Transportation on Water 361 



(a) With an angle of 180 the resultant is equal to the difference 

 of the components. 



(6) With an angle of zero the resultant is equal to the sum of the 

 components. 



3. No resultant can be greater than the sum, or less than the dif- 

 ference, of two components. 



SUMMARY 



Sailing at an angle into the wind was unknown to the ancients. 



A force may be measured in pounds and represented by a line 

 which shows its point of application, direction and magnitude. 



Two or more forces may be found which, if substituted for one 

 given force, would produce the same effect. This is called the Reso- 

 lution of Forces. 



A single force may be found which, if substituted for two or more 

 forces acting at a common point, would produce the same effect. 

 This is called the Composition of Forces. 



In either case what is not known about the directions or magnitudes 

 of the forces can be determined by means of a suitable parallelogram. 



The resolution of forces is illustrated in a multitude of devices, 

 such as the wall bracket, the truss bridge, the pushcart, the canal 

 boat, the sailboat, the kite, and the aeroplane. 



Sailing a boat into the wind may be explained by the principle of 

 the parallelogram of forces. 



REVIEW QUESTIONS 



1. By what means can apparently adverse conditions be utilized 

 by a sailing vessel? 2. (a) What is illustrated by the pushcart and 

 stick? (6) In what two directions is the force applied by the stick 

 working? (c) How may the forces involved be measured? (d) How 

 may they be represented graphically? 3. (a) Show graphically the 

 direction and magnitude of the forces when a force of 25 pounds is 

 applied to the stick which is at an angle of 45 with the horizontal 

 line. (6) When the angle is 15. (c) When the angle is 0. 4. Which 

 is the useful force and which the wasted? 5. Show graphically that 

 a long towline on a canal boat is more advantageous than a short one. 



6. (a) Explain from a diagram how a boat can sail across the wind, 

 (b) Into the wind. 7. Mention several instances when the effects of 

 one force are seen in two different directions. 8. State the principle 

 of the resolution of forces. 9. What are component forces ? What is 

 the resultant? 10. How is the composition of forces related to the 

 resolution of forces? 11. If a clothesline will break with a pull of 100 



