UNIT 5:Static

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Example 5
A hanging flower basket having weight, W2
23 N is hung out over the edge of a balcony
railing on a uniform horizontal beam AB of length
110 cm that rests on the balcony railing. The
basket is counterbalanced by a body of weight, W1
as shown in Figure 5.16. If the mass of the beam
is 3.0 kg, calculate a. the weight, W1 needed, b.
the force exerted on the beam at point O. (Given
g 9.81 m s?2)
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Solution The free body diagram of the beam
Let point O as the rotation axis.
0.20 m
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Solution Since the beam remains at rest thus
the system in equilibrium. a. Hence b.
and
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Example 6
A uniform ladder AB of length 10 m and mass 5.0
kg leans against a smooth wall as shown in Figure
5.17. The height of the end A of the ladder is
8.0 m from the rough floor. a. Determine the
horizontal and vertical forces the floor
exerts on the end B of the ladder when a
firefighter of mass 60 kg is 3.0 m from
B. b. If the ladder is just on the verge of
slipping when the firefighter is 7.0 m up
the ladder , Calculate the coefficient of
static friction between ladder and
floor. (Given g 9.81 m s?2)
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Solution a. The free body diagram of the ladder
Let point B as the rotation axis.
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Solution Since the ladder in equilibrium thus
Horizontal force
Vertical force
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Solution b. The free body diagram of the ladder
Let point B as the rotation axis.
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Solution Consider the ladder stills in
equilibrium thus
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Example 7
A floodlight of mass 20.0 kg in a park is
supported at the end of a 10.0 kg uniform
horizontal beam that is hinged to a pole as shown
in Figure 5.18. A cable at an angle 30? with the
beam helps to support the light. a. Sketch a free
body diagram of the beam. b. Determine i. the
tension in the cable, ii. the force exerted on
the beam by the pole. (Given g 9.81 m s?2)
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Solution a. The free body diagram of the beam
b. Let point O as the rotation axis.
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Solution b. The floodlight and beam remain at
rest thus i. ii.
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Solution b. ii. Therefore the magnitude of the
force is and its direction is given
by
from the x-axis anticlockwise
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Exercise 5.2
Use gravitational acceleration, g 9.81 m
s?2 1. Figure 5.19 shows the forces,
F1 10 N, F2 50 N and F3 60 N are applied to a
rectangle with side lengths, a 4.0 cm and b
5.0 cm. The angle ? is 30?. Calculate the
resultant torque about point D. ANS. -3.7 N m
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Exercise 5.2
2. A see-saw consists of a uniform board
of mass 10 kg and length 3.50 m supports a father
and daughter with masses 60 kg and 45 kg,
respectively as shown in Figure 5.20. The fulcrum
is under the centre of gravity of the board.
Determine a. the magnitude of the force exerted
by the fulcrum on the board, b.
where the father should sit from the fulcrum to
balance the system. ANS. 1128 N 1.31 m
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Exercise 5.2
3. A traffic light hangs from a
structure as show in Figure 5.21. The uniform
aluminum pole AB is 7.5 m long has a mass of 8.0
kg. The mass of the traffic light is 12.0 kg.
Determine a. the tension in the horizontal
massless cable CD, b. the vertical and
horizontal components of the force exerted
by the pivot A on the aluminum pole. ANS. 248
N 197 N, 248 N
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Exercise 5.2
4. A uniform 10.0 N picture frame is
supported by two light string as shown in Figure
5.22. The horizontal force, F is applied for
holding the frame in the position shown. a.
Sketch the free body diagram of the picture
frame. b. Calculate i. the tension in the
ropes, ii. the magnitude of the horizontal
force, F . ANS. 1.42 N, 11.2 N 7.20 N
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