1. The rear car, C, pulls back on the middle car, B, with a force of 100 lb., and the front car, A, pulls it forward with a force of 250 lb. If car, B, were taken out of the train what single forward force would draw it the same as it is being drawn in the train? 12 lb. 23 lb. 2. A force of 23 lb. is pulling the car (Fig. 2) toward the right and another of 12 lb. is pulling it toward the left. If the car is free to move, in which direction will it move? What single force would move the car in the same manner as do both of these forces pulling at the same time? 3. What single force will move the car (Fig. 3) the same way as 8x lb. acting toward the right with 5x lb. acting toward the left? 4. What single force will move the car (Fig. 4) in the same manner 5x lb. 6m lb. FIGURE 2 8x lb. FIGURE 3 2m lb. FIGURE 4 as 6m lb. pulling against 2m lb. will move it? When a force of 18 lb. is supposed to be pulling a car toward the right, it will be written thus: R 18 lb. When the same force pulls toward the left, it will be written thus: L 18 lb. When two forces, R 16 lb. and L 12 lb., act at the same time, their joint effect is the same as the effect of the single force, R 4 lb. 5. Find the joint effect of R 281⁄2 lb. and L 21 lb.? 6. What would be the joint effect of each of these 25 T., and a force of 18 T., pulling backward, may be written B 18 T. The joint effect of both would be written thus: F 7 T. 7. What is the joint effect of the three forces: F 17 T., F 12 T. and B 25 T.? 8. What is the joint effect of each of the following sets of forces? (1) F 80 (2) F 49 T., B 282 T., and B 963 T. (3) B 68% T., F 73 T., and B 123 T. 9. A force of 182 lb. pulling upward may be written U 182 lb. How would you write a force of 78 lb. pulling downward? 10. What is the joint effect of each of the following sets of forces? oz., and D 16ğ oz. oz., and D 42 oz. (4) D 293 oz., U 65 11. If we call a force of 16 lb. pulling forward, or upward, or eastward, or northward, or to the right, a positive force, and write it + 16 lb., we should call the same force pulling backward, or downward, or westward, or southward, or to the left, respectively, a negative force. How should we write it? 12. Give the joint effect, with proper sign (+ or -) of each of these sets of forces: (1) 2 forces, each + 81 lb., and one force, 127 lb. (2) 3 forces, each + 12 oz., and 4 forces, each - 87 oz. (3) 5 forces, each (4) 18 forces of 25 lb. each. 163 T., and 12 forces, each + 93 T. 16 lb. each, and 20 forces of + 2. Find the products and quotients as rapidly as you can work correctly, using cancellation when it makes the $50. Scale Drawings of Familiar Objects. 1. Notice the scale of the drawing of the playhouse (Fig. 1), and compute the lengths of the following dimensions: (1) The width; (2) the height of the lower side; of the higher side; (3) the rise (difference of higher and lower sides); (4) the height of the door; the width; (5) the distance from the right Scale 1:6 3/16 3/4" FIGURE 1 side of the door to the right corner of the house. 2. From the dimensions in Fig. 1, with ruler and triangles, make a drawing of the playhouse to a scale 4 times as large as that of the drawing (Fig. 1). Scale 1:20 3/16 FIGURE 2 3/16 3. From the scale of the drawing (Fig. 2) find the following dimensions of the house: (1) The width; (2) the height of the eaves; (3) the rise (ab); (4) the width and the height of the door; (5) the width and the height of the window. 4. Find the area of the end of the house, including the gable and excluding the areas of the door and the window. 7. Similarly, give the length and the width of the door B, also the length and the width of the upper panels, and the widths of the strips enclosing the panels. 8. Make an enlarged drawing of each of the doors to a scale 5 times as large as the scale of the drawings (Fig. 3, p. 72). 9. How long are the cross-pieces of the kite represented by the drawing (Fig. 1)? How long is the binding-string of the kite? (Measure unmarked lines to the nearest".) 10. Make an enlarged drawing of the kite to a scale 8 times as large as that of Fig. 1. 11. The cross-pieces divide the kite into 6 triangles. Call the altitude of the upper triangles in Fig. 1, ", and that of the 25 50 lower triangles, ". How many square feet of paper are needed to cover the kite? Scale 1:64" FIGURE 1 (Allow 144 sq. in. for folding and pasting over the strings.) Scale 1:40" 12. What is the length of each leg of the chair shown in the drawing (Fig. 2)? What is the length of the back? The depth of the seat to the extreme rear? Scale 1:96" 3. 32 13. Make a drawing of the chair to a scale 5 times as large as that of Fig. 2. 14. Find from the drawing of the gate (Fig. 3) (1) the height of the high end of the gate; (2) of the lower end; (3) the length of the long brace; (4) the length of the gate; (5) the width of the strips. 7/8 FIGURE 3 |