CHAPTER 2

FORCE SYSTEMS

PROBLEMS 1. Two force vectors

are applied to the construction bracket as shown. Determine the angle q which makes the resultant of the two vectors vertical. Determine the magnitude R of the resultant.

PROBLEMS

V

2.Determine the x-y components of the tension T which is applied to point A of the bar OA. Neglect the effects of the small pulley at B. Assume that r and q are known.

Also determine the n-t components of the tension T for T = 100 N and q = 35°.

3. The two structural members, one of which is in tension and

the other in compression, exert the indicated force vectors

on joint O. Determine the magnitude of the resultant of

the two forces and the angle q which makes with the

positive x-axis.

PROBLEMS

R

R

PROBLEMS 4. Write the vectors in terms of the unit

vectors and . Also determine; i

j

?

?

?

?

?

?

AB

BA

AB

BA

BA

BA

unitsA,A 85

15

8

(2,3)

24

7

unitsB,B 50

PROBLEMS 5. Determine the components Fa and Fb of the

4-kN force along the oblique axes a and b.

Also determine

the projections

Pa and Pb of F

onto the a- and b-

axes.

PROBLEMS 6. The position vector goes from point A to

a point on the straight line between B and C.

Its magnitude is . Express . mr 6

r

r

A (3, 5) m

y

x

B (7, 9) m

C (12, 3) m

r

PROBLEMS 7. Cables extend from A

to B and from A to C. The cable AC exerts a 1000 N force vector at A.

a) What is the angle a between the cables AB and AC?

b) Determine the vector component of parallel to the cable AB and write the vector expression

of this component.

F

F

F

A (0, 7, 0) m

y

x

a

z

B (0, 0, 10) m C (14, 0, 14) m

PROBLEMS

8. Consider the straight lines OA and OB.

a) Determine the components of a unit vector that is perpendicular to both OA and OB.

b) What is the minimum distance from point A to the line OB?

A (10, -2, 3) m

y

x q

z

B (6, 6, -3) m

O

PROBLEMS

9. Two vectors are given as

and . Their dot product is

, and the magnitude of their sum

is . What are the components Ux

and Vy?

kjiUU x

6

kjViV y

3

35VU

3VU

PROBLEMS

10. The vectors ,

and are

coplanar. What is the component Uy?

kjUiU y

4

kjiV

22 kjiW

23

PROBLEMS 11. Consider the triangle ABC.

a) What is the surface area of ΔABC?

b) Determine the unit vector of the outer normal of surface ABC.

A (12, 0, 0) m

y

x

z

B (0, 16, 0) m

C (0, 0, 5) m