WORK, ENERGY AND POWER 169
Assignment 4
This assignment covers the material con-
tained in chapters 11 to 14.
The marks for each question are shown
in brackets at the end of each question.
- A train is travelling at 90 km/h and has
wheels of diameter 1600 mm.
(a) Find the angular velocity of the
wheels in both rad/s and rev/min.
(b) If the speed remains constant for
2 km, determine the number of rev-
olutions made by a wheel, assum-
ing no slipping occurs. (7)
- The speed of a shaft increases uniformly
from 200 revolutions per minute to 700
revolutions per minute in 12 s. Find the
angular acceleration, correct to 3 signif-
icant figures. (5)
- The shaft of an electric motor, initially
at rest, accelerates uniformly for 0.3 s
at 20 rad/s^2. Determine the angle (in
radians) turned through by the shaft in
this time. (4)
- Determine the momentum of a lorry of
mass 10 tonnes moving at a velocity of
81 km/h. (4)
- A ball of mass 50 g is moving with a
velocity of 4 m/s when it strikes a sta-
tionary ball of mass 25 g. The velocity
of the 50 g ball after impact is 2.5 m/s
in the same direction as before impact.
Determine the velocity of the 25 g ball
after impact. (7)
- A force of 24 N acts on a body of mass
6 kg for 150 ms. Determine the change
in velocity. (4)
- The hammer of a piledriver of mass
800 kg falls a distance of 1.0 m on to a
pile. The blow takes place in 20 ms and
the hammer does not rebound. Deter-
mine (a) the velocity of impact (b) the
momentum lost by the hammer (c) the
average applied force exerted on the pile
by the hammer. (8)
8. Determine the mass of the moving head
of a machine tool if it requires a force of
1.5Ntobringittorestin0.75sfroma
cutting speed of 25 m/min. (5)
9. Find the weight of an object of mass
2.5 kg at a point on the earth’s surface
where the gravitational field is 9.8 N/kg.
(4)
- A van of mass 1200 kg travels round
a bend of radius 120 m, at 54 km/h.
Determine the centripetal force acting on
the vehicle. (4)
- A spring, initially in a relaxed state, is
extended by 80 mm. Determine the work
done by using a work diagram if the
spring requires a force of 0.7 N per mm
of stretch. (4)
- Water is pumped vertically upwards
through a distance of 40.0 m and the
work done is 176.58 kJ. Determine the
number of litres of water pumped.
(1 litre of water has a mass of 1 kg).
(4)
- 3 kJ of energy are supplied to a machine
used for lifting a mass. The force
required is 1 kN. If the machine has an
efficiency of 60%, to what height will it
lift the mass? (4)
- When exerting a steady pull of 450 N, a
lorry travels at 80 km/h. Calculate
(a) the work done in 15 minutes and
(b) the power required. (4)
- An electric motor provides power to a
winding machine. The input power to
the motor is 4.0 kW and the overall effi-
ciency is 75%. Calculate (a) the output
power of the machine, (b) the rate at
which it can raise a 509.7 kg load verti-
cally upwards (4)
- A tank of mass 4800 kg is climbing an
incline at 12° to the horizontal. Deter-
mine the increase in potential energy of
the tank as it moves a distance of 40 m
up the incline. (4)
- A car of mass 500 kg reduces speed
from 108 km/h to 36 km/h in 20 s.
Determine the braking power required to
give this change of speed. (4)
