What is a Lever? | Mechanical Comprehension Review

Hi, and welcome to this video on levers! We’re going to discuss what exactly levers are, the physics behind how they work, and what different types of levers exist.

A lever is a type of simple machine; in fact, it’s one of the simplest machines out there. In its simplest form, it consists of two parts: a rigid bar and a fulcrum, which acts as the pivot. Using a lever makes it easier to lift or move an object. That is, it makes it easier to do work on an object.

The force that is exerted on an object with the lever is referred to as the force on the load, and the force you must physically apply to the lever is called the effort.

The trick to easily lifting an object with a lever is the distance between the force applied and the object to which it is applied.

When we use a lever, we are able to apply a small force over a longer distance in order to achieve a greater force on the object we are doing work on. So, the lever enables us to exert a force that we may not be able to exert with our own strength. Conversely, we could apply a great force close to the fulcrum to lift an object a greater distance than we could reach.

Remember, work is defined by a force multiplied by the distance over which the force is applied:

\(W = F\times d\)

By the laws of physics, energy is always conserved, so when we put some amount of work into a lever by pushing one end up or down, we are actually still getting that same amount of work out of the lever at the other end (assuming no energy is lost in friction).

\(W_{in} = W_{out}\)

Then, we can substitute in F times d for the input and output work.

\(F_{in} d_{1} = F_{out}d_{2}\)

\(F_{in}\) is the force we apply to the lever when putting in effort, \(d_{1}\) is the distance over which we apply that force, \(F_{out}\) is the force the lever applies to the load we are moving, and \(d_{2}\) is the distance over which the lever applies the force. The important concept here is that, while the amount of work isn’t changing, the force applied by us can be different from the force on the load, as long as the distances are different.
This leads to the concept of mechanical advantage, or MA, which is a ratio that describes how much the force you are putting into the lever is amplified. MA > 1 is what we are looking for, meaning the lever is applying a greater force to the load than what was supplied by the effort to move the lever.
Often, the mechanical advantage of levers is described in terms of torque, or τ, which is a measure of the force applied to a position relative to the pivot point. The equation for torque is similar to work, except that the distance is measured from the pivot point to the location where the force is applied. As such, the equations look very similar and both relationships can be used to determine the mechanical advantage:
\(τ_{in} = τ_{out}\)
\(F_{in} \times r_{1t}= F_{out} \times r_{2}\)
\(MA = \frac{F_{out}}{F_{in}} = \frac{d_{1}}{d_{2}}= \frac{r_{1}}{r_{2}}\)
So, mechanical advantage can then be written as \(MA = \frac{r_{1}}{r_{2}}\), which is just the ratio of the lever arms.

For this lever, \(r_{1}\) is the distance from the pivot to the point that effort is applied, and \(r_{2}\) is the distance from the pivot to the load.
Not all levers look exactly like the levers we’ve shown so far. There are actually three different “classes” of levers. They represent the three different arrangements of fulcrum, load, and effort on a rigid object.
Class 1 levers are like the two we’ve already looked at. These levers are defined by having the pivot point between the effort point and the load. Examples of this type of lever would be a seesaw or a crowbar. It should be pointed out that the pivot can be anywhere along the line between the effort and the load, not just in the center.

In a class 2 configuration of levers, the load is in the center, between the pivot and the effort point. Examples of class two levers are wheelbarrows or bottle openers.

In the case of a wheelbarrow, the work is done on the load in the barrow, the pivot is at the wheel, and the user applies a force, or effort, on the handles.
Class 3 levers are devices where the effort or force is applied between the load and the pivot point. An example of this type of lever would be something like a broom.

When you hold a broom, one of your hands is the fulcrum and the other is supplying the force. In the case where your top hand is the fulcrum, this is a class 3 lever, since the load is the bristle end and the hand supplying the force is between the fulcrum and the load.

Levers are everywhere! You can actually find instances of each class of lever in the human body! Lever devices can get more complex by combining multiple levers, like in scissors, nail clippers, or bolt cutters. These are referred to as compound levers.
Now that we have discussed the types of levers and how they work, let’s test your knowledge with a couple of questions!
1. You have a simple, class 1 lever with the pivot point 2 meters away from one end with a box sitting on it. If the other end is 3 meters away, what is the mechanical advantage you get by pushing down on that end?

A. MA = 0.67
B. MA = 1.33
C. MA = 1.50
D. MA = 2.30
The correct answer is C! The mechanical advantage can be found by the ratio of a/b, which is the distance of pivot to effort over the distance of pivot to load. Here, MA = 3/2 = 1.5.
2. What type of lever is in action when you bend your arm?
A. Class 1
B. Class 2
C. Class 3
D. Compound
The correct answer is C! The elbow acts as a pivot, your biceps applies the effort on the forearm, and the load is the lower half of your arm and anything in your hand.

That’s all for our video on the physics of levers. Thanks for watching, and happy studying!

 

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by Mometrix Test Preparation | Last Updated: December 20, 2021