Question

What factors affect the mechanical advantage of a lever?

Answer 1

If on one end of a class 1 lever in equilibrium force `F` is applied on a distance `a` from a fulcrum and another force `f` is applied on the other end of a lever on distance `b` from a fulcrum, then
`F/f=b/a`

Explanation:

Consider a lever of the 1st class that consists of a rigid rod that can rotate around a fulcrum. When one end of a rod goes up, another goes down.

This lever can be used to lift up a heavy object with significantly weaker than its weight force. It all depends on the lengths of points of application of forces from the fulcrum of the lever.

Assume that a heavy load is positioned at a length `a` from the fulcrum, the force it pushes down on a rod is `F`.
On the opposite side of a rod at a distance `b` from the fulcrum we apply a force `f` down such that two a lever is in equilibrium.

The fact that a lever is in equilibrium means that the work performed by forces `F` and `f` when a lever is pushed on either side by a small distance `d` must be the same - whatever work we, using force `f`, perform to push down our end of a lever on a distance `b` from the fulcrum should be equal to work to lift a heavy object on a distance `a` on the other end of a lever.

Rigidity of a rod that serves as a lever means that the angle a lever turns around a fulcrum is the same on both ends of a lever.

Assume that a lever turned by a small angle `phi` around a fulcrum slightly lifting a heavy weight. Then this heavy weight that exhorts a force `F` on one end of a rod at a distance `a` from a fulcrum was lifted by `a*sin(phi)` height. The work performed must be
`W=F*a*sin(phi)`

On the other end of a rod, on distance `b` from the fulcrum, force `f` pushed the lever down by `b*sin(phi)`. The work performed equals to
`W=f*b*sin(phi)`

Both works must be the same, so
`F*a*sin(phi) =f*b*sin(phi)`
or
`F/f = b/a`

From the last formula we derive that the advantage of using a lever depends on a ratio between lever ends' distance from fulcrum. The more the ratio is - the more advantage we have and more weight we can lift.