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