FORCE SYSTEMS

PROBLEMS

1. The line of action of the 34-kN force runs through the points

A and B as shown in the figure. Express as a vector in terms

of the unit vectors and . i

F

j

F

2. In the design of a control mechanism, it is determined that rod AB transmits

a 260 N force P to the crank BC. Determine the x and y scalar components of

. Also find the scalar components Pt and Pn of which are tangent and

normal, respectively, to crank BC.

P

P

3. A cable stretched between the fixed supports A and B is under a

tension T of 900 N. Express the tension as a vector using the unit

vectors and , first, as a force acting on A and second, as a

force acting on B.

i

AT

j

BT

4. Determine the components of the 2-kN force along the oblique

axes a and b. Determine the projections of onto the a- and b-

axes.

F

5. The unstretched length of the spring of modulus k=1.2 kN/m is 100 mm.

a) When pin P is in the position q=30o, determine the x- and y-components of

the force which spring exerts on the pin. b) When q=20o, determine the n- and

t-components of the force which spring exerts on the pin.

6. In the design of the robot to insert the small cylindrical part into a close-

fitting circular hole, the robot arm must exert a 90 N force P on the parallel to

the axis of the hole as shown. Determine the components of the force which

the part exerts on the robot along axes (a) parallel and perpendicular to the

arm AB, and (b) parallel and perpendicular to the arm BC.

7. Express the force as a vector in terms of unit vectors ,

and . Determine the angles qx, qy and qz which makes with

the positive x-, y-, and z-axes.

i

F

j

F

k

8. The turnbuckle T is tightened until the tension in cable OA is 5 kN.

Express the force acting on point O as a vector. Determine the

projection of onto the y-axis and onto line OB. Note that OB and

OC lies in the x-y plane.

F

F

9. The cable BC carries a tension of 750 N. Write this tension as a

force acting on point B in terms of the unit vectors , ,

and . The elbow at A forms a right angle.

i

T

j

k

10. The access door is held in the 30o open position by the chain

AB. If the tension in the chain is 100 N, determine the projection of

the tension force onto the diagonal axis CD of the door.

11. The spring of constant k=2.6 kN/m is attached to the disk at point A to

the end fitting at point B as shown. The spring is unstretched when qA and

qB are both zero. If the disk is rotated 15o clockwise and the end fitting is

rotated 30o counterclockwise, determine a vector expression for the force

which the spring exerts at point A.

12. The cable AB carries a tension of 140 N. Write this tension as a

force acting on point A in terms of the unit vectors , ,

and .

i

T

j

k