Mechanical Engineering Principles

112 MECHANICAL ENGINEERING PRINCIPLES

Now try the following exercise

Exercise 45 Further problems on work

done and power transmitted

by a constant torque

1. A constant force of 4 kN is applied tan-
   gentially to the rim of a pulley wheel of
   diameter 1.8 m attached to a shaft. Deter-
   mine the work done, in joules, in 15 rev-
   olutions of the pulley wheel. [339.3 kJ]


2. A motor connected to a shaft develops a
   torque of 3.5 kN m. Determine the num-
   ber of revolutions made by the shaft if the
   work done is 11.52 MJ. [523.8 rev]


3. A wheel is turning with an angular veloc-
   ity of 18 rad/s and develops a power of
   810 W at this speed. Determine the torque
   developed by the wheel. [45 N m]


4. Calculate the torque provided at the shaft
   of an electric motor that develops an out-
   put power of 3.2 hp at 1800 rev/min.
   [12.66 N m]


5. Determine the angular velocity of a shaft
   when the power available is 2.75 kW and
   the torque is 200 N m. [13.75 rad/s]


6. The drive shaft of a ship supplies a torque
   of 400 kN m to its propeller at 400
   rev/min. Determine the power delivered
   by the shaft. [16.76 MW]


7. A motor is running at 1460 rev/min and
   produces a torque of 180 N m. Deter-
   mine the average power developed by the
   motor. [27.52 kW]


8. A wheel is rotating at 1720 rev/min and
   develops a power of 600 W at this speed.
   Calculate (a) the torque, (b) the work done,
   in joules, in a quarter of an hour.

[(a) 3.33 N m (b) 540 kJ]

9. A force of 60 N is applied to a lever of
   a screw-jack at a radius of 220 mm. If
   the lever makes 25 revolutions, determine
   (a) the work done on the jack, (b) the
   power, if the time taken to complete 25
   revolutions is 40 s.
   [(a) 2.073 kJ (b) 51.84 W]

9.3 Kinetic energy and moment of

inertia

The tangential velocityvof a particle of massm

moving at an angular velocityωrad/s at a radiusr

metres (see Figure 9.4) is given by:

v=ωr m/s

r

ω

m

v

Figure 9.4

The kinetic energy of a particle of mass m is

given by:

Kinetic energy=^12 mv^2 (from Chapter 14)

=^12 m(ωr)^2 =^12 mω^2 r^2 joules

The total kinetic energy of a system of masses

rotating at different radii about a fixed axis but with

the same angular velocity, as shown in Figure 9.5,

is given by:

Total kinetic energy =

1

2

m 1 ω^2 r 12 +

1

2

m 2 ω^2 r 22

+

1

2

m 3 ω^2 r 32

=(m 1 r 12 +m 2 r 22 +m 3 r 32 )

ω^2

2

r 2

r 1

r 3 m 3

m 2

m 1

ω

Figure 9.5