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Forces & Pivots: Explanation & Examples

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

To understand how a lever can be used to move a heavy object, you have to know something about how forces and pivots work together to create torque. In this lesson, learn how the torque generated by a force depends on the location of the pivot point.

Levers

John wants to pick up a heavy rock, so first he tries to just pick it straight up. Unfortunately, it's too heavy for him to move! What can he do?

After thinking for a few minutes, John decides to try a different approach. He gets a long stick and places it on a small rock in front of the heavy rock he wants to move. Then he places the end of the stick under the rock and pushes down on the other end. Now, he is able to make the rock move!

John used a simple machine called a lever to move the rock. A lever is a movable bar attached to a fixed pivot point called a fulcrum, and levers allow you to use small amounts of force to move heavy objects.

Torque

Before we can understand exactly how levers work, we need to know something about a quantity called torque. Torque is a force that, when applied, makes an object rotate. The force that John applied to the end of his lever created a torque that made the stick rotate, lifting the heaving rock.

In order to determine how much torque is being applied, you need to know two things: the amount of force (F) that is applied and the distance from the pivot point to the point where the force is applied (d).


Torque


So, how much torque did John apply to the stick when he pushed on it? Let's assume that he exerted a force of 600 Newtons, and he applied this force 0.8 meters from the pivot point. To find the amount of torque, simply multiply F and d.

Torque = F x d = (600 N) x (0.8 m) = 480 N m

The Principle of Levers

How can you tell if the amount of torque applied to the lever will actually be able to move the rock? In order for the rock to start moving, the torque exerted by John's pushing force on one end of the stick must be bigger than the torque exerted on the other end of the stick by the rock. This is known as the principle of levers, which asserts that if the torque on one side of the pivot point is equal to the torque on the other side of the pivot point, the system will be in equilibrium. If one torque is bigger than the other, then the system will start to rotate.

The principle of levers was explained by Archimedes thousands of years ago!
archimedes lever

Let's apply that to John and his heavy rock. We already know that John is able to produce a torque of 480 N m on one side of the pivot point. If the rock has a weight of 2000 N and the center of the rock is located 0.2 m from the pivot point, how much torque is it creating on the rock's side of the pivot?

Once again, multiply the force (2000 N) by the distance (0.2 m) to find the torque.

Torque = F x d = (2000 N) x (0.2 m) = 400 N m

Because the torque exerted by John (480 N m) is greater than the torque exerted by the rock (400 N m), John is able to rotate the lever and move the rock. Even though he was not able to produce the 2000 N necessary to pick the rock straight up, he could easily exert 600 N on the lever and the rock still moved!

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