Mechanical Engineering Principles

162 MECHANICAL ENGINEERING PRINCIPLES

4. A car towing another at 54 km/h exerts a
   steady pull of 800 N. Determine (a) the
   work done in^14 hr, and (b) the power
   required.

[(a) 10.8 MJ (b) 12 kW]

5. To what height will a mass of weight
   500 N be raised in 20 s by a motor using
   4 kW of power? [160 m]


6. The output power of a motor is 10 kW.
   Determine (a) the work done by the
   motor in 2 hours, and (b) the energy
   used by the motor if it is 72% efficient.

[(a) 72 MJ (b) 100 MJ]

7. A car is travelling at a constant speed
   of 81 km/h. The frictional resistance to
   motion is 0.60 kN. Determine the power
   required to keep the car moving at this
   speed. [13.5 kW]


8. A constant force of 2.0 kN is required
   to move the table of a shaping machine
   when a cut is being made. Determine the
   power required if the stroke of 1.2 m is
   completed in 5.0 s. [480 W]


9. A body of mass 15 kg has its speed
   reduced from 30 km/h to 18 km/h in
   4.0 s. Calculate the power required to
   effect this change of speed. [83.33 W]


10. The variation of force with distance for a
    vehicle that is decelerating is as follows:

Distance (m) 600 500 400 300 200 100 0

Force(kN) 24201612 8 40

If the vehicle covers the 600 m in 1.2

minutes, find the power needed to bring

the vehicle to rest. [100 kW]

11. A cylindrical bar of steel is turned in
    a lathe. The tangential cutting force
    on the tool is 0.5 kN and the cutting
    speed is 180 mm/s. Determine the power
    absorbed in cutting the steel. [90 W]

14.4 Potential and kinetic energy

Mechanical engineering is concerned principally
with two kinds of energy, potential energy and
kinetic energy.

Potential energyis energy due to the position of

the body. The force exerted on a mass ofmkg is

mgN (whereg= 9 .81 m/s^2 , the acceleration due to

gravity). When the mass is lifted vertically through

a heighthm above some datum level, the work

done is given by: force×distance=(mg (h)J. This

work done is stored as potential energy in the mass.

Hence,

potential energy=mghjoules

(the potential energy at the datum level being taken

as zero).

Kinetic energyis the energy due to the motion

of a body. Suppose a forceF acts on an object of

massmoriginally at rest (i.e.u=0) and accelerates

it to a velocityvin a distances:

work done=force×distance=Fs

=(ma)(s) (if no energy is lost)

whereais the acceleration

Sincev^2 =u^2 + 2 as(see Chapter 11) andu=0,

v^2 = 2 as, from which

a=

v^2

2 s

,

hence,

work done=(ma)(s)

=(m)

(

v^2

2 s

)

(s)=

1

2

mv^2

This energy is called the kinetic energy of the mass

m, i.e.

kinetic energy=^12 mv^2 joules

As stated in Section 14.2, energy may be converted

from one form to another. Theprinciple of con-

servation of energystates that the total amount of

energy remains the same in such conversions, i.e.

energy cannot be created or destroyed.

In mechanics, the potential energy possessed by

a body is frequently converted into kinetic energy,

and vice versa. When a mass is falling freely, its

potential energy decreases as it loses height, and

its kinetic energy increases as its velocity increases.

Ignoring air frictional losses, at all times:

Potential energy + kinetic energy = a constant