5 Displacement and Force in Two Dimensions
3 Forces in Two Dimensions
MAINIDEA
Write the Main Idea for this section.
REVIEW VOCABULARY
Recall and write the definition of the Review Vocabulary term.
equilibrium
equilibrium
NEW VOCABULARY
Use your book to define each term.
equilibrant
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equilibrant
Science Notebook • Displacement and Force in Two Dimensions
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3 Forces in Two Dimensions (continued)
Student Edition, pp. 136–137
Explain what must be true for an object to be in equilibrium.
Refer to Figure 14 and Figure 15 in your textbook, and explain the
relationship between the forces acting on the ring in the vector diagrams.
Identify the relationship between the equilibrant and the
resultant vector.
GET IT?
Science Notebook • Displacement and Force in Two Dimensions
84
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Draw a vector diagram below that shows a net force of zero acting on an
object. Use four vectors in your drawing.
3 Forces in Two Dimensions (continued)
Student Edition, pp. 138–139
Identify the system in the problem illustrated in Figure 17. Then
describe the factors involved in the first step of solving the problem.
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
Identify the factors involved in choosing the coordinate system for
solving the problem described in Figure 17.
Identify the force described in Figure 17 that has both x- and y-vector
components that must be used to solve the problem.
Explain why you would choose the x-direction to be parallel
to the slope of an inclined plane.
GET IT?
Science Notebook • Displacement and Force in Two Dimensions
85
3 Forces in Two Dimensions (continued)
Student Edition, p. 140
Use with Example Problem 6.
Use this column for
scratch work and
sketches.
TRY IT !
Problem
SLIDE Afrin, who has a mass of 35 kg, is going down a slide sloped at 29°.
The coefficient of kinetic friction is 0.23. How fast does she slide 1.5 s after
starting from rest?
1. ANALYZE AND SKETCH THE PROBLEM
KNOWNS
UNKNOWNS
m=
ϕ=
=?
μk =
vi =
=?
μk =
=?
2. SOLVE FOR THE UNKNOWNS
Find the angle of Fg from the +x-axis:
Add forces in the y-direction to write an equation for FN.
Because vi, a, and t are all known, use the relationship between velocity,
acceleration, and time.
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86
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Use the net force in the x-direction and Newton’s second law to solve
for a.
3 Forces in Two Dimensions (continued)
Student Edition, p. 140
TRY IT ! (CONTINUED)
3. EVALUATE THE ANSWER
• Are the units correct?
• Is the magnitude of the velocity realistic?
SUMMARIZE
How does the MAINIDEA for this section relate to the chapter’s BIGIDEA?
REVIEW IT !
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41. MAINIDEA A rope pulls a 63-kg water skier up a 14.0° incline with a tension of 512 N.
The coefficient of kinetic friction between the skier and the ramp is 0.27. Find the
magnitude and direction of the skier’s acceleration.
42. Forces One way to get a car unstuck is to tie one end of a strong rope to the car and
the other end to a tree, then pull the rope at its midpoint at right angles to the rope.
Draw a free-body diagram and explain how even a small force on the rope can exert a
large force on the car.
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3 Forces in Two Dimensions (continued)
43. Mass A scoreboard is suspended from an arena’s ceiling by ten cables. Six of the cables
make an 8.0° angle with the vertical while the other four make a 10.0° angle. The
tension in each cable is 1300 N. Find the scoreboard’s mass?
44. Vector Addition What is the sum of three vectors that, when placed tip to tail, form a
triangle? If these vectors represent forces on an object, what does this imply about the
object? Describe the motion resulting from these three forces acting on the object.
45. Equilibrium You are hanging a painting using two lengths of wire. The wires will break
if the force is too great. Should you hang the painting as shown in the top or the
bottom image of Figure 20? Explain.
46. Vector Addition Can the coefficient of friction ever have a value such that a child
would be able to slide up a slide at a constant velocity? Explain why or why not. Assume
that no one pushes or pulls on the child.
Science Notebook • Displacement and Force in Two Dimensions
88
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Figure 20