Resultant of Coplanar forces

1. Determine the resultant of the four forces acting on the body as shown.

(Answer: FR = 303.47 lb and = 68.86)

2. Shown in the figure are five forces acting on point M with a resultant of magnitude R.

If the component of R along the A-axis is thrice the value of its component along the

A-axis, find the magnitude of F and R. Note that the A-A axes are perpendicular to

each other and the A axis is measured 57 West of North.

Equilibrium of Particle

3. The cords for the system shown can each support a maximum load of 100 lb. Determine the

maximum weight of the crate that can be hoisted, and the angle for equilibrium. Take c = 12 and d = 5.

4. Determine the unstretched length of the spring AC if a force P=80 lb causes the angle =60 for equilibrium. Cord AB is 2 ft long. Take k = 50 lb/ft, a = 2 ft , and b = 2 ft

(Answer: lAC = 2.66 ft)

5. Determine the weight that can be suspended for the system to be in equilibrium. The

initial length of spring AB is 5.5 ft and kAB = 1000 lb/ft. Also, determine the force in

spring DG and CF.

Resultant of Force Systems (Moment)

6. Determine the magnitude and directional sense of the resultant moment of the forces at

A and B about point P.

(Answer: 1.17 kip-in)

Couple

7. The ends of the triangular plate are subjected to three couples. Determine the plate

dimension d so that the resultant couple is 350 Nm clockwise.

(Answer: d = 1.54 m)

x O

40 lb

P

B

A

6 in

3 in

3 in

60 lb

45

6 in

5 in

12 in

30

Equivalent System of Forces

8. Replace the system of forces acting on the frame by a resultant force R through B and a

couple acting 45 from the horizontal axis through C and E.

9. Determine the magnitude and direction of the force that must be added to the force and

couple system shown so that the five forces and the couple moment is equivalent to a 3

kN downward vertical force at H and a clockwise couple moment. B) What is the

magnitude of the equivalent clockwise couple moment if the force to be added is

applied at point D?