Understanding and calculating mechanical advantage

In my most recent post on machines, we saw that there are 3 categories or classes of machines. The difference in each is the position of the load, effort and fulcrum. In first class machines, the fulcrum is located in-between and load and effort. Second class machines have the load placed in-between the effort and fulcrum. While third class machines station place the effort at the middle, while the load and fulcrum are at either ends.

In this presentation, we will try to explain a term that is usually mentioned in discussions of simple machines. That term is Mechanical advantage. We will also see how to calculate the mechanical advantage of any machine.

What is mechanical advantage

A machine is used to overcome load by applying some effort. Compared to the size of the load, the effort is usually very small. The mechanical advantage of any machine is usually explained in terms of the amount of load and the effort or force required to overcome it. So for any machine, the mechanical advantage is its ability to use a very small force or effort to overcome a large load.

Mechanical advantage is also referred as force ratio since it tries to define the amount of force or effort needed to overcome a large load. Both the effort and load produces some form of force. But for there to be a mechanical advantage, the ratio of input force to that of the output force must be small.

When there is friction which creates some opposition to the applied force, then more force would be required to overcome the load. The more friction there is, the less mechanical advantage there would be. Generally, machines that have less friction as they overcome load perform more efficiently than ones with more friction present.

Expressing the mechanical advantage mathematically, we can define the relationship between load and effort this way:

Since mechanical advantage is a measure of force, the S.I unit of mechanical advantage is Newtons (N)

Calculating Mechanical advantage

Question 1. A pulley system uses a force of 100 Newtons to overcome a load of 2000 Newtons. Calculate its mechanical advantage.

Solution:

M.A = Load/Effort
M.A = 2000/100
M.A = 20N

Question 2: A machine with mechanical advantage of 4N was used to overcome a load of 200N. How much force was applied by the machine to accomplish this job?

Solution

M.A = Load/Effort
4 = 200/E (Making E the subject)
4E = 200
E = 200/4
E = 50N

Question 3: A simple lever machine with a mechanical advantage of 10N was used to raise a log of wood. The force applied is 200N. What is the weight of the log of wood?

Solution:

M.A = Load/Effort
10 = Load/2000
Load = 200x10
Load = 2000N

Conclusion

In each case of the calculations above, we will note that the amount of force applied is usually smaller compared to the size of the load. If friction is negligible, the mechanical advantage of a machine should reasonably reflect the fact the a small amount of force applied to the machine is used to overcome a much larger load or resistance.