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10 Problems in Statics of Rigid Bodies

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Christine Baterbonia

on 7 October 2013

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Transcript of 10 Problems in Statics of Rigid Bodies

10 Problems in Statics of Rigid Bodies

Consider the wedge used to lower and raise block A
The vertical position of a machine (block A) is adjusted by moving wedge B.
The coefficient of static friction between all surfaces is 0.3. Determine the horizontal force, P, acting on wedge B, that is required to

a) raise the block A (acting on the right side)

The first part of this problem asks for the the smallest value of the force, P, to raise the machine. This force will act on the right side of the wide of block A, as shown, in order to push block A upward. As with all static problems, a free-body diagram will help identify all forces acting on an object.
Free body diagram
Since there is a known force of 1,500 lb acting on block A,
this object will be analyzed first. All forces acting on the block 'A' are shown in the free-body diagram on the left. The frictional forces are,


f1 = μ N1 = 0.3 N1
f2 = μ N2 = 0.3 N2
Applying the equilibrium equations gives,

ΣFx = 0
N1 - f2 cos 12 - N2 sin 12 = 0
N1 - (0.3) (0.9781) N2 - 0.2079 N2 = 0
N1 = 0.5013 N2

ΣFy = 0
N2 cos 12 - f1 - 1,500 - f 2 sin 12 = 0
0.9781 N2 - 0.3 N1 - 1,500 - (0.3)(0.2079) N2 = 0
0.9158 N2 - 0.3 N1 = 1,500
Solving above two equations gives,

N2 = 1,960 lb
N1 = 982.4 lb

and the frictional forces are,

f2 = 587.9 lb
f1 = 294.7 lb
Now that the forces on the bottom surface of block A are known,wedge B can be analyzed. First, sum the forces in the vertical direction, to give,
ΣFy = 0
N3 + f2 sin 12 - N2 cos 12 = 0
N3 + (587.9) (0.2079) - (1,960) (0.9781) = 0
N3 = 1,795 lb and f3 = 538.5 lb
Finally, P can be determined by summing forces on wedge B in the horizontal,

Fx = 0
N2 sin 12 + f3 + f2 cos 12 - P = 0
(1,960) (0.2079) + 538.5 + (587.9) (0.9781) = P

P = 1,521 lb

Problem 2
Problem 1

Two sleds are tied together with a rope (Figure 3). The
coefficient of static friction between each sled and the snow is
0.22. A small child is sitting on sled 1 (total mass of 27 kg) and
a larger child sits on sled 2 (total mass of 38 kg). An adult pulls
on the sleds.
(a) What is the greatest horizontal force that the adult can exert
on sled 1 without moving either sled?
Solution
(a) The two sleds do not move when the adult pulls on sled 1. This
means that the net force acting on the sleds is zero and
the applied force must be cancelled by the total maximum
force of static friction acting on the two sleds. To calculate
the static friction, we combine the two masses and treat
the sleds as one single object.
Given: m=27 kg + 38 kg= 65 kg;
u=0.22
If the force of F = 100 lb is applied to the handle of
the bar bender.
determine the horizontal and vertical
components of reaction at pin A and the reaction of the
roller B on the smooth bar.
Problem 3
The jib crane is supported by a pin at C and rod AB.
If the load has a mass of 2 Mg with its center of mass located
at G, determine the horizontal and vertical components of
reaction at the pin C and the force developed in rod AB on
the crane when x = 5 m.
Problem 4
Determine the horizontal and vertical components
of reaction at the pin A and the normal force at the smooth
peg B on the member
Problem 5

Spring CD remains in the horizontal position at all
times due to the roller at D. If the spring is unstretched
when angle is= 0 degrees and the bracket achieves its equilibrium
position when the angle is= 30 degrees , determine the stiffness k of the
spring and the horizontal and vertical components of
reaction at pin A.
Problem 6
Determine the horizontal and vertical components
of reaction at the pin A and the reaction of the smooth
collar B on the rod
Problem 7
Determine the horizontal and vertical components
of force at the pin A and the reaction at the rocker B of the
curved beam.
Problem 8
The floor crane and the driver have a total weight
of 2500 lb with a center of gravity at G. If the crane is
required to lift the 500-lb drum, determine the normal
reaction on both the wheels at A and both the wheels at B
when the boom is in the position shown.
Problem 9
Determine the magnitude of force F that must be
exerted on the handle at C to hold the 75-kg crate in the
position shown. Also, determine the components of reaction
at the thrust bearing A and smooth journal bearing B.
Problem 10
by:
Christine Baterbonia
Maurice Ancanan
Jennalyn Castro
Marie Kirsty Onia
:)
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