PART 2 Answers to End-of-chapter Conceptual Questions
Chapter 1
Position in Metres
1. It is possible for an object to be accelerating
and at rest at the same time. For example, consider an object that is thrown straight up in
the air. During its entire trajectory it is accelerating downward. At its maximum height it
has a speed of zero. Therefore, at that point it
is both accelerating and at rest.
2. A speedometer measures a car’s speed, not its
velocity, since the speedometer gives no indication as to the direction of the car’s motion.
3.
Position-Time
m
5
4
3
2
1
1 2 3 4 5 6 7
t
Time in Seconds
Time in Seconds
Velocity in Metres per Second
1 2 3 4 5 6 7
t
–1
–2
–3
–4
–5
–6
–7
–8
–9
–10
m
4. Displacement, velocity, and acceleration are
all vector quantities. Therefore, a negative displacement, velocity, or acceleration is a negative vector quantity, which indicates that the
vector’s direction is opposite to the direction
designated as positive.
5. The seconds are squared in the standard SI
unit for acceleration, m/s2, because acceleration is the change in velocity per unit of time.
Therefore, the standard SI unit for acceleration is (m/s)/s, which is more conveniently
written as m/s2.
6. Assume for all cases that north is positive and
south is negative.
a) Positiontime graph: The object sits
motionless south of the designated zero
point. The object then moves northward
with a constant velocity, crossing the zero
point and ending up in a position north of
the zero point.
Velocitytime graph: The object moves
southward with a constant velocity. The
object then slows down while still moving
southward, stops, changes direction, and
speeds up northward with a constant
acceleration.
b) Positiontime graph: The object starts at
the zero point and speeds up while moving
northward, then continues to move northward with a constant velocity.
Velocitytime graph: The object starts at
rest and speeds up with an increasing
acceleration while moving northward. The
object then continues to speed up with a
constant acceleration northward.
c) Positiontime graph: The object starts
north of the zero point and moves southward past the zero point with a constant
velocity. The object then abruptly slows
down and continues to move southward
with a new constant velocity.
Velocitytime graph: The object slows
down while moving northward, stops,
changes direction, and speeds up southward with a constant acceleration. The
object then abruptly reduces the magnitude of its acceleration and continues to
speed up southward with a new constant
acceleration.
d) Positiontime graph: The object starts at
the zero point and moves northward and
slows down to a stop, where it sits motionless for a period of time. The object then
quickly speeds up southward and moves
southward with a constant velocity, going
Answers to End-of-chapter Conceptual Questions
2-1
past the zero point.
Velocitytime graph: The object starts at
rest and speeds up while moving northward. The acceleration in this time period
is decreasing. The object then continues to
move northward with a constant velocity.
The object then slows down while moving
northward, stops, changes direction, and
speeds up southward with a constant acceleration.
dtot
7. a) vavg ttot
1000 m
(5)(60 s)
3.3 ms
dtot
b) vavg ttot
1000 m
(4)(60 s)
4.2 ms
dtot
c) vavg ttot
2000 m
(9)(60 s)
3.7 ms
d) The answer for c) is the average speed of
the bus over the whole trip, whereas half
the sum of its speed up the hill and its
speed down the hill is an average of the
average speeds up and down the hill.
8. In flying from planet A to planet B, you would
need to burn your spacecraft’s engines while
leaving planet A in order to escape its gravitational pull and then to make any necessary
course corrections, and while arriving at
planet B in order to slow down and stop.
Assuming there were no forces acting on the
craft in between, it would travel with constant
velocity once the engines were turned off.
9. A free-body diagram shows the forces acting
on an object, as these are the only forces that
can cause the body to accelerate. Since, by
Newton’s third law, for every action force
there is a reaction force, equal in magnitude
and opposite in direction, then each of the
forces acting on an object is half of an
2-2
actionreaction pair. If both the action forces
and the reaction forces were included in a
free-body diagram, then all the forces would
cancel. For example, a free-body diagram for a
ball being kicked must not include the reaction force provided by the ball on the foot, or
else the forces would cancel and the ball
would have no reason to accelerate.
10.
Fn
Fm
Motorcycle
Ff
Fg
11. Dear Cousin,
You asked me to explain Newton’s first law of
motion to you. Newton’s first law of motion
says that an object will keep moving at a constant speed in the same direction unless a
force makes it slow down, speed up, or change
direction. Here’s an example. Suppose you’re
pushing a hockey puck across the carpet.
When you let go, the puck quickly stops moving. This is because the carpet is not very slippery; we say that it has a lot of friction. The
force of friction is making the puck slow
down. What if you slide the puck across a surface with less friction, like ice? The puck will
take longer to stop moving, because the force
of friction is much less than on the carpet.
Now suppose you slide the puck across an air
hockey table. The force of friction is so small
that the puck will slide for a much, much
longer time. So, you can imagine sliding a
puck on a surface with no friction at all. The
puck never stops, because there is no force to
slow it down! Perhaps you’re wondering
about a motionless object that isn’t experiencing a force — why isn’t it moving at a constant speed in the same direction? But it is!
Zero is a constant speed.
Answers to End-of-chapter Conceptual Questions
Fn
Fn
Puck
on
carpet
Ff
Fg
Fg
Ff
Fg
Fn
Puck
on
air table
Puck
on
ice
Fn
Ff
Puck
on
frictionless
surface
Fg
12. The gravitational force applied by the Moon
on Earth does not cancel with the gravitational force applied by Earth on the Moon
because these forces act on different bodies.
Only forces applied on the same body can possibly cancel one another.
13. When you fire a rifle, the forces applied to the
bullet and the rifle make up an actionreaction pair. By Newton’s third law, the force
applied to the bullet is equal and opposite to
its reaction force, the force applied to the rifle.
This reaction force causes the rifle and you to
recoil in the opposite direction.
14. While in the air, the ball’s vertical acceleration
is constant and equal to g 9.8 m/s2. The
ball travels the same distance upward as
downward, and therefore the ball’s speed is
the same when it reaches the ground as when
it leaves the ground, since its acceleration is
constant. Suppose the lengths of time it takes
the ball to travel upward and downward are t1
and t2, respectively. We can use the equations
t1(v1i v1f)
t2(v2i v2f)
and d2 d1 2
2
for the distances travelled upward and downward, respectively, where v1i and v1f are the initial and final velocities during the upward flight,
respectively, and v2i and v2f are the initial and
final velocities downward, respectively. Since
d1 d2, we can write the following equation:
t2(v2i v2f)
t1(v1i v1f)
2
2
On the left side, the final velocity upward, v1f,
is equal to zero. On the right side, the initial
velocity downward, v2i, is equal to zero. The
equation simplifies:
t2(v2f)
t1(v1i)
2
2
But v1i is equal to v2f and is not zero, and
therefore t1 t2.
15. The ball is undergoing uniform circular
motion, as it is travelling in a circle at a constant speed. Because its trajectory is curved, it
cannot be undergoing uniform motion, which
requires an object to be travelling at a constant speed in a straight line.
Chapter 2
1. Frictional forces are forces that oppose motion.
A frictional force will only try to prevent an
object from moving, it will not actually cause
an object to move.
2. It is not possible to swing a mass in a horizontal circle above your head. Since gravity is
always pulling down on the mass, an upward
component of the tension force is required to
balance gravity. As the speed of rotation
increases, the angle relative to the horizontal
may approach 0° but will never reach 0°.
3. If the gravitational force downward and the
normal force upward are the only two vertical
forces acting on an object, we can be certain
that they are balanced if the object is not accelerating. If one of these forces were greater
than the other, the object would accelerate in
the direction of the greater force.
4. The most common way to describe directions
in three dimensions is by the use of three unit
vectors (and their opposites). Traditionally,
the three unit vectors used are labelled as i, j,
and k. One of these unit vectors will represent
right, one will represent up, and one will represent coming out of the plane of the page
toward you.
Answers to End-of-chapter Conceptual Questions
2-3
5. The bullets reach the ground in the same
amount of time. Recall that the horizontal and
vertical motions of each bullet are independent
of each other. Since both identical objects are
accelerating downward at the acceleration due
to gravity and they are both dropped from the
same height, it takes the same time for them to
reach the ground.
6. Dear Wolfgang,
You asked whether the time it takes to paddle
a canoe across a river depends on the strength
of the current. When you are paddling a canoe
across a river, the variables that determine
how long it takes are the width of the river
and the forward velocity of the canoe due to
your paddling. The canoe’s forward velocity
and the current velocity are perpendicular to
each other, so they don’t affect each other. As
a result, the current does not affect the length
of time required to cross the river. The only
effect of the current on the motion of the
canoe is to cause it to move downstream from
where it would otherwise have landed.
7. The student who wants to apply the force
above the horizontal has the better idea. The
horizontal component of the applied force in
the direction of motion will be the same
regardless of whether the force is applied
above or below the horizontal. It is in the students’ best interest to minimize the amount of
friction. Recall that the frictional force is
directly proportional to the normal force. If
they apply the force above the horizontal, this
will reduce the magnitude of the normal force
needed to be supplied by the floor on the sofa,
which will therefore reduce the frictional force
and make it easier to move the sofa. On the
other hand, if they apply the force below the
horizontal, this will increase the normal force
required and thereby increase the frictional
force, making it harder to move the sofa.
8. a) The baseball’s velocity will be upward with
a magnitude less than its initial velocity.
The acceleration will be downward at
9.8 m/s2.
b) The baseball’s velocity will be zero. The
2-4
acceleration will be downward at 9.8 m/s2.
c) The baseball’s velocity will be downward
with the same magnitude as in a). The
acceleration will be downward at 9.8 m/s2.
9. You would still need a pitcher’s mound on the
Moon because the ball would still accelerate
downward due to gravity. Since the Moon has
a smaller mass than Earth, the acceleration
due to gravity on the Moon is less than that on
Earth. As a result, the height of the mound
would not have to be as great as that on Earth.
10. She could jump twice as far on a planet that
has one-half the gravity of Earth. If we assume
that her initial speed and the direction for
launch are the same, and that her initial vertical displacement is zero, we can write the following.
1
dy v1 t ayt2
2
1
0 v1 ayt
2
2v1
t ay
If the acceleration, ay, is halved, then the time
in flight, t, will be doubled. Therefore, the
horizontal distance travelled will also be doubled, assuming that her horizontal speed is
constant.
11. As your bicycle’s rear tire spins, it takes water
with it due to adhesion. Inertia causes the
water to try to move in straight line. As a
result, the water leaves the wheel with a velocity tangential to the tire and may spray your
back if your bicycle does not have a protective
rear fender.
12. Inertia causes the water in your clothing to try
to move in a straight line. If the drum in the
washing machine were solid, it would apply a
centripetal force on the water which would
keep it moving in a circle. Since the drum has
holes in it, however, the water is able to leave
the drum as it is spins.
13. The aircraft can be flown in one of two ways,
or a combination of these, to provide “weightlessness.” If the aircraft accelerates downward
at the acceleration due to gravity, the astroy
y
y
Answers to End-of-chapter Conceptual Questions
nauts inside the aircraft will experience
“weightlessness.” The other possibility is to
travel in a vertical arc. If the aircraft flies in a
vertical arc at such a speed that at the top of
the arc the gravitational force provides all the
centripetal force required to keep the aircraft
and its occupants travelling in a circle, they
will experience “weightlessness.”
Answers to End-of-chapter Conceptual Questions
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Answers to End-of-chapter Conceptual Questions