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REVIEW
REVIEW
Concept Summary
••••••
For: Self-Assessment
Visit: PHSchool.com
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think! Answers
2.2
In the first case, the reading on each scale
will be half her weight. In the second case,
when more of her weight is supported
by the left ring, the reading on the right
reduces to less than half her weight. But in
both cases, the sum of the scale readings
equals her weight.
Zero, as the scale is at rest. The scale reads
the support force (which has the same
magnitude as weight), not the net force.
In the first case, the reading on each scale
is half your weight. (The sum of the scale
readings balances your weight, and the net
force on you is zero.) In the second case, if
you lean more on one scale than the other,
more than half your weight will be read on
that scale but less than half on the other. In
this way they add up to your weight.
Neither, for both forces have the same strength.
Call the thrust positive. Then the air resistance
is negative. Since the plane is in equilibrium,
the two forces combine to equal zero.
The tension is greater in the ropes hang-
ing at an angle. The angled ropes are more
likely to break than the vertical ropes.
No way! If the 10-N load is to hang in
equilibrium, there must be a supporting
10-N upward resultant. The tension in
each half of the guitar string must form
a parallelogram with a vertically upward
10-N resultant. For a slight sag, the sides of
the parallelogram are very, very long and
the tension force is very large. To approach
no sag is to approach an infinite tension.
•
•
•
•
•
A force is needed to change an object’s
state of motion.
You can express the equilibrium rule
mathematically as F 0.
For an object at rest on a horizontal
surface, the support force must equal the
object’s weight.
Objects at rest are said to be in static
equilibrium; objects moving at constant
speed in a straight-line path are said to be
in dynamic equilibrium.
To find the resultant of two nonparallel
vectors, construct a parallelogram where-
in the two vectors are adjacent sides. The
diagonal of the parallelogram shows the
resultant.
••••••
   Teaching Tip How much
work to assign to your students?
At least enough to keep them
engaged. But not so much as
to overload them and make
your course a chore. The Check
Concepts problems are a review
of student reading, and answers
can be picked from the chapter.
All students should be successful
with Check Concepts. Critical
thinking, rather than recall, is
called for in the Think and Rank
problems (a new feature in this
edition). Likewise with the Think
and Explain and Think and Solve
problems.
2.3.1
2.3.2
Key Terms
2.4
force (p. 13)
net force (p. 13)
vector (p. 14)
vector quantity
  (p. 14)
scalar quantity (p. 14)
mechanical
  equilibrium (p. 16)
equilibrium rule
  (p.16)
support force (p. 17)
resultant (p. 20)
2.5.1
2.5.2
Teaching Resources
• TeacherEXPRESS
• Virtual Physics Lab 1
CHAPTER 2
MECHANICAL EQUILIBRIUM
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ASSESS
Check Concepts
ASSESS
Check Concepts
Section 2.1
••••••
12. What two forces compress a spring inside a
    weighing scale when you weigh yourself?
13. When you are at rest and supported by a
    pair of weighing scales, how does the sum
    of the scale readings compare with your
    weight?
Section 2.4
1. What is the difference between force and
   net force on an object?
2. What is the net force on a box that is be-
   ing pulled to the right with a force of 40 N
   and pulled to the left with a force of 30 N?
3. What name is given to the stretching
   force that occurs in a spring or rope
   being pulled?
4. What two quantities are necessary to
   determine a vector quantity?
5. How does a vector quantity differ from a
   scalar quantity?
6. Give an example of a vector quantity.
   Give an example of a scalar quantity.
Section 2.2
14. Can an object be moving and still be in
    equilibrium? Defend your answer.
15. If you push a crate across a factory floor at
    constant speed in a constant direction, what
    is the magnitude of the force of friction on
    the crate compared with your push?
16. Distinguish between static equilibrium and
    dynamic equilibrium.
Section 2.5
7. How much tension is in a rope that
   holds up a 20-N bag of apples at rest?
8. What does F
0 mean?
17. According to the parallelogram rule for two
    vectors, what does the diagonal of a con-
    structed parallelogram represent?
18. Consider the suspension of Nellie in Figure
    2.11. Name the three forces that act on her.
    What is your evidence that they cancel to
    zero?
19. Consider Nellie in Figure 2.12. What chang-
    es in rope tension occur when the ropes
    make a greater angle with the vertical?
20. When Nellie hangs from ropes at different
    angles, as shown in Figure 2.13, how does
    the vector resultant of the two rope tensions
    compare with her weight?
9. What is the net force on an object
   at rest?
10. When you do pull-ups and you hang at rest,
    how much of your weight is supported by
    each arm?
Section 2.3
11. What is the angle between a support force
    and the surface on object rests upon?
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Think and Rank
••••••
Rank each of the following sets of scenarios in
order of the quantity or property involved. List
them from left to right. If scenarios have equal
rankings, then separate them with an equal sign.
(e.g., A = B)
ASSESS
24. Percy does gymnastics, suspended by one
    rope in A and by two ropes in positions B,
    C, and D. Rank the tensions in the ropes
    from greatest to least.
21. Blocks A and B are supported by the table.Concept Summary ••••••
Block C is partly supported by the table and
partly by the rope. Rank the support forces
provided by the table from greatest to least.
Think and Rank
22. In the diagram below, identical blocks are
    suspended by ropes, each rope having a
    scale to measure the tension (stretching
    force) in the rope. Rank the scale readings
    from greatest to least.
Think and Explain
••••••
25. A cat lies on the floor. Can you say that no
    force acts on the cat? Or is it correct to say
    that no net force acts on the cat? Explain.
26. Consider two forces, one having a magni-
    tude of 20 N and the other a magnitude of
    12 N. What is the maximum net force pos-
    sible for these two forces? The minimum ?
27. When a box of chocolate bars is in mechani-
    cal equilibrium, what can be correctly said
    about all the forces that act on it? Must the
    net force necessarily be zero?
28. Faina says that an object cannot be in
    mechanical equilibrium when only a single
    force acts on it. Do you agree or disagree?
29. Phyllis Physics hangs at rest
    from the ends of the rope, as
    shown at right. How does the
    reading on the scale compare
    to her weight?
Think and Explain
23. Burl and Paul stand on their sign-painting
    scaffold. Tension in the left rope is measured
    by a scale. Rank the tensions in that rope
    from greatest to least.
CHAPTER 2
MECHANICAL EQUILIBRIUM
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30. 
ASSESS
(continued)
30. Harry the Summary after yearConcept painter swings year••••••
from his bosun’s chair. His weight is 500 N
and the rope, unknown to him, has a break-
ing point of 300 N. Why doesn’t the rope
break when he is supported as shown at the
left? One day Harry is painting near a flag-
pole, and, for a change, he ties the free end
of the rope to the flagpole instead of to his
chair as shown at the right. Why did Harry
end up taking his vacation early?
36. Consider a heavy refrigerator at rest on a
    kitchen floor. When Anthony and Daniel
    start to lift it, does the support force on the
    refrigerator provided by the floor increase,
    decrease, or remain unchanged? What hap-
    pens to the support force on Anthony’s and
    Daniel’s feet?
37. Sneezlee is supported by
    two thin wires. Is the ten-
    sion in each wire less than,
    equal to, or more than half
    his weight? Use the paral-
    lelogram rule to defend
    your answer.
38. Sneezlee’s wire
    supports are repo-
    sitioned as shown.
    How does the ten-
    sion in each wire
    compare with the
    tension of the previ-
    ous question?
39. If a picture frame were supported by a pair
    of vertical wires, tension in each wire would
    be half the weight of the frame. When the
    frame is supported by wires at an angle, as
    shown below, how does the tension in each
    wire compare with that of vertical wires?
31. How many significant forces act on a your
    physics book when it is at rest on a table?
    Identify the forces.
32. Why doesn’t the support force that acts on
    a book resting on a table cause the book to
    rise from the table?
33. Nicole stands on a bathroom scale and
    reads her weight. Does the reading change if
    she stands on one foot instead of both feet?
    Defend your answer.
34. Justin sets a hockey puck sliding across the
    ice at a constant speed. Is the puck in equi-
    librium? Why or why not?
35. Alyssa pulls horizontally on a crate with a
    force of 200 N, and it slides across the floor
    at a constant speed in a straight line. How
    much friction is acting on the crate?
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40. A monkey hangs by a strand of rope and45. The sketch shows a painter’s staging in
    holds onto the zoo cage as shown. Since hermechanical equilibrium. The person in the
    arm holding the cage is horizontal, only themiddle weighs 250 N, and the tensions in
    rope supports her weight. How does the ten-both ropes are 200 N. What is the weight of
    sion in the rope compare with her weight?the staging?
ASSESS
Concept Summary
••••••
200 N
200 N
Think and Solve
250 N
W=?
                                              47. A staging that weighs 300 N supports two
                                                  painters, one 250 N and the other 300 N. The
41. Why can’t the strong man pull hard enough
                                                  reading in the left scale is 400 N. What is the
    to make the chain perfectly straight?
                                                  reading in the right scale?
400 N
?
250 N
300 N
300 N
Think and Solve
••••••
42. Two vertical chains are used to hold up
    a 1000-N log. One chain has a tension of
    400 N. Find the tension in the other chain.
47. Two children push on a heavy crate that
    rests on a basement floor. One pushes hori-
    zontally with a force of 150 N and the other
    pushes in the same direction with a force of
    180 N. The crate remains stationary. Show
    that the force of friction between the crate
    and the floor is 330 N.
                                               48. Two children push on a crate. They find that
                                                   when they push together horizontally with
                                                   forces of 155 N and 187 N, respectively, the
                                                   crate slides across the floor at a constant
43. Lucy Lightweight stands with one foot on
                                                   speed. Show that the force of friction be-
    one bathroom scale and her other foot on a
                                                   tween the crate and the floor is 342 N.
    second bathroom scale. Each scale reads
    300 N. What is Lucy’s weight?
44. Harry Heavyweight, who weighs 1200 N,
    stands on a pair of bathroom scales so that
    one scale reads twice as much as the other.
    What are the scale readings?
CHAPTER 2
Teaching Resources
More Problem-Solving Practice
Appendix F
MECHANICAL EQUILIBRIUM
• Computer Test Bank
• Chapter and Unit Tests
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