O Level Revision : O Level Revision : Combined Science - Science in Structures and Mechanical Systems - Machines

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

 Machines

Levers

• 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

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  
                                                     effort

MA                             =            L  
                                                E

• 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    
               E

=           1000
               500

MA =       L    
               E

=   1000
       750

=         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
                 XL

• Velocity ratio has no units because it is a ratio. The bigger the velocity ratio the easier it is to do the work.

Efficiency

•  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

× 100

Also efficiency (ŋ)  =    MA   VR

×  100

• 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.

Pulleys

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).

Inclined plane

MA =          LOAD   
                 EFFORT

=       L  
         E

VR        =        Distance moved by effort (d)  
                        Distance moved by load (h)

VR         =        d  
                        h

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.

Gears

• 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   
                  r

• The bigger R is and the smaller r is the easier it is to use the winch.