Vectores

Capítulo 3. Vectores
Adición de Vectores por el Método Gráfico

8 km
8 km
3-11. Una mujer camina 4 km al Este y después 8 km al Norte. (a) Use el método del polígono para hallar la resultante del desplazamiento. (b) Verify the result by the parallelogram method.
R
R

Let 1 cm = 1 km; Then: R = 8.94 km, = 63.40

4 km
4 km

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?
67 m
38 m, 1800

67 m
38 m, 1800

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 m
Measure angle  = 60.10 S of W
= 1800 + 60.10 = 240.10 R =76.2 m, 240.10
B
D
R

C
A
B
D
R

C
A
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,  = 53.10 N of E or = 126.90.


R
200 N
500 N

R
200 N
500 N
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,  = 21.80 S. of E.

B
C
R
A
B
C
R
A
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,  = 51.40 S of E

R
C
B
A

R
C
B
A
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

B
A
R
B
A
R
3-17. Two ropes A and 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

36.90
40 lb
F
R
36.90
40 lb
F
R
3-18. Two forces A andB act on the same object producing a resultant force of 50 lb at 36.90 N of W. The force A = 40 lb due west. Find the magnitude and direction of force B?
Draw R = 50 lb, 36.90 N of W first, then draw 40 lb, W.
F = 30 lb, 900

Trigonometry and Vectors
300
340
600
(a)
(b)
(c)
300
340
600
(a)
(b)
(c)
3-19. Find the x and y-components of: (a) adisplacement of 200 km, at 340. (b) a velocity of 40 km/h, at 1200; and (c) A force of 50 N at 330o.
(a) Dx = 200 cos 340 = 166 km
Dy = 200 sin 340 = 112 km
(b) vx = -40 cos 600 = -20.0 km/h
vy = 40 sin 600 = +34.6 km/h
(c) Fx = 50 cos 300 = 43.3 N; Fy = - 50 sin 300 = -25.0 N

540 N
540 N
400
400
3-20. A sled is pulled with a force of 540 N at an angle of 400 withthe horizontal. What are the horizontal and vertical components of this force?
(a)
(a)
Fx = 540 cos 400 = 414 N Fy = 540 sin 400 = 347 N


F

F
3-21. The hammer in Fig. 3-26 applies a force of 260 N at an angle of 150 with the vertical. What is the upward component of the force on the nail?
F = 260 lb,  = 750; Fxy = 260 sin  Fy = 251 N.


R

R3-22. A jogger runs 2.0 mi west and then 6.0 mi north. Find the magnitude and direction of the resultant displacement.
6.32 mi ;  = 71.60 N of W

50 km/h
20 km/h
R
50 km/h
20 km/h
R
* 3-23. A river flows south with a velocity of 20 km/h. A boat has a maximum speed of 50 km/h in still water. In the river, at maximum throttle, the boat heads due west. What is the...