FORCE SYSTEMS

PROBLEMS on

PROBLEMS 1. It is desired to remove the spike from the timber by applying force along its horizontal axis. An obstruction A prevents direct access, so that two forces, one 1.6 kN and the other , are applied by cables as shown. Compute the magnitude of necessary to ensure a resultant directed along the spike. Also find T.

P

PROBLEMS

T P

2. Express each of the three forces acting on the bracket in Cartesian vector form with respect to the x- and y-axes. Determine the magnitude and direction q of F1 so that the resultant force is directed along the positive x' axis and has a magnitude of R = 600 N.

PROBLEMS

PROBLEMS 3. 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 part 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.

4. The three concurrent

forces acting on the post

produce a resultant force

R = 0. If and

is to be 90° from as

shown, determine the

required magnitude F3

expressed in terms of F1

and the angle q.

PROBLEMS

122

1FF

1F

2F

PROBLEMS 5. The unstretched

length of the spring is r.

When pin P is in an

arbitrary position q,

determine the x- and y-

components of the

force which the spring

exerts on the pin. Fspring=kd

Evaluate your answer for r = 400 mm, k = 1.4 kN/m and q = 40°.

Also when pin P is in the position q = 20°, determine the n- and

t-components of the F which the spring of modulus k = 1.4 kN/m

exerts on the pin.

until it produces a tension T in CD of 1.2 kN. Express as a vector in terms of its unit vectors , and . Determine the direction angles qx, qy and qz which makes with the positive x-, y-, and z-axes. Does it make any difference in the result which coordinate system is used?

6. The rigid pole and cross arm assembly is supported by the three cables shown. A turnbuckle at D is tightened

i

T

j

k

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T

7. Three forces are acting on the eye bolt. If the

resultant force has a magnitude and direction as

PROBLEMS

shown,

determine the

magnitude and

direction angles

of .

RF

3F

PROBLEMS

8. Specify the

magnitude F3 and

direction angles

a3, b3, g3 of

so that the

resultant of the

three forces is

kN.

3F

jR

9

PROBLEMS 9. The positions of

point A on the building

and point B on the

antenna have been

measured relative to

the electronic

distance meter at O.

Determine the

distance between A

and B.

10. Two cables

exert forces on the

pipe. Determine the

magnitude of the

projected

component of

along the line of

action of . Also

determine the angle

q between the two

cables.

1F

PROBLEMS

2F q

11. The shafts and attached brackets are twisted in

opposite directions to maintain a tension T of 500 N in

the wire joining A and B. Express the tension, considered

PROBLEMS

T

as a force acting on A

in terms of its

magnitude and unit

vector and determine

the projection of

onto the line DC.

12. An overhead crane is used to reposition the boxcar within a railroad car-repair shop. If the boxcar begins to move along the rails when the x-component of the cable tension reaches 3 kN, calculate the necessary tension T in the cable. Determine the angle qxy between the cable and the vertical x-y plane.

PROBLEMS

13. The spring of constant k = 2.6 kN/m is attached to the disk at point A and 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 15° clockwise and the end fitting is rotated 30° counterclockwise, determine a vector expression for the force which the spring exerts at point A.

PROBLEMS