Machines
Machines are devices that enables us to do work more easily. Simple machine such as levers, pulleys, gears and screws are used to build more complicated machines. For example, a crane is a combination of pulleys, gears and levers.
Work
In science, work is done when a force moves. For example, when you lift a pile of books you are doing work. However if there is no movement, no work is done. For example if you are holding s heavy pile of books, you are not doing an work if there is no movement in any direction.
Work done is calculated as follows:
Work done = Force × distance moved in the direction of the force.
Whereby Force is measured in newtons(N), distance in metres(m) and work done in joules (J).
Example 1
Calculate the work done in pulling a box with a force of 10N for a distance of 2m.
Solution 1
Work done = Force × distance
= 10 × 2
= 20J
Energy
Energy is the ability to do work, and work done is equal to the energy converted from one form to another. In example 1 we calculated that the work done in moving pulling the box is 20J which therefore means 20J is the energy converted from chemical energy to kinetic energy when pulling the box.
Types of simple machines
Levers
A lever basically consists of a beam and a pivot (fulcrum).
The diagram above shows a simple lever with a pivot in the middle. A lever works on the principle of moments which states that:
Anti-clockwise moments = Clockwise moments
Load × OA = Effort × OB
500 × 1 = Effort × 2
500 ÷ 2 = Effort
Effort = 250N
An effort of 250N can be used to lift a load of 500N using the lever shown above. From the calculation, we can see that the longer OB is in relation to OA the smaller the effort required.
A lever is therefore called a force multiplier and it multiplies the effort by a ratio called the Mechanical Advantage.
Mechanical Advantage
Mechanical advantage is the ratio of the load lifted to the effort applied.
On the lever above, Mechanical Advantage = 500 ÷ 250
= 2
Mechanical advantage is a ratio and it has no units.
Velocity Ratio
When a machine multiplies the effort, it also means the effort moves a longer distance in relation to the load. Velocity ratio is ratio of the distance moved by the effort to the distance moved by the load.
Velocity ratio is a ratio and it has no units.
Efficiency
Although machines make work easier, they do not reduce the amount of work to be done. In actually fact, no machine is 100% efficient. This means that if you apply 100J on the effort, work done on the load will be less than 100J.
Energy loses in machines are due to:
- some of the input energy being used to overcome friction.
- some of the input energy being used to lift the moving parts of the machine.
For example in our lever above, when you lift the load you are also doing work against the friction between the pivot and the level and also lift the level beam in the process.
OR
OR
Efficiency is usually given as a percentage.
Efficiency of a machine can be improved in the following ways:
- oiling the moving parts to reduce friction
- using ball bearings and roller bearings between the moving parts to reduce friction.
- using lighter moving parts.
Example 2
A load of 60N is lifted by a level to a height of 0.5m when an effort of 20N moves a distance of 2m. Calculate:
- The mechanical advantage
- The velocity ratio
- The efficiency
Solution
Therefore M.A. = 60N ÷ 20N
= 3
Therefore V.R. = 2m ÷ 0.5m
= 4
Therefore efficiency = (3 × 100) ÷ 4
= 75%
Pulleys
A pulleys consists of a rope connecting the effort and the load while passing through a wheel. There are different types of pulley systems depending on the wheel-rope configuration.
Single fixed pulley
The effort lifts the load upwards by pulling downwards.
Taking the pulley to be ideal:
- M.A. = 1
- V.R. = 1
Single movable pulley
The pulley wheel moves with the load. The effort is multiplied by the fact that the tension in the other string also act as effort.
Taking the pulley to be ideal:
- M.A. = 2
- V.R = 2
Block and Tackle
This configuration consists of both fixed pulleys and movable pulleys. In this type of a pulley system:
- M.A. = L/E
- V.R. = Number of Wheels. (In this case V.R. = 2)
Inclined Plane
Also known as a ramp consists of a plane surface at an inclination to the horizontal.
- M.A. = L/E
- V.R. = d/h
