Mechanical Engineering Principles

WORK, ENERGY AND POWER 161

(b) Power output =force×velocity,

from which, velocity=

power output

force

.

Force acting on the 300 kg load due to

gravity=300 kg× 9 .81 m/s^2

=2943 N

Hence,

velocity=

1500

2943

= 0 .510 m/s or 510 mm/s.

Problem 20. A lorry is travelling at a

constant velocity of 72 km/h. The force

resisting motion is 800 N. Calculate the

tractive power necessary to keep the lorry

moving at this speed.

Power=force×velocity.

The force necessary to keep the lorry moving at

constant speed is equal and opposite to the force

resisting motion, i.e. 800 N.

Velocity=72 km/h=

72 × 1000

60 × 60

m/s

=20 m/s.

Hence, power=800 N×20 m/s

=16 000 N m/s=16 000 J/s

=16 000 W or 16 kW.

Thus the tractive power needed to keep the lorry

moving at a constant speed of 72 km/h is 16 kW.

Problem 21. The variation of tractive force

with distance for a vehicle which is

accelerating from rest is:

force (kN) 8.0 7.4 5.8 4.5 3.7 3.0

distance (m) 0 10 20 30 40 50

Determine the average power necessary if

the time taken to travel the 50 m from rest is

25 s.

8.0

6.0

4.0

Force (kN)

2.0

01020

Distance (m)

30 40 50

y 1 y 2 y 3 y 4 y 5

Figure 14.9

The force/distance diagram is shown in Figure 14.9.

The work done is determined from the area under

the curve. Using the mid-ordinate rule with five

intervals gives:

area=

(

width of

interval

)(

sum of

mid-ordinate

)

=( 10 )[y 1 +y 2 +y 3 +y 4 +y 5 ]

=( 10 )[7. 8 + 6. 6 + 5. 1

+ 4. 0 + 3 .3]

=( 10 )[26.8]=268 kN m,

i.e. work done=268 kJ

Average power=

work done

time taken

=

268000 J

25 s

=10720 Wor 10 .72 kW.

Now try the following exercise

Exercise 70 Further problems on power

1. The output power of a motor is 10 kW.
   How much work does it do in 1 minute?
   [600 kJ]


2. Determine the power required to lift a
   load through a height of 20 m in 12.5 s
   if the force required is 2.5 kN. [4 kW]


3. 25 kJ of work is done by a force in mov-
   ing an object uniformly through 50 m in
   40 s. Calculate (a) the value of the force,
   and (b) the power.

[(a) 500 N (b) 625 W]