Page 111 Practice Problem 4.7: The weight of the reflector (the earth's gravitational pull) and the force the reflector exerts on the earth form an action-reaction magnitude and direction of each of these forces. Answers: 1960 N up. pair. Determine the

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Chapter5: Three-dimensional Equilibrium
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Page 111 Practice Problem 4.7: The weight of the reflector (the earth's gravitational pull) and
the force the reflector exerts on the earth form an action-reaction pair. Determine the
magnitude and direction of each of these forces. Answers: 1960 N up.
Transcribed Image Text:Page 111 Practice Problem 4.7: The weight of the reflector (the earth's gravitational pull) and the force the reflector exerts on the earth form an action-reaction pair. Determine the magnitude and direction of each of these forces. Answers: 1960 N up.
ban
6. Check to make sure that your forces bey
the direction of the net force, make sure that its direction is the same as that of the
acceleration, as required by Newton's second law.
wester
och Later (in Chapter 5), we'll expand this strategy to deal with more complex problems,
but it's important for you to use it consistently from the very start, to develop good hab-
its in the systematic analysis of problems.
EXAMPLE 4.7 Tension in a massless chain
Now let's apply our problem-solving strategy to a system in equilibrium. To improve the acoustics in an
auditorium, a sound reflector with a mass of 200 kg is suspended by a chain from the ceiling. What is its
weight? What force (magnitude and direction) does the chain exert on it? What is the tension in the chain?
Assume that the mass of the chain itself is negligible.
SOLUTION
SET UP The reflector is in equilibrium, so we use Newton's first law,
EF = 0. We draw separate free-body diagrams for the reflector and
the chain (Figure 4.26). We take the positive y axis to be upward, as
shown. Each force has only a y component. We give symbolic labels to
the magnitudes of the unknown forces, using T to represent the tension
in the chain.
SOLVE The magnitude of the weight w of the reflector is given by
Equation 4.9:
w = mg = (200 kg) (9.80 m/s²) = 1960 N.
Armed with this number and Newton's first law, we can compute the
unknown force magnitudes.
Video Tutor Solution
The weight of the reflector is a force pointing in the -y direction,
so its y component is -1960 N. The upward force 7 exerted on the re-
flector by the chain has unknown magnitude T. Because the reflector is
in equilibrium, the sum of the y components of force on it must be zero:
ΣF, T+ (-1960 N) = 0,
T = 1960 N.
SO
The chain pulls up on the reflector with a force 7 of magnitude 1960 N.
By Newton's third law, the reflector pulls down on the chain with a
force of magnitude 1960 N.
The chain is also in equilibrium, so the vector sum of forces on
it must equal zero. For this to be true, an upward force with magni-
tude 1960 N must act on it at its top end. The tension in the chain is
T= 1960 N.
CONTINUED
Transcribed Image Text:ban 6. Check to make sure that your forces bey the direction of the net force, make sure that its direction is the same as that of the acceleration, as required by Newton's second law. wester och Later (in Chapter 5), we'll expand this strategy to deal with more complex problems, but it's important for you to use it consistently from the very start, to develop good hab- its in the systematic analysis of problems. EXAMPLE 4.7 Tension in a massless chain Now let's apply our problem-solving strategy to a system in equilibrium. To improve the acoustics in an auditorium, a sound reflector with a mass of 200 kg is suspended by a chain from the ceiling. What is its weight? What force (magnitude and direction) does the chain exert on it? What is the tension in the chain? Assume that the mass of the chain itself is negligible. SOLUTION SET UP The reflector is in equilibrium, so we use Newton's first law, EF = 0. We draw separate free-body diagrams for the reflector and the chain (Figure 4.26). We take the positive y axis to be upward, as shown. Each force has only a y component. We give symbolic labels to the magnitudes of the unknown forces, using T to represent the tension in the chain. SOLVE The magnitude of the weight w of the reflector is given by Equation 4.9: w = mg = (200 kg) (9.80 m/s²) = 1960 N. Armed with this number and Newton's first law, we can compute the unknown force magnitudes. Video Tutor Solution The weight of the reflector is a force pointing in the -y direction, so its y component is -1960 N. The upward force 7 exerted on the re- flector by the chain has unknown magnitude T. Because the reflector is in equilibrium, the sum of the y components of force on it must be zero: ΣF, T+ (-1960 N) = 0, T = 1960 N. SO The chain pulls up on the reflector with a force 7 of magnitude 1960 N. By Newton's third law, the reflector pulls down on the chain with a force of magnitude 1960 N. The chain is also in equilibrium, so the vector sum of forces on it must equal zero. For this to be true, an upward force with magni- tude 1960 N must act on it at its top end. The tension in the chain is T= 1960 N. CONTINUED
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