Supplementary problems 1. The post is to be pulled out of the ground using two ropes A and B. Rope A is subjected to force

F1 and is directed at angle θ1 from the horizontal. If the resultant force acting on the post is to be FR, vertically upward, determine the force T in rope B and the corresponding angle θ.

Given: F1=600 N, FR=1200 N, θ1=60 deg

1. Determine the magnitude of the resultant force and its direction, measured clockwise from the

positive x axis.

Given: F1=70 N, F2=50 N, F3=65 N, α=30deg, β=45 deg

2. The eye bolt is subjected to the cable force F which has a component Fx along the x axis, a component Fz along the z axis, and a coordinate direction angle β. Determine the magnitude of F. Given: Fx=60 N, Fz=-80 N, β=80 deg

3. The cable OA exerts force F on point O. If the length of the cable is L, what are the coordinates (x, y, z) of point A?

Given:

NF

70

60

40

L=3 m Solution:

F

FLr

4. The lamp fixture has weight W and is suspended from two springs, each having unstretched

length L and stiffness k. Determine the angle θ for equilibrium.

Given: W=10 N, L=4 m, k=5 N/m, a=4 m

),T(FindT

5. The man pulls on the rope with a force F. Determine the moment that this force exerts about the base of the pole at O. Solve the problem two ways, i.e., by using a position vector from O to A, then O to B. Given: F=20 N, a=3 m, b=4 m, c=1.5 m, d=10.5 m

dc

a

b

rAB

d

rOA 0

0

c

a

b

rOB

AB

AB

r

rFFv

xFvrM OAO 1

xFvrM OBO 2

6. Determine the length b of the triangular load and its position a on the beam such that the equivalent resultant force is zero and the resultant couple moment is M clockwise. Given: w1=4 kN/m, w2=2.5 kN/m, M=8 kNm, c=9 m

7. Determine the reactions at the supports. Given: w=250 N/m, a=6 m, b=6 m, c=6 m. 8. Determine the force in each member of the truss and state if the members are in tension or

compression. Given: P1=0 N, P2=1000 N, a=10 m, b=10 m

9. Determine the force in members BF, BG, and AB, and state if the members are in tension or compression. Given: F1=5 kN, F2=10 kN, F3=5 kN, F4=10 kN, a=4 m, b=4 m

10. Determine the internal normal force, shear force, and moment at points E and D of the compound beam. Given: M=200 Nm, F=800 N, a=2 m, b=2 m, c=4 m, d=2 m, e=2 m.