Assignment: Equilibrium
Q 1.1:
• A worker encounters
rocks while digging a
small hole. If he exerts a
horizontal 225-N force
on the prybar (with
negligible weight) as
shown, what is the
horizontal force exerted
on rock C?
(Note that a small ledge
on rock C supports a
vertical force reaction
there. Neglect friction at
B.)
Q 1.2:
• In the same case,
what is the horizontal
force exerted on rock
C if the mass of prybar
is 18-kg?
Q: 2
Determine the reactions
at A and E if P = 500 N.
Varying the angle at B,
find the maximum and
minimum value P can
attain.
Q3. A person is performing slow arm
curls with a 10-kg weight as indicated
in the figure.
Determine the magnitude F of the
brachialis-muscle- group force and
the magnitude E of the elbow joint
reaction at point E for the forearm
position shown in the figure.
Take the dimensions shown to locate
the effective points of application of
the two muscle groups; these points
are 200 mm directly above E and 50
mm directly to the right of E.
Include the effect of the 1.5-kg
forearm mass with mass center at
point G. State any assumptions.
Plot the force, if the length 200 is
varying from 100 to 250 mm
Q 4. The load on the bent rod
is supported by a smooth
inclined surface at B and
Find:
Support reactions at A and B.
a collar at A. The collar is free
to slide over the fixed inclined
rod.
Find the support reactions at
A and B.
Calculate and plot the same
when the position of the load
(100lb) is varied along the
horizontal span of AB in steps
of 0.1ft.
Q 5. Suppose rod AB is hinged to a fixed
wall. Rope CDE is attached to the rod at C,
4’ from the hinge. The rope passes over a
pulley D, which is mounted on another
fixed wall. The angle ACD is 60 . The other
end of the rope is connected to a
mechanism (not shown), which
requires 50 lb force to be actuated.
How much downward hand force will be
required at point B, 5’ from the hinge, to
actuate the mechanism?
When the hand force is applied, what
reaction force will be developed in hinge
A?
Plot the variation of both when the
position of C is moved along AB such that
the angle is varied between 120 to 30
degrees in steps of one degree.
(Assume the rod is weightless and rigid)
Q6. The 220-kg V-8
engine is supported on an
engine stand and rotated
90􏰑 from its upright
position so that its center
of gravity G is in the
position shown.
Determine the vertical
reaction at each roller of
the stand. Neglect the
weight of the stand itself.
Plot the reaction forces if
the weight is between
100 kg to 350 kg
Q7. Each of the three uniform
1200-mm bars has a mass of 20
kg. The bars are welded together
into the configuration shown and
suspended by three vertical wires.
Bars AB and BC lie in the horizontal
x-y plane, and the third bar lies in
a plane parallel to the x-z plane.
Compute the tension in each wire.
Plot how the tensions will vary if
the angle shown in the figure is
varied between 0-90 degrees in
steps of 1 degree.
Q8. Determine the tension T
required to hold the
rectangular solid in the
position shown. The 125-kg
rectangular solid is
homogeneous. Friction at D is
negligible.
Plot the value of T required
when the position of D is
varied within the rectangular
area (AB x 0.4m) parallel to xz plane in steps of 0.01m in
each direction.
Q9. Determine the
magnitudes of the force R
and couple M exerted by
the nut and bolt on the
loaded bracket at O to
maintain equilibrium.
Plot the values of both
when the angle between
1.6N force and x-axis is
varied between -90º to +
90º in steps of 1 degree.
Q10. Determine the
compression in each of the
three legs of the tripod
subjected to the vertical 2-kN
force. The weight of the legs
is negligible compared with
the applied
load. Solve by
`
using the force–equilibrium
equation ΣF = 0.
Plot the same when the
height OD is varied from –
2000mm in steps of 10mm.
Q11. A force P of 200 N on
the handle of the cable reel is
required to wind up the
underground cable as it
comes from the manhole.
The drum diameter is 1000
mm. For the horizontal
position of the crank handle
shown, calculate the
magnitudes of the bearing
forces at A and B. Neglect the
weight of the drum.