Machines – SS2 Physics Lesson Note (First Term)

A machine is a device by which a large force, called the load, can be overcome by a small applied force, called the effort. Machines make work easier. Their performance is described by three terms: mechanical advantage, velocity ratio and efficiency.

Behavioural objectives

By the end of the lesson, students should be able to:

• define a machine, effort and load;
• define and calculate mechanical advantage, velocity ratio and efficiency;
• state the relationship between efficiency, M.A and V.R;
• describe the main types of machines and give examples of each;
• explain the effects of friction on a machine.

What terms are used to describe machines?

• Force ratio (mechanical advantage)
• Velocity ratio
• Efficiency

Mechanical advantage (M.A)

Effort is the force applied to a machine. Load is the resistance overcome by the machine. The ability of a machine to overcome a large load through a small effort is known as its mechanical advantage. It is given by:

M.A = Load ÷ Effort

The mechanical advantage of a machine is influenced by friction in its parts.

Velocity ratio (V.R)

The velocity ratio is the ratio of the distance moved by the effort to the distance moved by the load in the same interval.

V.R = Distance moved by effort ÷ Distance moved by load

The velocity ratio depends on the geometry of the machine.

Efficiency (Ef)

The efficiency of a machine is defined as:

Ef = (Useful work done by the machine ÷ Work put into the machine) × 100%

Work = force × distance

Ef = (Load × distance moved by load) ÷ (Effort × distance moved by effort) × 100%

Therefore, Ef = (M.A ÷ V.R) × 100%.

What are the types of machines?

Lever

This is the simplest form of machine. It consists of a rigid rod pivoted about a point called the fulcrum F. A small effort is applied at one end of the lever to overcome a large load L at the other end. There are various types of levers, depending on the relative positions of the load, effort and fulcrum.

Taking moments about F:

E × a = L × b

L ÷ E = a ÷ b = M.A

a ÷ b = V.R

• First-class lever: the fulcrum is between the effort and the load. Examples are the crowbar, pair of scissors or pincers, claw hammer, see-saw and pliers.
• Second-class lever: the load is between the fulcrum and the effort. Examples are the wheelbarrow, nutcracker, trap door and oar.
• Third-class lever: the effort is between the fulcrum and the load. Examples are the human forearm and laboratory tongs.

Wheel and axle

It consists of a large wheel to which a rope or string is attached, and an axle or small wheel with a rope or string wound around it in the opposite direction. The load to be lifted is hung at the free end of the rope on the axle. The effort is applied at the end of the rope on the wheel.

For each complete rotation, the effort and the load move through distances equal to the circumference of the wheel and of the axle respectively.

V.R = R ÷ r

The principle of the wheel and axle is used in the brace, screwdrivers, spanners, windlasses and gearboxes.

Gear wheels

Simple mechanical system with gear wheels, illustration.

In gearboxes, toothed wheels of different diameters are interlocked to give turning force at low speeds, depending on which gear is the driver and which is the driven.

V.R = Number of teeth on the driven wheel ÷ Number of teeth on the driving wheel

The hydraulic press

The machine is widely used for compressing waste paper and cotton into compact bales, and for forging different alloys into desirable shapes. Its work is based on Pascal’s principle, which states that pressure applied to an enclosed fluid is transmitted equally through the fluid. Oil is the liquid normally used in a hydraulic press.

V.R = R² ÷ r²

The wedge

The wedge is a combination of two inclined planes. It is used to separate bodies which are held together by a large force. Examples of wedge-type machines are axes, chisels and knives.

Pulley

A simple pulley is a fixed wheel hung on a suitable support, with a rope passing around its groove.

Block and tackle

This is a more practical system of pulleys. One or more pulleys are mounted on the same axle, with one continuous rope passing all round the pulleys.

What are the effects of friction on a machine?

1. Work is always wasted in machines to overcome the frictional forces between the moving parts and to lift part of the machine. The greater the friction, the greater the effort required and the smaller the M.A. V.R. is independent of friction and depends on the geometry of the moving parts.
2. The efficiency of nearly all machines varies with the load. The effort E and the load L are related by E = aL + b, where a and b are constants. This is called the linear law for a machine. It follows that E varies linearly with L.
3. The value of b gives the effort required to operate the moving parts of the machine when no load is present, while a gives a measure of the friction present.

In practical machines, the efficiency is usually less than 100% because of friction in the moving parts of the machine.

Evaluation

1. (a) What is a machine? (b) Explain why a machine can never be 100% efficient.
2. Define the following terms as applicable to a machine: (a) velocity ratio, (b) mechanical advantage, (c) efficiency.
3. A pulley with a velocity ratio of 5 is used to lift a load of 400 N through a vertical height of 8 m by exerting an effort of 100 N. Calculate: (a) the work done by the effort and (b) the efficiency of the pulley system.

Assignment

1. State the relationship between efficiency, mechanical advantage and velocity ratio.
2. Name the three classes of lever and give one example of each.
3. State Pascal’s principle and name one use of the hydraulic press.