Question

What is the ideal mechanical advantage in using a (frictionless) ramp to raise a mass of 9 kg that is at an angle of theta θ = 22 degrees. Explanation needed please. Thank you..

Answer 1

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 an inclined plane.

Then, we have

F = m g

When we solve a free body diagram for force required to push a block up the plane with friction coefficient, then we have

F = mg [ cos + sin ]                                                              { eq.1 }

The actual mechanical advantage is given by -

AMA = 1 / [ cos + sin ]                                                               { eq.2 }

This function has a maximum only at 0 in the range [0, /2].

Inserting the value of = 0 in the AMA equation.

The ideal mechanical advantage is given by -

IMA = 1 / sin                                                                                     { eq.3 }

where, = angle of an inclinaton = 22 degree

then, we get

IMA = 1 / sin 22⁰

IMA = 1 / (0.3746)

IMA = 2.67