What factors affect the mechanical advantage of a lever?

1 Answer
Jul 20, 2015

Answer:

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.