Mechanical and Velocity Ratios

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This is a basic physics GCSE tutorial exploring mechanical and velocity ratios. Video tutorial to come.

Levers as force multipliers

As we've seen, class one and two levers reduce the effort needed to move a load by increasing the distance over which the effort force is acting. They allow relatively small effort forces to have relatively large effects. Consequently, levers are sometimes referred to as force multipliers. This can be referred to as their mechanical advantage.

What is the mechanical ratio?

The more effective a first or second class tool is, the better the mechanical advantage it offers. You can compare the mechanical advantage that different tools offer by calculating their mechanical ratio (as shown below).


The more efficient a tool is, the greater its mechanical ratio will be. Ideal mechanical advantage assumes that no energy is lost through friction, heat etc.

What is the velocity ratio?

The velocity ratio is a ratio of the relative distances which the effort force and the load force are acting across.

You're probably wondering: why is it referred to as velocity ratio if we're comparing distances? See below for an explanation of why this is the case.

Let's work through an example

You would have seen these two images in the levers introduction tutorial. Let's work out the mechanical ratio and the velocity ratio for the see-saw lever in the images.

Mechanical advantage = load force ÷ effort force
mechanical advantage = 400 N ÷ 160 N
mechanical advantage = 2.5

Velocity ratio = effort distance ÷ load distance
Velocity ratio = 1.25 m ÷ 0.5 m
Velocity ratio = 2.5

Ideal Levers

In the above example, you'll notice that the mechanical advantage and velocity ratio are the same. This is because the system we've used in the example is an ideal one i.e. one in which the energy put into the system is the same as the energy that you get out of the system. Or in other words, in an ideal system:

work in = work out

The above example assumes that none of the energy put into the lever (i.e. the effort force) is lost, for example, due to friction. In reality, this would not be the case, and hence there can be differences between the calculated mechanical advantage and velocity ratio of a machine/lever.

Why do we call it velocity ratio?

Although we're not strictly comparing velocities with the velocity ratio, we get the same answer by comparing distances as we would if we were comparing velocities; this is because the two distances are covered within the same time period i.e. the denominator (time) would be the same (and thus cancel each other) out if we did compare velocities.

Let's work through an example, just to confirm this is the case. Imagine the above lever was said to work over 2 seconds. The relative velocities would therefore be:

The ratio of these two would be calculated by dividing 0.625 m/s by 0.25 m/s, which gives us 2.5 again.

As you can see, we get the same answer, whether we compare velocity ratios or distance ratios. So we compare the distances over which the two forces are acting to save us having to do the extra work of actually working out the respective velocities.