O Level Revision : O Level Revision : Combined Science - Science in Structures and Mechanical Systems - Machines
The human race is always trying to find ways of making work easier. Machines are devices that make work easier. The principle involves lessening the effort required to lift or move a load or changing the direction in which the force is applied to a more convenient one. Levers and pulley systems help to move loads using by reducing the effort required. Mechanical advantage is the ratio of the load to the effort. A large mechanical advantage indicates that a much smaller effort is required to lift a heavier load. Friction affects the way machines work and their efficiency. Pumps use the concept of pressure to move fluid substance and act as machines.
- A machine is a device that makes work easier either by:
- reducing the effort needed to lift a load or
- changing the direction of application of effort to a more convenient one.
- Carrying a 50 litre container full of water from a borehole can be tiresome. Using a wheelbarrow makes this work easier.
Types of machines
(i) Levers (ii) Pulleys (iii) Inclined planes
(iv) Gears (v) Wheels and axles
- These are force multipliers which enable a large load to be lifted using a smaller effort.
Consider a crowbar
A crowbar at balanced point
Principles of moments
- The principle of moments states that a system is in equilibrium (balanced) if total clockwise moments equal total anticlockwise moments.
- A moment is the turning effect of a force about a pivot.
- The moment is found by multiplying the force by the perpendicular distance of the force from the pivot.
- The pivot is the point that does not move as rotation takes place.
a) For the crowbar to balance;
Clockwise moment = anticlockwise moment
Load × distance from pivot = effort × distance from pivot
Candidates forget to check that they are using distances expressed in a common unit.
b) If distance of effort from pivot is reduced to 75m from I; then using the principle of moments
1 000N × 0.75
Note: For a lever, the further effort is applied from pivot the easier it becomes to do the work, the more useful the machine becomes.
Mechanical advantage (MA)
- Is a ratio of load to effort.
Mechanical advantage = load
MA = L
- Mechanical advantage has no units because it is a ratio.
- The bigger the mechanical advantage the more useful the machine is.
In situation (a) of the crowbar: In situation (b) of the crow bar:
MA = L
MA = L
= 2 = 1.33
- MA in (b) is less than MA in (a).
- In (a) the crowbar is more useful than in (b) because in (a) work is done more easily (a smaller effort needed).
Velocity ratio (VR)
- (VR) - is the ratio of distance moved by effort to distance moved by load.
- Velocity ratio = (distance moved by effort) (distance moved by load)
VR = XE
- Velocity ratio has no units because it is a ratio. The bigger the velocity ratio the easier it is to do the work.
- It is a ratio of work done by the machine to work done on the machine (work output to work input).
- It is the effectiveness of a device in converting energy from one form to another (doing work).
- It is usually expressed as a percentage.
Efficiency (ŋ) = work output work input
ŋ = Wout
Win × 100
Also efficiency (ŋ) = MA VR
- No machine is 100% efficient because of energy losses that occur due to friction.
- Efficiency is improved by reducing friction through:
- lubrication - use of oil and grease
- use of ball bearings and rollers
- smoothing moving parts.
A pulley is a wheel with a grooved rim around which moves a string.
Block and tackle
- This a combination of fixed pulley(s) and movable pulley(s).
1 fixed, 1 movable
2 fixed, 1 movable
2 fixed, 2 movable
VR = 2
VR = 3
VR = 4
ŋ = 100%
MA = 2 MA = 3
MA = 4
MA = LOAD
VR = Distance moved by effort (d)
Distance moved by load (h)
VR = d
LOAD = weight
- The smaller it is the greater the mechanical advantage hence the easier it is to lift the load.
- Lubrication of the inclined plane increases efficiency.
- These are simple machines that are made up of wheels and cogs, which are locked into each other.
- Gears are toothed wheels that work together to alter speed or power output of a machine.
- VR = number of teeth on load gear
number of teeth on effort gear
- In high gear VR is low because wheels are of the same size.
- High gear is used when the load is lighter.
- In low gear VR is high because effort wheel is smaller.
- Low gear is used when the load is heavy.
F. Wheel and axle
These are used in door knobs, wells and bicycles as shown in Fig. 16.6 below.
Door knob Windlass Bicycle wheel and axle
- A small axle turns a large wheel hence the force on the axle is much greater than wheel e.g. on the bicycle wheel.
- In a winch a large wheel is used to turn a small axle hence a small effort on wheel lifts a bigger load on axle e.g. on the windlass or door knob shown.
- VR = circumference of wheel
circumference of axle
VR = radius of wheel
Radius axle for the winch
VR = R
- The bigger R is and the smaller r is the easier it is to use the winch.