Simple Machines · 8 min read
Mechanical advantage, velocity ratio and efficiency
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Introduction to simple machines
A machine is a device that helps us do work more easily. Imagine trying to pull a heavy bucket of water out of a deep borehole with just your bare hands. It is hard, right? But if you use a rope and a pulley, it becomes much easier. The machine helps you overcome a large force by applying a smaller force.
In simple terms, a machine is any tool that makes your work less stressful.
Mechanical Advantage (MA)
Think about using a long stick to lift a heavy stone in your compound. The weight of the stone is the Load, and the force you apply to the stick is the Effort. If you use a small effort to lift a very heavy load, we say the machine has a high Mechanical Advantage.
So, MA = Load / Effort. Since it is a ratio of two forces, it has no unit.
Velocity Ratio (VR)
When you use a machine, your hand usually moves a long distance while the load moves only a short distance. For example, when using a car jack, you pump the handle many times (large distance) just to lift the car a few centimeters (small distance).
The formula is VR = Distance moved by effort / Distance moved by load. Like MA, it has no unit.
Efficiency of a machine
In a perfect world, all the energy you put into a machine should come out as useful work. But in Nigeria, we know things are rarely perfect! Some energy is always lost because of friction between moving parts, like a rusty generator chain. This energy usually turns into heat.
The formula for Efficiency is (Work Output / Work Input) x 100%. A better way to calculate it for Physics exams is: Efficiency = (MA / VR) x 100%.
Worked Example
Let us look at a machine with a velocity ratio of 5. If it requires an effort of 200 N to lift a load of 800 N, let us find the efficiency:
1. First, find the Mechanical Advantage (MA). MA = Load / Effort = 800 / 200 = 4.
2. We already know the Velocity Ratio (VR) is 5.
3. Apply the efficiency formula: Efficiency = (MA / VR) x 100 = (4 / 5) x 100.
4. Final result: 0.8 x 100 = 80%.
Key points
- •Mechanical Advantage (MA) is Load divided by Effort.
- •Velocity Ratio (VR) is Effort distance divided by Load distance.
- •Efficiency is always less than 100% in real life due to friction.
- •Efficiency = (MA / VR) x 100%.
- •VR depends on the machine's design and does not change with friction.