Mechanical Engineering Principles

154 MECHANICAL ENGINEERING PRINCIPLES

500

Force / N

020

Extension / mm

Figure 14.2

=^12 ×( 20 × 10 −^3 )m×500 N

=5J

It is shown in Chapter 13 that force = mass×
acceleration, and that if an object is dropped from
a height it has a constant acceleration of around
9.81 m/s^2. Thus if a mass of 8 kg is lifted vertically
4 m, the work done is given by:

work done=force×distance

=(mass×acceleration)×distance

=( 8 × 9. 81 )× 4 = 313 .92 J

The work done by a variable force may be found by
determining the area enclosed by the force/distance
graph using an approximate method such as themid-
ordinate rule.
To determine the area ABCD of Figure 14.3
using the mid-ordinate rule:

(i) Divide baseADinto any number of equal

intervals, each of width d (the greater the

number of intervals, the greater the accuracy)

(ii) Erect ordinates in the middle of each interval

(shown by broken lines in Figure 14.3)

(iii) Accurately measure ordinatesy 1 ,y 2 ,y 3 ,etc.

(iv) AreaABCD=d(y 1 +y 2 +y 3 +y 4 +y 5 +y 6 )

A

dddddd

B

C

D

y 1 y 2 y 3 y 4 y 5 y 6

Figure 14.3

In general, the mid-ordinate rule states:

Area=

(

width of

interval

)(

sum of

mid-ordinates

)

Problem 1. Calculate the work done when

a force of 40 N pushes an object a distance

of 500 m in the same direction as the force.

Work done=force×distance moved in the

direction of the force

=40 N×500 m

=20000 J(since 1 J=1Nm)

i.e. work done=20 kJ

Problem 2. Calculate the work done when

a mass is lifted vertically by a crane to a

height of 5 m, the force required to lift the

mass being 98 N.

When work is done in lifting then:

work done=(weight of the body)

×(vertical distance moved)

Weight is the downward force due to the mass of an

object. Hence

workdone=98 N×5m=490 J

Problem 3. A motor supplies a constant

force of 1 kN which is used to move a load

a distance of 5 m. The force is then changed

to a constant 500 N and the load is moved a

further 15 m. Draw the force/distance graph

for the operation and from the graph

determine the work done by the motor.

The force/distance graph or work diagram is shown

in Figure 14.4. Between points A andB a con-

stant force of 1000 N moves the load 5 m; between