Chapter 3. Technical Measurement and Vectors
3-1. A soccer field is 100 m long and 60 m across. What are the length and width of the field in feet?
[pic] L = 328 ft
[pic] W = 197 ft
3-2. A wrench has a handle 8 in. long. What is the length of the handle in centimeters?
[pic] L = 20.3 cm
3-3. A 19-in. computer monitor has a viewable area that measures18 in. diagonally. Express this distance in meters. .
[pic] L = 0.457 m
3-4. The length of a notebook is 234.5 mm and the width is 158.4 mm. Express the surface area in square meters.
[pic] A = 0.0371 m2
3-5. A cube has 5 in. on a side. What is the volume of the cube in SI units and in fundamental USCS units? .
[pic] V = 0.00205 m3
[pic]V = 0.0723 ft3
3-6. The speed limit on an interstate highway is posted at 75 mi/h. (a) What is this speed in kilometers per hour? (b) In feet per second?
(a) [pic] 121 km/h (b) [pic]= 110 ft/s
3-7. A Nissan engine has a piston displacement (volume) of 1600 cm3 and a bore diameter of 84 mm. Express these measurements in cubic inches and inches. Ans. 97.6in.3, 3.31 in.
(a) [pic]= 97.6 in.3 (b) [pic]= 3.31 in.
3-8. An electrician must install an underground cable from the highway to a home located 1.20 mi into the woods. How many feet of cable will be needed?
[pic] L = 6340 ft
3-9. One U.S. gallon is a volume equivalent to 231 in.3. How many gallons are needed to fill a tank that is 18 in. long, 16 in. wide, and 12 in.high? Ans. 15.0 gal.
V = (18 in.)(16 in.)(12 in.) = 3456 in.3
[pic] V = 15.0 gal
3-10. The density of brass is 8.89 g/cm3. What is the density in kg/m3?
[pic] ( = 8890 kg/m3
Addition of Vectors by Graphical Methods
3-11. A woman walks 4 km east and then 8 km north. (a) Use the polygon method to find her resultant displacement. (b) Verify the result by theparallelogram method.
Let 1 cm = 1 km; Then: R = 8.94 km, ( = 63.40
3-12. A land-rover, on the surface of Mars, moves a distance of 38 m at an angle of 1800. It then turns and moves a distance of 66 m at an angle of 2700. What is the displacement from the starting position?
Choose a scale, e.g., 1 cm = 10 m
Draw each vector to scale as shown.
Measure R = 7.62 cm or R = 76.2 mMeasure angle φ = 60.10 S of W
( = 1800 + 60.10 = 240.10 R = 76.2 m, 240.10
3-13. A surveyor starts at the southeast corner of a lot and charts the following displacements: A = 600 m, N; B = 400 m, W; C = 200 m, S; and D = 100 m, E. What is the net displacement from the starting point? .
Choose a scale, 1 cm = 100 m
Draw each vector tail to tip until all are drawn.Construct resultant from origin to finish.
R = 500 m, φ = 53.10 N of E or ( = 126.90.
3-14. A downward force of 200 N acts simultaneously with a 500-N force directed to the left. Use the polygon method to find the resultant force.
Chose scale, measure: R = 539 N, φ = 21.80 S. of E.
3-15. The following three forces act simultaneously on the same object. A = 300 N, 300 N of E; B = 600 N,2700; and C = 100 N due east. Find the resultant force
using the polygon method. Choose a scale, draw and measure: R = 576 N, φ = 51.40 S of E
3-16. A boat travels west a distance of 200 m, then north for 400 m, and finally 100 m at 300 S of E. What is the net displacement? (Set 1 cm = 100 N)
Draw and measure: R = 368 N, ( = 108.00
3-17. Two ropes Aand B are attached to a mooring hook so that an angle o 60 exists between the two ropes. The tension in rope A is 80 lb and the tension in rope B is 120 lb. Use the parallelogram method to find the resultant force on the hook.
Draw and measure: R = 174 lb
3-18. Two forces A and B act on the same object producing a resultant force of 50 lb at 36.90 N of W. The force A = 40 lb...
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