What factors affect the mechanical advantage of a lever?

Question

Lily Adams · Accepted 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# Imagine a first-class lever made of a rigid rod that can rotate around a fulcrum so that one end of the rod rises and the other falls. Depending on the lengths of points of application of forces from the lever's fulcrum, this lever can be used to raise a heavy object with a force that is much weaker than its weight. 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. A rod that functions as a lever is said to be rigid if its angle of rotation around a fulcrum remains constant at both ends. 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 previous formula, we can infer that the benefit of using a lever is determined by the ratio of the distances between the lever ends and the fulcrum; the greater the ratio, the greater the benefit and the amount of weight we can lift.

Carson Alexander · Answer

undefined The mechanical advantage of a lever is affected by three main factors:

1. The length of the lever arms
2. The position of the fulcrum
3. The applied force