Efficiency

Efficiency is the measure of the ‘usefulness’ of a machine, process or operation.

Efficiency (η)=[work (or power) output]/[work (or power) input]

Efficiency can be expressed as a percentage (%) or as a decimal fraction of 1 (per-unit efficiency). In practice the efficiency of a device can never achieve 100% or 1.

Example

If the efficiency of the hoist in the previous example is 80%, calculate the actual power required.

Efficiency (%) =(power output×100)/power input

Therefore

80% =7.5 kW/power input

Hence

Power input =(7.5×100)/80

=9.375kW

 

Speed, velocity and acceleration

• Speed is a scalar quantity since it has magnitude only (e.g. 30 km/h).
• Velocity is a vector quantity since it has magnitude and direction (e.g. 30 km/h due north).
• Acceleration is the rate of change of velocity.

 

Speed

Speed is the rate of change of distance. That is: speed=distance/time. Typical units of speed are kilometres per hour (km/h) and metres per second (m/s).

Note: s (roman type) stands for seconds; s (italic type) stands for distance. They may both appear in the same calculation.

Velocity

Velocity is the rate of change of distance in a particular direction. A body moving in a straight line is said to have uniform velocity in a straight line. Uniform velocity occurs when a body moving in a straight line covers equal distances in equal interval of time.

Velocity =ds/dt in a particular direction

 

Acceleration

Acceleration is the rate of change of velocity. That is:

• Uniform acceleration occurs when a body experiences equal changes in velocity in equal time intervals. The basic unit of acceleration =m/s².
• Retardation or deceleration is the reverse process to acceleration. It is frequently referred to as negative acceleration.

 

Equations relating to velocity and acceleration

The symbols that will be used in the following equations are:

v₁ =initial velocity in metres per second (m/s);

v₂ =the final velocity in metres per second (m/s);

a =acceleration in metres per second squared (m/s²);

s =the distance travelled in metres (m);

t =the time taken in seconds (s).

1. Average velocity =(v₁+v₂)/2
2. Final velocity v₂ =v1+at
3. Distance travelled s =(v₁+v₂)t/2
4. Distance travelled s =v1t +1⁄2at²
5. Acceleration a =(v2-v1)/t
6. Acceleration a =(v₂²–v₁²)/2s