Inclined Plane Efficiency
Name: Brenda R.
How does the efficiency of an inclined plane vary with the angle of
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
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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Update: June 2012