1. No category

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
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
V
and q are known.
Also determine
the n-t
components of
the tension T
for T = 100 N
and q = 35°.
PROBLEMS
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
the two forces and the angle q which
positive x-axis.

R

R of
makes with the
PROBLEMS
4. Write the vectors in terms of the unit


vectors i and j . Also determine;


B , B  50 units
 
A B  ?
 
A B  ?
 
A B  ?
 
B A  ?
 
A B  ?
 
B A  ?
24
7
(2,3)
8
15

A,

A  85 units
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 baxes.
PROBLEMS

6. The position vector r goes from point A to
a point on the straight line between B and C.


Its magnitude is r  6 m. Express r .
y
B (7, 9) m

r
A (3, 5) m
C (12, 3) m
x
PROBLEMS
y
7. Cables extend from A
to B and from A to C.
A (0, 7, 0) m
The cable AC exerts a
1000 N force vector F
at A.

a F
a) What is the angle a
between the cables AB
and AC?
x
b) Determine thevector
component of F
parallel to the cable
B (0, 0, 10) m
AB and write the
C (14, 0, 14) m
vector expression
z
of this component.
PROBLEMS
y
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?
B (6, 6, -3) m
O
q
x
A (10, -2, 3) m
z
PROBLEMS


 
9. Two vectors are given as U  U x i  6 j  k


 
and V  3i  V y j  k . Their dot product is
 
U V  35, and the magnitude of their sum
 
is U V  3 . What are the components Ux
and Vy?
PROBLEMS

 

10. The vectors U  i  U y j  4k ,




 
 
V  2i  j  2k and W  3i  j  2k are
coplanar. What is the component Uy?
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.
z
C (0, 0, 5) m
B (0, 16, 0) m
y
x
A (12, 0, 0) m