UNIT
1
dynamics
oVeRAll
eXpectAtions
• analyze technological devices that
apply the principles of the dynamics of
motion, and assess the technologies’
social and environmental impact
• investigate, in qualitative and
quantitative terms, forces involved in
uniform circular motion and motion in
a plane, and solve related problems
• demonstrate an understanding of the
forces involved in uniform circular
motion and motion in a plane
Big iDeAs
• Forces affect motion in predictable
and quantifiable ways.
• Forces acting on an object will
determine the motion of that object.
• Many technologies that utilize the
principles of dynamics have societal
and environmental implications.
UNiT TASK PrEvIEw
In the Unit Task, you will apply some of the principles of physics
that are used in sports and games. The Unit Task is described in
detail on page 146. As you work through the unit, look for Unit
Task Bookmarks to see how information in the section relates
to the Unit Task.
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Focus on STSE
Applying the Dynamics of Motion
One of the most exciting and dangerous winter sports is the one-person luge (sled),
where athletes race down icy tracks with high banked curves on top of a small luge, as
seen in the image on the facing page.
The thrill of the luge comes from the high levels of speed the athlete can reach. To
help reduce air resistance and reach high speeds, athletes try to be as aerodynamic as
possible by lying down and keeping their heads down and toes pointed. They also wear
specially designed aerodynamic racing helmets and suits and use lightweight luges. In
fact, many racers spend hours in wind tunnels designed to help them find the ideal body
position to minimize drag.
The terrain and the mass of the luge also affect the speed. The steeper the hill, the faster
the luge goes. However, if the luge crashes, the impact will be greater as well. The smoother
the track, the less friction between the ice and the sled, and the faster the luge will go. The
only brakes are the athlete’s feet. Their shoes are covered with treads, like tire treads, to
help protect them from the tremendous amount of friction created by braking.
The most dangerous points on a luge run are the turns and turn combinations, where
circular motion and high velocities buffet the athlete. To maintain speed, the athlete must
find just the right spot on the luge to perfectly balance the opposing forces.
Think about all the different kinds of motion and forces that occur as the luger speeds
down the track. Which forces, if any, do you think have no direct effect on the motion of
the luge? Which forces speed it up or slow it down? Gravity pulls the luger down the track,
but some of this force is balanced by the other forces acting on the luge. For example,
friction between the sled and the track works against gravity.
Questions
1. Which features of the luge and the athlete’s technique help decrease the time
of the run?
2. Why are the turns banked? Explain what you know about the forces acting on the
athlete in the turns.
3. What are the main forces that cause the luge to speed up? When do the largest
accelerations occur?
4. In what direction is the net force on the luge and the athlete when going around a
banked curve? Explain your reasoning.
5. The sport of luging is extremely dangerous. In your opinion, should more stringent
conditions or rules be implemented for luge courses? Explain your reasoning.
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unit
1
Are you ready?
Concepts
•
•
•
•
•
•
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kinematics
Newton’s laws of motion
vectors and scalars
friction
Pythagorean theorem
trigonometric ratios
sine law and cosine law
Concepts Review
1. Two students travel to school by different means. One
takes the bus, and his path includes many turns and stops.
The other student rides her bicycle and travels directly to
school without any stops and turns. Describe each
student’s displacement. K/U C
2. Which object has more acceleration, a jet cruising with a
constant speed of 600 km/h or a baseball player just after
he hits the ball and starts running from rest? K/U
3. Describe a specific case in which an object’s velocity and
acceleration vectors point in opposite directions. K/U C A
4. (a) Some people dry their hands by flicking the water
off (moving the hands rapidly and then stopping
them suddenly). Explain how this action illustrates
one of Newton’s laws of motion.
(b) Explain, using Newton’s laws, how this knowledge
can help you get ketchup out of a glass bottle in the
most efficient way.
(c) Explain, using Newton’s laws, why hitting the
bottom of a ketchup bottle is not the most effective
way to get the ketchup out. Then explain why it
works at all. K/U T/I C A
5. With some effort, a man can push his car to a nearby
service station, even though the car is much more massive
than he is (Figure 1). Describe the forces between the
man and the car. Discuss where friction helps him and
where friction hinders him in this situation. K/U A
Skills
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•
•
•
•
•
solving for unknown lengths and angles using trigonometry
communicating scientific information clearly and accurately
analyzing graphs
solving motion problems using kinematics equations
drawing free-body diagrams and force diagrams
determining vector components and net force
6. A large football player collides with a smaller football
player during a game. They exert forces on each other
when they collide. K/U A
(a) How do the magnitude and direction of the
forces compare?
(b) Which player is more likely to experience a
greater acceleration? Explain your reasoning.
(c) Explain why football players wear protective
equipment even though it slows them down.
7. You push on a large heavy box with a horizontal and
gradually increasing force. At first, the box does not
move, but eventually it begins to accelerate. K/U T/I C
(a) Which force keeps the box at rest when you start
to push? Describe the magnitude and direction of
this force.
(b) Which forces act on the box when it is moving?
Draw a free-body diagram of the box when it
is moving.
(c) Sketch a simple graph of the force of friction acting
on the box (vertical axis) as a function of the
applied force on the box (horizontal axis). Explain
your reasoning.
8. You slide a dynamics cart up an incline. The cart
moves directly up the ramp and then back down to the
bottom, where you catch it. Sketch the three motion
graphs for the cart when it is moving freely on the
ramp without you exerting an applied force on it.
Justify your reasoning. K/U T/I C
Skills Review
9. A hockey puck slides across the ice, eventually
coming to rest a long distance from where it
was hit. K/U T/I C
(a) Draw a system diagram of the side view of the
puck as it is sliding to the right.
(b) Draw a free-body diagram of the puck.
Figure 1
4 Unit 1 • Dynamics
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Acceleration
Acceleration
10. For many centuries, people believed Aristotle’s
theory of free fall, which said two things: (a) objects
immediately reach a constant velocity after they are
released, and (b) the constant falling velocity depends
on the mass of the object. Describe an investigation
that you could conduct to test the validity of Aristotle’s
claims. K/U T/I C
11. A launcher applies a constant force to several different
masses. An observer measures the acceleration during
the launch for each mass. Which of the graphs in
Figure 2 shows the correct plot of acceleration versus
mass? K/U T/I
Mass
Mass
(c)
Acceleration
(a)
14. A 12 kg mass is pushed by two forces, A and B. Force A
is 55 N [W], and force B is 82 N [E]. K/U T/I
(a) Calculate the net force due to forces A and B on
the mass.
(b) Calculate the acceleration of the mass.
15. Calculate the magnitude of all the forces acting on each
mass below. K/U T/I
(a) A 14 kg mass sits at rest on top of a desk.
(b) A 3.2 kg mass is pulled horizontally across the
floor at a constant velocity with a force of 4.5 N.
(c) A 4.7 kg mass is pushed horizontally forward
by an 8.6 N force, and the mass accelerates at
1.1 m/s2 [forward].
16. A 15 kg mass sits on top of a scale calibrated in newtons.
You push straight down on the mass with a force of 22 N,
and the reading on the scale goes up. K/U T/I
(a) What was the reading on the scale before you
pushed down?
(b) What was the reading on the scale after you
pushed down?
(c) The reading on the scale provides the magnitude of
one of the forces acting on the mass. Which force
is it? Explain your reasoning.
17. Solve for the unknown lengths, a, b, c, and d, in the
right-angled triangles in Figure 3. T/I
a
17 m
52°
25 m
Mass
37°
(b)
K/U
T/I
(a) How far will the boat travel in 15 min?
(b) Determine the net force acting on the boat.
(c) How does the total of all the frictional forces acting
on the boat compare to the applied force of the
water on the boat?
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c
b
Figure 2
12. A storm front moving in approximately a straight
line reaches Toronto at 3:45 p.m. and Peterborough
at 4:30 p.m. the same day. If the storm continues
moving at the same rate, when will it reach Ottawa
(nearly in a line with the other cities)? Peterborough
is 90 km from Toronto, and Ottawa is 220 km from
Peterborough. K/U T/I A
13. A speed boat cruises with a velocity of 41.0 km/h [N].
d
Figure 3
18. Solve for the unknown length, c, and the unknown
angles, x and y, in the scalene triangle in Figure 4.
c
y
T/I
9 cm
x
21°
12 cm
Figure 4
CAREER PATHWAYS Preview
Throughout this unit, you will see Career Links. Go to the Nelson
Science website to find information about careers related to
Dynamics. On the Chapter Summary page at the end of each
chapter, you will find a Career Pathways feature that shows you
the educational requirements of the careers. There are also some
career-related questions for you to research.
Are You Ready? 5
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