95-] INTRODUCTION. 5! 



act along the common normal of the surfaces at the point of 

 contact, is called the resistance of B, and a force equal and 

 opposite to it is called the pressure exerted by A on B. 



95. Exercises. 



(1) Find the resultant of two equal forces acting at right angles to 

 each other. 



(2) Show that the resultant R of two equal forces P including an 

 angle is R= 2/ ? cos((9/2). 



(3) If the resultant of two equal forces /'be equal to P, what is the 

 angle between the components ? 



(4) Find the magnitude and direction of the resultant of two 

 forces of 100 and 200 Ibs., including an angle of 60. 



(5) Let R be the effective piston pressure of a steam engine and < 

 the angle between the direction of motion of the piston and the con- 

 necting rod at any moment ; show that the thrust in the connecting rod 

 is R sec cf> and the pressure on the guide-bars R tan <f>. For what 

 position of the crank is the pressure on the guides greatest ? 



(6) A weight W is suspended from two fixed points A, B by means 

 of a string A CB, C being the point of the string where the weight W 

 is attached. If AC, BC be. inclined to the vertical at angles a, (3, find 

 the tensions in AC, BC : (a) analytically; (b) graphically. 



(7) Resolve a force of 20 Ibs. into two components making angles 

 of 45 and 30 with the given force : (a) analytically ; (b] graphically. 



(8) Find the rectangular components of a force P if one of the 

 components is to make an angle of 30 with P. 



(9) The resultant R, one of the components P, and the angle 

 between the two components, = 60, being given, find the other 

 component Q. 



(10) A particle is acted on by two forces P, Q lying in the same 

 vertical plane and inclined to the horizon at angles /, q. Find their 

 resultant in magnitude and direction, if ^=527 Ibs., (2=2 72 Ibs., 

 P= 127 52', ^ = 32 13'. 



(n) Prove that the moments of the two components of a force 

 about any point on the line of the force are equal and opposite. 





