Sheet no.3

1) Consider the volleyball net shown in figure 1.

Determine the angle formed by guy wires AB

and AC, also the angle formed by the guy wires

AC and AD.

2) Ropes AB and BC are two of the ropes used to

support a tent as shown in figure 2. The two

ropes are attached to a stake at B. if the

tension in rope AB is 540N, determine:

a) The angle between rope AB and the stake,

b) The projection on the stake of the force

exerted by rope AB at point B.

3) Determine the volume of the parallelepiped shown in figure 3 when P = 4i -3j +2k , Q = -2i

-5j +k and

S= 7i +j k

4) Given the vectors P = 3i j +k, Q = 4i +Qyj -2k, and S = 2i -2j +2k, determine the value of Qy for which

the three vectors are coplanar.

5) It is known that a vertical force of 800 N is required to remove the nail at C from the board

as shown in figure 4. As the nail first starts

moving, determine:

a) The moment about B of the force exerted

on the nail,

b) The magnitude of the force P which

creates the same moment about B if 1=10o

,

c) The smallest force P which creates the

same moment about B.

6) A crate of mass 80Kg is held in the position

shown in figure 5. Determine:

a) The moment produced by the weight W of

the crate about E,

b) The smallest force applied at B which

creates a moment of equal magnitude and

opposite sense about E.

7) Before the trunk of a large tree is felled, cables

AB and BC are attached as shown in figure 6.

Knowing that the tensions in cables AB and BC

are 555N and 660 N, respectively, determine

the moment about O of the resultant force

exerted on the tree by the cables at B.

8) The triangular plate ABC is supported by ball and socket joints at B and D and is held in the

position shown in figure 7 by cables AE and

CF. if the force exerted by cable AE at A is 55

N, determine the moment of that force about

the line joining points D and B.

9) A sign erected on uneven ground is guyed by

cables EF and EG as shown in figure 8. If the

force exerted by cable EF at E is 230 N,

determine the moment of that force about the

line joining points A and D.