How is the angle between ramp and surface related to the efficiency of inclined plane. what is to be done to increase the efficiency of inclined plane?
Answers
Mechanical advantage of an inclined plane is the force required to raise it to a height h and the force required to do the same without the inclined plane i.e, vertically upward. This force is mg
When we solve the free body diagram for force required to push a block up a plane with friction coefficient μ we get the following equations:
F=mg(μcos(θ)+sin(θ))
where θ is the angle of the incline.
The actual mechanical advantage(AMA) then is given by the formula:
AMA=1/μcos(θ)+sin(θ)
This function has a maximum only at 0 in the range [0,π//2].
The efficiency is got by the ratio of actual mechanical advantage and ideal mechanical advantage(with no friction).
IMA=1/sin(θ) This is got by setting μ= 0 in the AMA equation.
Using this we get the equation for efficiency as :
E= AMA/IMA = sin(0) / μcos(θ)+sin(θ)
Plotting this function shows that we have a maximum at θ=π/2