Mechanical Engineering Principles

WORK, ENERGY AND POWER 163

If friction is present, then work is done overcoming
the resistance due to friction and this is dissipated
as heat. Then,

Initial energy=final energy

+work done overcoming

frictional resistance

Kinetic energy is not always conserved in collisions.
Collisions in which kinetic energy is conserved
(i.e. stays the same) are calledelastic collisions,
and those in which it is not conserved are termed
inelastic collisions.

Problem 22. A car of mass 800 kg is

climbing an incline at 10°to the horizontal.

Determine the increase in potential energy of

the car as it moves a distance of 50 m up the

incline.

With reference to Figure 14.10,

sin 10°=

opposite

hypotenuse

=

h

50

,

from which, h=50 sin 10°= 8 .682 m.

h

50 m

10 °

Figure 14.10

Hence, increase in

potential energy=mgh

=800 kg× 9 .81 m/s^2

× 8 .682 m

=68140 J or 68 .14 kJ

Problem 23. At the instant of striking, a

hammer of mass 30 kg has a velocity of

15 m/s. Determine the kinetic energy in the

hammer.

Kinetic energy=^12 mv^2 =^12 (30 kg)(15 m/s)^2

i.e.

kinetic energy in hammer=3375 Jor 3 .375 kJ

Problem 24. A lorry having a mass of 1.5 t

is travelling along a level road at 72 km/h.

When the brakes are applied, the speed

decreases to 18 km/h. Determine how much

the kinetic energy of the lorry is reduced.

Initial velocity of lorry,

v 1 =72 km/h

= 72

km

h

× 1000

m

km

×

1h

3600 s

=

72

3. 6

=20 m/s,

final velocity of lorry,

v 2 =

18

3. 6

=5m/sandmassoflorry,

m= 1. 5 t=1500 kg

Initial kinetic energy of the lorry

=^12 mv^21 =^12 ( 1500 )( 20 )^2 =300 kJ

Final kinetic energy of the lorry

=^12 mv^22 =^12 ( 1500 )( 5 )^2 = 18 .75 kJ

Hence,the change in

kinetic energy= 300 − 18. 75 = 281 .25 kJ

(Part of this reduction in kinetic energy is converted

into heat energy in the brakes of the lorry and is

hence dissipated in overcoming frictional forces and

air friction).

Problem 25. A canister containing a

meteorology balloon of mass 4 kg is fired

vertically upwards from a gun with an initial

velocity of 400 m/s. Neglecting the air

resistance, calculate (a) its initial kinetic

energy, (b) its velocity at a height of 1 km,

(c) the maximum height reached.