70 ELEMENTARY GENERAL SCIENCE CHAP. 



of the two shall be 33 Ibs. , and shall act in a direction at right angles 

 to their resultant. 



25. Two strings, the lengths of which are 12 inches and 16 inches, 

 have their ends fastened to two points in the same horizontal line ; 

 their other extremities are fastened together and they are strained 

 tight by a force equivalent to 5 Ibs. at the knot, acting vertically ; 

 the angle between the strings is then found to be a right angle. Find 

 the tensions of the strings. 



26. The resultants of two forces, when they act in the same and 

 opposite directions, are 5P + 7Q and P + Q respectively. Find the 

 forces and show that, if each force is increased by a force P, the 

 resultant of the two new forces acting at a point at right angles to 

 one another is 5(P + Q). 



27. Two lines AOB and COD are at right angles ; and four forces 

 act at O, one of 2 Ibs. along OA, one of 3 Ibs. along OC, one of 5 Ibs. 

 along OB, and one of 7 Ibs. along OD. Find the value of the resultant 

 and show, geometrically, how to find its direction. 



28. A force 65P is resolved into two forces at right angles to one 

 another. If one of them is 16P, what is the other ? 



29. Forces of 7 and 16 units have a resultant of 21 units ; find the 

 directions of the forces by a construction drawn to scale. 



30. Draw an equilateral triangle ABC ; a force of 10 units acts 

 from A to B, and one of 15 units from A to C. Find their resultant 

 by construction. Also find what their resultant would be if the 

 force of 15 units acted from C to A. 



31. A force equal to the weight of 20 Ibs., acting vertically 

 upwards, is resolved into two forces, one of which is horizontal and 

 equal to the weight of 10 Ibs. What is the magnitude and 

 direction of the other component ? 



32. Draw a diagram, as well as you can. to scale, showing the 

 resultant of two forces equal to the weights of 7 and 11 Ibs. 

 acting on a particle with an angle of 60 between them ; and by 

 measuring the resultant, find its numerical value. 



33. Two forces, each equal to a weight of lOlbs. act in directions 

 making an angle of 120. Find their resultant. 



34. A boat is towed by two ropes, including an angle of 60. One 

 rope is pulled with a force of 20 Ibs. , and the other with a force of 

 55 Ibs. Find the resultant force which moves the boat. 



35. A ball weighing 24 Ibs. is kept at rest by two strings, one of 

 which is horizontal and the other inclined to the vertical at an angle 

 of 30. Find the tensions of the two strings. 



36. Four forces, A, B, C, D, of 1, 2, 3, and 4 Ibs. respectively, act 

 at a point. B acts at right angles to the direction of A ; C to that 

 of the resultant of A and B ; D to that of the resultant of A, B and 

 C. All the right angles are to be measured in the same angular 

 direction. Draw, as accurately as you can, a figure showing how 

 the resultant of all four forces may be found graphically ; and show 

 independently, by calculation, that its magnitude is ^30. 



37. The same force F is made to act continuously on two separate 

 masses of 15. Ibs and 75 Ibs. ; compare the accelerations produced. 



38. Two equal masses of 6 Ibs. each are connected by different 



