42 FORCES ACTING ON A SINGLE PARTICLE 



4. Forces acting at a point are represented by OA, OB, OC, , 07V. Show 

 that if they are in equilibrium, is the centroid of the points A, B, C, , N. 



5. ABCDEF is a regular hexagon. Find the resultant of the forces repre- 

 sented by AB, AC, AD, AE, AF. 



6. ABCDEF is a regular hexagon. Show that the resultant of forces repre- 

 sented by AB, 2 AC, 3 AD, 1AE, 5AF is represented by V351 AB, and find 

 its direction. 



7. ABC is a triangle, and P is any point in BC. If PQ represent the resultant 

 of the forces represented by AP, PB, BC, show that the locus of Q is a straight 

 line parallel to BC. 



TYPES OF FORCES 

 Weight of a Particle 



34. The weight of a particle acts always vertically down- 

 ward; for at a given place on the earth it is found that the 

 weights of all particles act in parallel directions, and this direc- 

 tion is called the vertical at the place in question. The weight is 

 the gravitational force with which the particle is attracted by the 

 earth, except for a small correction which has to be introduced 

 on account of the facjt that axes fixed in the earth do not move 

 without acceleration. This correction we shall not discuss here. 

 When the weight of a body is said to be W, it is meant that to 

 keep the body at rest relatively to the earth's .surface a force W is 

 required to act vertically upward. 



Tension of a String 



35. A string or rope supplies a convenient means of applying 

 force to a body, and this force is spoken of as the tension of the 



p Qr s string. Let ABCD be the string, 



P* \ l B l G ' D ' E an( * ^ et ^ be a particle tied to the 



string at its end. Let the divisions A B, 

 BC, of the string be so small that 

 each may be regarded as a particle. 



There will be three forces acting on any particle such as BC: 

 first, its weight; second, a force exerted on BC by the particle CD 

 of the string ; and third, a force exerted on BC by the particle AB. 



