by the same h increases so the work (W = Fd) remains the same.

On the other hand, if there is friction, more work is needed as the angle decreases. This is easily seen if you take the two extremes. If the plane is at 90 degrees (vertical), there is no friction and W = mgh. If, in the other extreme, the plane is horizontal, the block's height does not change as it is pushed along the (un)inclined plane, but work is done against friction.

So efficiency can be less than 1 in the case of an inclined plane with friction, but otherwise it is always 1.

Best, Dick Plano...

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