Mechanical Advantage and Levers, Grade 11 physics
We can use our knowlegde about the moments of forces (torque) to determine whether situations are balanced. For example two mass pieces are placed on a seesaw as shown in Figure 12.20.

The one mass is 3 kg and the other is 6 kg. The masses are placed a distance 2 m and 1 m, respectively from the pivot. By looking at the clockwise and anti-clockwise moments, we can determine whether the seesaw will pivot (move) or not. If the sum of the clockwise and anti-clockwise moments is zero, the seesaw is in equilibrium (i.e. balanced).

The clockwise moment can be calculated as follows:

τ = F$_{⊥}$ · r
τ = (6)(9,8)(1)
τ = 58,8N · m clockwise​

The anti-clockwise moment can be calculated as follows:

τ = F$_{⊥}$ · r
τ = (3)(9,8)(2)
τ = 58,8N · m anti-clockwise​

The sum of the moments of force will be zero:

The resultant moment is zero as the clockwise and anti-clockwise moments of force are in opposite directions and therefore cancel each other.

As we see in Figure 12.20, we can use different distances away from a pivot to balance two different forces. This principle is applied to a lever to make lifting a heavy object much easier.

Definition: Lever
A lever is a rigid object that is used with an appropriate fulcrum or pivot point to multiply the mechanical force that can be applied to another object.

Archimedes reputedly said: Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.

The concept of getting out more than the effort is termed mechanical advantage, and is one example of the principle of moments. The lever allows to do less effort but for a greater distance. For instance to lift a certain unit of weight with a lever with an effort of half a unit we need a distance from the fulcrum in the effort’s side to be twice the distance of the weight’s side. It also means that to lift the weight 1 meter we need to push the lever for 2 meter. The amount of work done is always the same and independent of the dimensions of the lever (in an ideal lever). The lever only allows to trade effort for distance.

Ideally, this means that the mechanical advantage of a system is the ratio of the force that performs the work (output or load) to the applied force (input or effort), assuming there is no friction in the system. In reality, the mechanical advantage will be less than the ideal value by an amount determined by the amount of friction.

mechanical advantage = \[\dfrac{load}{effort}\]
​

For example, you want to raise an object of mass 100 kg. If the pivot is placed as shown in Figure 12.22, what is the mechanical advantage of the lever?In order to calculate mechanical advantage, we need to determine the load and effort.

Important: Effort is the input force and load is the output force.

The load is easy, it is simply the weight of the 100 kg object.

F$_{load}$ = m · g = 100 kg · 9,8 m · s$^{−2}$ = 980 N​

The effort is found by balancing torques.

F$_{load}$· r$_{load}$ = F$_{effort}$ · r$_{effort}$
980 N · 0.5 m = Fef f ort · 1 m
F$_{effort}$ = 490 N​

The mechanical advantage is:

mechanical advantage = \[\dfrac{load}{ effort }\] = 2​

Since mechanical advantage is a ratio, it does not have any units.
Classes of levers
Class 1 levers
In a class 1 lever the fulcrum is between the effort and the load. Examples of class 1 levers are the seesaw, crowbar and equal-arm balance. The mechanical advantage of a class 1 lever can be increased by moving the fulcrum closer to the load.

Class 2 levers
In class 2 levers the fulcrum is at the one end of the bar, with the load closer to the fulcrum and the effort on the other end of bar. The mechanical advantage of this type of lever can be increased by increasing the length of the bar. A bottle opener or wheel barrow are examples of class 2 levers.

Class 3 levers
In class 3 levers the fulcrum is also at the end of the bar, but the effort is between the fulcrum and the load. An example of this type of lever is the human arm.

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Physics 11.II Force, Momentum, Impulse

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