72 MECHANICAL WORK. 



After 1 second (1 x 19-6 = 19*6) - 4-9 = 14 m 7. 

 After 2 seconds (2 x 19-6 = 39-2) - 19-6 = 19 m -6. 

 After 3 seconds (3 x 19*6 = 58'8) - 44-1 = 14 m 7. 

 After 4 seconds (4 x 19*6 = 78-4) - 78-4 = O m -7. 



The direction A B is inclined to the horizontal direction at an 

 angle of 53'13 degrees (53 '13). The whole circumference is di- 

 vided into 360 equal parts, which are called degrees ; the symbol 

 placed at the top and to the right of the number of degrees 

 in an angle is used as an abbreviation for this word. A right angle 

 contains 90. An angle of 45 is half of a right angle, an angle of 30 

 a third, etc. In Fig. 52 one right angle is divided into degrees, the 

 remaining portion of the circumference into parts of 10 degrees each. 

 Acute angles are those between and 90; obtuse angles are those 

 between 90 and 180. 



12. Mechanical Work. The expenditure of force, 

 which, as has been explained in Art. 8, is required for 

 changing the state of rest or of motion of a body, 

 is called mechanical zuorJc. In general, work is done 

 when a resistance is overcome, and it remains to investi- 

 gate the relations between force, mass, space, velocity, 

 and work. 



In lifting a body work is done ; we overcome in 

 this case the resistance of gravity. If other circum- 

 stances are equal, the work will be the greater the 

 higher the body is lifted, or, in other words, the greater 

 the space through which the resistance of gravity has 

 to be overcome. The work done is directly propor- 

 tional to this space. In lifting a body through 3 m 

 three times as much work is done as when it is raised 

 l m , and five times as much work will have to be done 

 to lift it through 15 m as is required for 3 m . The work, 

 however, does not only depend upon /the space alone, 

 but also upon the magnitude of the resistance which is 

 to be overcome. To move a ball upon a very smooth 



