CHAPTER III 
WORK AND ENERGY 
38. Work.—When a force acting on a body causes that body to 
move, the force is said to do work. Also, if a body is moved against a 
resistance, work is done in overcoming the resistance. The amount of 
work done depends on the magnitude of the force and also on the distance 
through which it acts. 
In measuring work the unit which is generally used by engineers is 
the work done when a force of one pound acts through a distance of one 
foot, this unit being called a foot-pound. If the unit taken be the wofk 
done when a force of one ton acts through a distance of one foot, it is 
called a foot-ton. The foot-ton is used in measuring large quantities of 
work. For measuring small quantities of work the inch-pound, or the 
work done when a force of one pound acts through a distance of one inch, 
is frequently used. 
The work done by a force is found by multiplying the magnitude of 
the force by the distance through which it acts. 
39. Work by an Oblique Force.—lIf a force acting on a body acts in 
a direction inclined to that of the body’s motion the force may be resolved 
into two components, as explained in Chapter IV., one 
acting in the direction of the body’s motion, and the Bee 
other perpendicular to that direction. The latter com- [A | 
ponent does no work, and the work done by the former OHOTTT 
is its magnitude multiplied by the distance through Fic. 21. 
which the body moves. For example, if a body A 
(Fig. 21) is dragged along a horizontal plane by a force P whose lin 
of action is inclined at an angle @ to the horizontal, the horizontal com- 
ponent of P is P cos. @ and the work done is S x P cos 0, where S is the 
distance through which A is moved. 
40. Work in Raising a System of Weights.—When a number of 
weights are raised through different heights, or when all the parts of one 
weight are not raised through the same height, the amount of work done 
is obtained by multiplying the total weight lifted by the distance through 
which the centre of gravity of the system is raised. The proof of the 
foregoing rule is as follows :—Let w,, w,, ws, ete., be the weights of the 
parts of a system of weights, or the weights of the parts of a single body. 
Let h,, hy, hg, ete., be the heights of above a fixed horizontal plane 
before they are lifted, and let /,, k,, %s, etc., be their heights above the 
fixed horizontal plane after they are lifted. Also, let H and K be the 
heights of the centre of gravity of the system above the fixed horizontal 
plane before and after lifting respectively, and let W =the total weight 
of the system = 2, + w, + Ww, + ete. 
24 
