Simple Machine

Every day we do many different jobs. Water has to be drawn from a well, doors have to be opened, firewood has to be split, heavy goods have to be carried up to a higher place, and sometimes a nut has to be tightened. Doing these jobs with bare hands is very hard, so we use tools to make them easy. The screwdriver, the pulley, the wheel and axle, the tongs, the jack that lifts a car, the sickle and the axe are all tools used in household work.

These tools share one feature. They need no electricity, no diesel and no petrol to run. Human force alone is enough to operate them. Their construction is simple too, so they are easy to make and easy to use.

Devices like these do not do the work by themselves. We still do the work, but the device lets the same job be finished with less force, in less time and in a more convenient way. Because they share this quality, they are given one common name.

On the basis of their construction, simple machines are of four types. Every one of them can be met in daily life.

• The lever: a strong rod resting on a support, used to raise or prise up a heavy load.
• The pulley: a turning wheel with a groove for a rope round its rim, like the wheel used to draw water from a well.
• The wheel and axle: a large wheel and a thin rod that turn together, like the knob of a door.
• The inclined plane: a sloping surface used to move a heavy load up to a higher place, like a plank laid up to the back of a truck.

The screw and the wedge are special forms of the inclined plane itself. The thread of a screw is a sloping surface wound round a rod, and a wedge, like the edge of an axe, is also built from sloping surfaces. That is why these two are not counted as separate types.

Using a simple machine, force can be increased. A strong rod resting on a triangular support makes a lever. A load of 600 N sits 5 m from the support, and on the other side a force of 400 N is applied 10 m from the support. Here the weight that has to be raised is called the load, and the force we apply is called the effort.

Here an effort of 400 N has raised a load of 600 N. In other words, the load lifted is 1.5 times the force used to lift it. Raising a large weight with a small force is the great advantage of a simple machine.

The number that measures how many times a simple machine has multiplied our force is its mechanical advantage.

\[ \text{MA} = \frac{\text{Load}}{\text{Effort}} \]

Let us work out the mechanical advantage of the lever above.

Step 1: Putting the load 600 N and the effort 400 N into the formula:

\[ \text{MA} = \frac{600\ \text{N}}{400\ \text{N}} \]

Step 2: Dividing the two numbers:

\[ \text{MA} = 1.5 \]

Mechanical advantage is a ratio of two forces. When we divide, the newton on the top and the newton on the bottom cancel each other. So mechanical advantage has no unit.

While a simple machine works, the load and the effort both move, but they do not always move equal distances. On a lever the end where the effort acts is farther from the support, so that end moves faster and farther than the end carrying the load. Comparing the two movements gives us the second important number.

\[ \text{VR} = \frac{\text{Velocity of effort}}{\text{Velocity of load}} \]

When a machine works, the load and the effort move together, so both take the same time to cover their distances. When the times are equal, the ratio of the velocities is exactly the ratio of the distances. So we can also write \( \text{VR} = \frac{\text{effort distance}}{\text{load distance}} \).

On the same lever the effort acts 10 m from the support and the load sits 5 m from it. When the lever turns a little, the effort end covers twice the distance the load end covers. For example, while the effort moves 10 cm down, the load rises only 5 cm. So:

\[ \text{VR} = \frac{10\ \text{cm}}{5\ \text{cm}} = 2 \]

Velocity ratio is a ratio of two velocities, so it too has no unit.

These two formulas do not belong to one machine only. Whether it is a lever, a pulley, a wheel and axle or an inclined plane, the mechanical advantage and the velocity ratio of every kind of simple machine are found from these same formulas. The table below places the two side by side.