# Quantification of Levers and Similar Mechanical Devices

Peppino
Hello everyone.

I am fairly familiar with physics. However I have a question regarding the math behind a lever mechanism. Why is it easier to exert force on something the longer the arm of the lever is? What is the math/equations behind this?

cmmcnamara
It's not necessarily easier to exert "force" on something the longer the lever arm is, but the resulting moment/torque created about the lever's pivot is greater the longer the lever arm. Wikipedia has an excellent description of this and can be found here: http://en.wikipedia.org/wiki/Torque

The article describes the necessary mathematics behind this as well. Note that its not necessarily the length of the lever that produces the larger torque (on an actual lever however, the handle is undoubtedly at the end) but the larger distance from the pivot point.

Peppino
So let's say we have a lever and a fulcrum located at the center, and there's a 1 kg box on one end of the lever. How much Torque must be exerted on the other side to lift the box?

Mentor
So let's say we have a lever and a fulcrum located at the center, and there's a 1 kg box on one end of the lever. How much Torque must be exerted on the other side to lift the box?
Whatever torque is created by the weight of the box about the fulcrum is what you'll have to exert to lift the box. If you're pushing down at the end of the lever you'll have to exert a force equal to the weight of the box (or a bit more), since the fulcrum is in the middle.

cmmcnamara
So let's say we have a lever and a fulcrum located at the center, and there's a 1 kg box on one end of the lever. How much Torque must be exerted on the other side to lift the box?

The same amount of torque must be exerted in the opposite direction to lift the box. The amount of force needed to generate the opposing torque is dependent on the location that force is applied. If applied at the opposing end, you'd only need to exert the same amount of force which is generated by the mass of the box. In this case since you've conveniently chosen 1 kg, you'd have to exert 9.81 N. However if you'd placed your force closer towards the fulcrum you'd have solve for the required force as governed by τ=Fd, where τ would be the amount of torque, F is your force, and d is your distance to the fulcrum.