Objectives

At the end of this section you should be able to:

• describe potential energy as energy due to position and derive potential energy as mgh
• describe kinetic energy as energy due to motion and derive kinetic energy as mv²/2
• state conservation of energy laws and solve problems where energy is conserved
• define power as rate of energy transfer
• define couple, torque and calculate work done by variable force or torque
• solve problems where energy is lost due to friction

 

 

• Example 3.1
• Example 3.2

When the point at which a force acts moves, the force is said to have done work.

When the force is constant, the work done is defined as the product of the force and distance moved.

Consider the example in Figure 3.1, a force F acting at the angle q moves a body from point A to point B.

The distance moved in the direction of the force is given by

So the work done by the force F is

When the angle is 90 then the work done is zero.

The SI units for work are Joules J (with force, F, in Newton's N and distance, s, in metres m).

Worked Example 3.1

How much work is done when a force of 5 kN moves its point of application 600mm in the direction of the force.

Solution

Worked Example 3.2

Find the work done in raising 100 kg of water through a vertical distance of 3m.

Solution

The force is the weight of the water, so

Work done by a variable force

Forces in practice will often vary. In these cases Equation 3.1 cannot be used. Consider the case where the force varies as in Figure 3.2

For the thin strip with width ds - shown shaded in Figure 3.2 - the force can be considered constant at F. The work done over the distance ds is then

This is the area of the shaded strip.

The total work done for distance s is the sum of the areas of all such strips. This is the same as the area under the Force-distance curve.

So for a variable force

In general you must uses some special integration technique to obtain the area under a curve. Three common techniques are the trapezoidal, mid-ordinate and Simpson's rule. They are not detailed here but may be found in many mathematical text book.