LEVERS I (Definition and Equilibrium)
Levers can be found in many everyday situations. Consider this one that you may see on a playground.
A lever consists of a beam and a point about which the beam pivots called the “Fulcrum”. There are 3 classes of levers. The class is determined by the location of the fulcrum and the forces being applied to the beam. There is a direct relationship between the forces and their distance from the fulcrum. One of the forces is known as the “load” and is always a downward force. The other force is called the “effort” and is the force needed to keep the lever balanced on the fulcrum. This balancing is known as the “equilibrium”.
We know from Physics that Force times Distance equal Work (F x D = W). For a lever to reach equilibrium, the Work created by the load and the effort forces must be equal.
The Mathematics of Levers
1st Class Lever
- FR = Force provided by the load
- dR = distance from load to the pivot point
- FE = Force applied to lever
- dE = distance from effort to the pivot point
To produce Balance (equilibrium)
FR x dR = FE x dE
2nd Class Lever
- FR = Force provided by the load
- dR = distance from load to the pivot point
- FE = Force applied to lever
- dE = distance from effort to the pivot point
To produce Balance (equilibrium)
FR x dR = FE x dE
3rd Class Lever
- FR = Force provided by the load
- dR = distance from load to the pivot point
- FE = Force applied to lever
- dE = distance from effort to the pivot point
To produce Balance (equilibrium)
FR x dR = FE x dE
Determining Equilibrium
We can use the equation to determine the equilibrium for each class of lever.
1st Class Lever
Using the lever equation to determine equilibrium of a 1st class lever
Example 1:
We want to know how much force is required to lift a 1 lb weight to an equilibrium position using the 1st class lever shown. Assume the rod has no weight.
- FR = 1 lb
- dR = 6 inches
- FE = ?
- dE = 6 inches
FR x dR = FE dE
(1lb)(6in) = FE
6 in
1lb = FE
1 lb of force is needed to produce equilibrium
Example 2:
We want to know how much force is required to lift a 1 lb weight to an equilibrium position using the 1st class lever shown. Assume the rod has no weight.
- FR = 1 lb
- dR = 9 inches
- FE = ?
- dE = 3 inch
FR x dR = FE
dE
(1lb)(9in) = FE
3 in
3 lb = FE
3 lbs of force is needed to produce equilibrium
Example 3:
We want to know how much force is required to lift a 1 lb weight to an equilibrium position using the 1st class lever shown. Assume the rod has no weight.
- FR = 1 lb
- dR = 3 inches
- FE = ?
- dE = 9 inch
FR x dr = FE
dE
(1lb)(3in) = FE
9 in
0.33 lb = FE
0.33 lbs of force is needed to produce equilibrium
2nd Class Lever
Using the lever equation to determine equilibrium using 2nd class lever
Example 4:
We want to know how much force is required to lift a 1 lb weight to an equilibrium position using the 2nd class lever shown. Assume the rod has no weight.
- FR = 1 lb
- dR = 3 inches
- FE = ?
- dE = 12 inch
FR x dR = FE
dE
(1lb)(3in = FE
12 in
0.25 lb = FE
0.25 lbs of force is needed to produce equilibrium
3rd Class Lever
Using the lever equation to determine equilibrium using 3rd class lever
Example 5:
We want to know how much force is required to lift a 1 lb weight to an equilibrium position using the 2nd class lever shown. Assume the rod has no weight.
- FR = 1 lb
- dR = 3 inches
- FE = ?
- dE = 12 inch
FR x dR = FE
dE
(1lb)(12in) = FE
3 in
4 lb = FE