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Exam #1 Review
What we’ve learned:
Uniform, constant acceleration and circular motion.
Acceleration is caused by forces.
Newton’s 3 laws and the Law of Gravity.
Where We are Headed:
• Lecture: We’ll spend the day reviewing for
Friday’s test.
• Homework: I’ll post solutions for HW #5
by the end of the day.
• Exam: Exam #1 is on Friday, Oct. 4:
• 9:00 Folks: Come in, get seated.
• 10:00 Folks: Wait until you are invited
in, then get seated ASAP.
• Everyone: Enter through the upper
doors, leave through the lower doors.
• You can use a one-page study sheet
(both sides) and a calculator.
Warming Up:
Questions
a
.
en
in.
If
to
its
wy
ou
if
14.b.Raindrops
canoffall
different
speeds;
fall quite quickly,
The weight
anatobject
depends
on some
its location.
slowly. describe
Why might
bething
true? in different units.
c.others
Massquite
and weight
thethis
same
15.
An
airplane
moves
through
the
air
at
speed.
5. An astronaut takes his bathroom scale atoconstant
the moon
and The
then
engines’
thrust
applies
a
force
in
the
direction
of
motion,
and
stands on it. Is the reading of the scale his true weight? Explain.
this
force
is
equal
in
magnitude
and
opposite
in
direction
to
6. A light block of mass m and a heavy block
the
drag
force.
Reducing
thrust
will
cause
the
plane
to
fly
at
a
of mass M are attached to the ends of a rope.
stillthe
constant—speed.
Explain
Aslower—but
student holds
heavier block and
lets why
the this is so.
M
16.lighter
Is it possible
for
an
object
to
travel
in
air
faster
block hang below it, as shown in Figurethan its terminal
speed? If not, why not? If so, explain how this might happen.
Q5.6
. Then she lets go. Air resistance can be
Forneglected.
Questions 17 through 20, determine the tension in the rope at the
a. indicated
What is with
the atension
point
dot. in the rope while the
blocks are falling, before either hits the
r ground?
"MMPCKFDUTBSFBUSFTU
m
b.r Would
yourand
answer
be are
different
if she
The strings
pulleys
massless,
andhad
the pulleys are
FIGURE Q5.6
been
holding the lighter block initially?
frictionless.
7.
17.a. Can the normal force
18. on an object be directed
19.
horizontally? If not, why not? If so, provide an example.
b. Can the normal force on an object be directed downward? If
not, why not? If so, provide an example.
8. A ball is thrown straight up. Taking the drag force of air into
account, does it take longer for the ball to travel to the top of its
kg
motion or for it to fall back 5down
again?
5 kg
9. You are going sledding with your friends, sliding down a snowy
hill.
Friction can’t be ignored. Riding solo on your sled, you
FIGURE Q5.17
5 kg
5 kgchange if
have a certain acceleration. Would the acceleration
you let a friend ride with you, increasing the mass? Explain.
FIGURE Q5.18
5 kg
10. Suppose you are holding a box in front of
you and away from your body by squeezFIGURE Q5.19
ing the sides, as shown in Figure Q5.10.
20.Draw a free-body diagram showing all of
the forces on the box. What is the force
that is holding the box up, the force that is
opposite the weight force?
5 kg
n
v
t
0
A.
For Questions 17 through 20, determine the tension in the rope at th
point indicated with a dot.
r "MMPCKFDUTBSFBUSFTU
r The strings and pulleys are massless, and the pulleys are
frictionless.
17.
18.
19.
v
t
0
B.
v
t
0
C.
t
0
D.
FIGURE Q5.26
27. | Eric has a mass of 60 kg. He is standing on a scale in an elevator that is accelerating downward at 1.7 m/s2. What is the
approximate reading on the scale?
A. 0 N
B. 400 N
C. 500 N
D. 600 N
28. | The two blocks in Figure Q5.28 are at rest on frictionless surfaces. What must be the mass of the right block in order that the
5 kg
5 kg
FIGURE Q5.17
5 kg
5 kg
FIGURE Q5.18
5 kg
FIGURE Q5.19
20.
5 kg
5 kg Q5.10
FIGURE
25. | A 3.0 kg puck slides due east on a horizontal frictionless surface
at a constant
speed of 4.5 m/s. Then a force of magnitude
FIGURE
Q5.20
6.0 N, directed due north, is applied for 1.5 s. Afterward,
a. What is the northward component of the puck’s velocity?
A. 0.50 m/s
B. 2.0 m/s
C. 3.0 m/s
4.0
m/s
4.5
m/s
D.
E.
ap_05.indd 153
b. What is the speed of the puck?
A. 4.9 m/s
B. 5.4 m/s
C. 6.2 m/s 25/06/13
D. 7.5 m/s
E. 11 m/s
26. | A rocket in space, initially at rest, fires its main engines at
a constant thrust. As it burns fuel, the mass of the rocket
decreases. Which of the graphs in Figure Q5.26 best represents
the velocity of the rocket as a function of time?
v
15. An airplane moves through the air at a constant speed. Th
engines’ thrust applies a force in the direction of motion, an
this force is equal in magnitude and opposite in direction t
the drag force. Reducing thrust will cause the plane to fly at
slower—but still constant—speed. Explain why this is so.
16. Is it possible for an object to travel in air faster than its termina
speed? If not, why not? If so, explain how this might happen.
5 kg
FIGURE Q5.20
25/06
10:44 AM
C. The friction force is zero.
D. There’s not enough information to tell.
23. || A 2.0 kg ball is suspended
by two light strings as shown
50°
in Figure
FIGURE
Q6.15Q5.23. What is
T
the tension T in the angled
y
16. A
small projectile is launched parallel to the ground at height
string?
m = 2.0 kg
h = 1 m with sufficient speed to orbit a completely smooth, airFIGURE Q5.23
A.
N AB.bug
15rides
N in a small
less9.5
planet.
hole inside the projectile. Is
e
the
bugNweightless?
Explain.
C. 20
D. 26 N
E. 30 N
17.
is itstanding
impossible
astronaut
inside
anarms
orbiting
space
24. Why
| While
in a for
lowan
tunnel,
you raise
your
and push
l
station
from one
to the
byYour
walking
against to
thegoceiling
withend
a force
of other
100 N.
massnormally?
is 70 kg.
d
18. If
in the
feelson
anyou?
attractive gravitational
a. every
What object
force does
theuniverse
ceiling exert
e
force
due
to
every
other
object,
why
don’t
you feelC.a 690
pull N
from
A. 10 N
B. 100 N
someone
seated
next
to
you?
D. 790 N
E. 980 N
19. A mountain climber’s weight is slightly less on the top of a tall
b. What force
floor
exert his
on you?
t
mountain
than does
at thethe
base,
though
mass is the same. Why?
A.
10
N
B.
100
N
690smaller
N
d
20. Is the earth’s gravitational force on the sun larger C.
than,
D.or790
N to the sun’s gravitational
E. 980 N force on the earth? Explain.
than,
equal
f
25. | A 5.0 kg dog sits on the floor of an elevator that is accelerating
downward at 1.20 m/s2.
Multiple-Choice
Questions
a. What is the magnitude of the normal force of the elevator
floor on the dog?
21. | A ball on a string moves around a complete circle, once a
A. 34 N
B. 43 N
C. 49 N
D. 55 N
E. 74 N
second, on a frictionless, horizontal table. The tension in the
26. ||string
cylindrical
space
stations,
the
second
four
times
the
b.Two
What
is
the
magnitude
of
the
force
of
the
dog
on
the
elevator
is measured to be 6.0 N. What would the tension be if the
diameter
the first,
rotate
as to provide the same amount
ballfloor?
went of
around
in only
halfso
a second?
of
artificial
gravity.
If
the
first
station
A.
4.2
N
B.
49
N
C.
55 N
N
D.makes
43 N
74 N
A. 1.5 N
B. 3.0 N
C. 12
D.
24
N oneE.rotation
in the time T, then the second station makes one rotation
in time
A. T/4
B. 2T
C. 4T
D. 16T
27. || The radius of Jupiter is 11 times that of earth, and the freefall acceleration near its surface is 2.5 times that on earth. If we
someday put a spacecraft in low Jupiter orbit, its orbital speed
18/07/13
Section
will 5.1
be Equilibrium
Greater
thatinfor
an earth
1. A.
| The
threethan
ropes
Figure
P5.1 satellite.
are tied to a small, very light
B.
The
same
as
that
for
an
earth
satellite.
ring. Two of the ropes are anchored
to walls at right angles, and
C.
an earthWhat
satellite.
theLess
thirdthan
rope that
pullsfor
as shown.
are T1 and T2 , the magnitudes
28. | ofAthenewly
discovered
planet
tension
forces in the
firsthas
twotwice
ropes?the mass and three times
the
radius
of
the
earth.
What
is
the
at its
2. ||| The three ropes in Figure P5.2 are free-fall
tied to a acceleration
small, very light
surface,
inofterms
the are
free-fall
acceleration
at the
surface
ring. Two
theseof
ropes
anchored
to walls atgright
angles
withof
the
the earth?
tensions shown in the
figure.
What
are
the
magnitude
and
3
2
2 u
4
A.
B. 3 gT3 in the third
C.rope?
D. 3 g
direction
of the tension
9g
4g
29. || Suppose one night the radius of the earth doubled but its mass
stayed the same. What would be an approximate new value for
the free-fall acceleration at the surface of the earth?
A. 2.5 m/s2
B. 5.0 m/s2
C. 10 m/s2
D. 20 m/s2
30. | Currently, the moon goes around the earth once every 27.3
days. If the moon could be brought into a new circular orbit with
a smaller radius,
its orbital period would be
G9721_03_chap_05.indd
154
A. More than 27.3 days.
B. 27.3 days.
C. Less than 27.3 days.
31. || Two planets orbit a star. You can ignore the gravitational
interactions between the planets. Planet 1 has orbital radius r1
and planet 2 has r2 = 4r1 . Planet 1 orbits with period T1 . Planet 2
orbits with period
A. T2 = 12 T1
B. T2 = 2T1
C. T2 = 4T1
D. T2 = 8T1
the two blocks remain stationary?
A. 4.9 kg
B. 6.1 kg
C. 7.9 kg
D. 9.8 kg
E. 12 kg
10 kg
40°
23°
FIGURE Q5.28
29. | A football player at practice pushes a 60 kg blocking sled
across the field at a constant speed. The coefficient of kinetic
friction between the grass and the sled is 0.30. How much force
must he apply to the sled?
A. 18 N
B. 60 N
C. 180 N
D. 600 N
30. | Two football players are pushing a 60 kg blocking sled across
the field at a constant speed of 2.0 m/s. The coefficient of kinetic
friction between the grass and the sled is 0.30. Once they stop
pushing, how far will the sled slide before coming to rest?
A. 0.20 m
B. 0.68 m
C. 1.0 m
D. 6.6 m
31. || Land Rover ads used to claim that their vehicles could climb a
slope of 45°. For this to be possible, what must be the minimum
coefficient of static friction between the vehicle’s tires and the road?
A. 0.5
B. 0.7
C. 0.9
D. 1.0
32. || A truck is traveling at 30 m/s on a slippery road. The driver
slams on the brakes and the truck starts to skid. If the coefficient
of kinetic friction between the tires and the road is 0.20, how far
will the truck skid before stopping?
A. 230 m
B. 300 m
C. 450 m
D. 680 m
PROBLEMS
10:51 AM
0.60 m
Rope 2
T2 = 80 N
0.80 m
Rope 1
30°
T1 = 50 N
u
100 N
FIGURE P5.1
T3
FIGURE P5.2
the free-fall acceleration at the surface of the earth?
A. 2.5 m/s2
B. 5.0 m/s2
C. 10 m/s2
D. 20 m/s2
30. | Currently, the moon goes around the earth once every 27.3
days. If the moon could be brought into a new circular orbit with
a smaller radius, its orbital period would be
A. More than 27.3 days.
B. 27.3 days.
C. Less than 27.3 days.
31. || Two planets orbit a star. You can ignore the gravitational
interactions between the planets. Planet 1 has orbital radius r1
and planet 2 has r2 = 4r1 . Planet 1 orbits with period T1 . Planet 2
orbits with period
A. T2 = 12 T1
B. T2 = 2T1
C. T2 = 4T1
D. T2 = 8T1
6. || The horse on a carousel is 4.0 m from the central axis.
a. If the carousel rotates at 0.10 rev/s, how long does it take the
horse to go around twice?
b. How fast is a child on the horse going (in m/s)?
7. ||| The radius of the earth’s very nearly circular orbit around
the sun is 1.50 * 1011 m. Find the magnitude of the earth’s
(a) velocity and (b) centripetal acceleration as it travels around
the sun. Assume a year of 365 days.
8. | Modern wind turbines are
larger than they appear, and
despite their apparently lazy
motion, the speed of the blades
tips can be quite high—many
times higher than the wind
speed. A typical modern
turbine has blades 56 m long
that spin at 13 rpm. At the tip of a blade, what are (a) the speed
and (b) the centripetal acceleration?
18/07/13 10:51 AM
Dark Matter Surrounds Our Galaxy.
One Step Beyond.
Optional Evening Session
Details TBA
Exam #1
4 scenarios, 3 questions on each
Steps
! Prepare
• Translate
• Draw pictures
• Have you seen this before?
! Solve
• Set up equations
• Solve
! Assess
• Does your answer make sense?
Look at the big picture.
Practicing:
Spot the Physics
Why does the exhaust go back and up?
The plane can’t stay upside down for very long. Why?
What are the forces during the giant swing?
Data
v = 5.0 m/s
r = 1.0 m
m = 41 kg
w = 400 N
Questions
Acceleration = ?
Apparent weight = ?
Compare with w.
Practicing:
Scenarios
Scenario #3: Cavorting Crustaceans
Copepods are small, abundant crustaceans that form a significant percentage of the ocean’s
biomass.
One species forms much of the diet of herring. To escape capture, these copepods have
evolved a very rapid escape response; typical speed vs. time data is shown in the graph at
right. From 0.10 to 0.20 s, rapid swimming motion results in a thrust force that gives a
large acceleration; from 0.20 to 0.40 s, the large drag force on this small animal (assume a
mass of 1.8 mg) slows it to rest.
In what follows, we’ll make the approximation that the drag force works like a kinetic
friction force—it opposes the motion and has a constant magnitude as long as the creature
is in motion.
Speed (m/s)
0.80
0.60
0.40
0.20
0.10 0.20 0.30 0.40
Time (s)
Multiple Choice Questions (3 points):
5) When the copepod is speeding up, what is the approximate magnitude of
the acceleration?
A. 7 m/s2
B. 14 m/s2 C. 20 m/s2 D. 30 m/s2
6) What is the approximate distance the copepod travels during the entire
escape response, including both phases, the speeding up and the slowing
down?
A. 10 cm
B. 20 cm
C. 30 cm
D. 40 cm
Speed (m/s)
0.80
0.60
0.40
0.20
0.10 0.20 0.30 0.40
Time (s)
Short Answer Question (6 points):
Given that the copepod is floating in water, the upward buoyant force offsets the
downward weight force. There are only two forces you need consider, thrust and
drag.
Draw force and motion diagrams for both phases of the motion: the speeding up
and the slowing down. Now, compute:
• What is the magnitude of the drag force while the copepod is slowing down?
• What is the magnitude of the thrust force while the copepod is speeding up?
How do these forces compare to the creature’s weight?
Scenario #2: Lifting a Load
Jordan is using a rope and pulley to raise a 20 kg crate,
as in the diagram at right. The crate is being held at a
constant height of 2.5 m above the floor.
Multiple Choice Questions (3 points):
3) With the crate held at a constant height, what is the
approximate tension in the rope?
A. 50 N
B. 100 N
C. 150 N
D. 200 N
4) Suddenly the rope breaks, and the crate falls to the
floor. After the break, how much time does it take for
the crate to reach the floor, to the nearest 0.1 s?
A. 0.4 s
B. 0.5 s
C. 0.6 s
D. 0.7 s
Short Answer Question (6 points):
Jordan now attaches a rope to the crate that can support
a tension of up to 250 N—but no more. What is the
minimum time required to raise the crate from the floor
back to its original height?
Scenario #4: Marsupial Motion
A gray kangaroo bounding across a flat stretch of ground will execute a series of jumps, moving in a
series of parabolic arcs. The following problem uses typical data for a kangaroo moving at a good clip.
With each jump, the kangaroo leaves the ground at a speed of 12 m/s, at an angle of 20° with respect to
the horizontal. The kangaroo then moves through the air. When the kangaroo lands, the vertical
component of the velocity points downward. A short time later, the stout legs of the kangaroo have
reversed this vertical motion. The kangaroo’s vertical motion is now upward, and the kangaroo leaves
the ground again. The horizontal component of the velocity stays the same while the kangaroo is on the
ground and in the air, so the kangaroo is bouncing up and down, but is moving forward at a steady
speed.
This particular kangaroo is female, and has a 0.51 kg baby—called a joey—supported in her pouch.
Multiple Choice Questions (3 points):
7) At the highest point of her motion, what are the kangaroo’s vertical velocity and vertical
acceleration?
A. vy = +4.1 m/s; ay = 0 m/s2
B. vy = 0 m/s; ay = 0 m/s2
C. vy = 0 m/s; ay = -9.8 m/s2
D. vy = -4.1 m/s; ay = -9.8 m/s2
8) The kangaroo has landed, and her vertical speed is changing. At some instant, her vertical speed is
zero, but her acceleration is upward at 30 m/s2—as is that of the joey. What is the joey’s approximate
apparent weight at this instant?
A. 5 N
B. 10 N
C. 15 N
D. 20 N
Short Answer Question (6 points)
After the kangaroo leaves the ground, how far does she travel before reaching the ground again?
Human vs. Horse
How do humans stack up vs. horses in track
events? Horses are faster, but humans are capable
of greater acceleration.
A typical running speed for a fast horse is 20 m/s,
much faster than a human, but the horse can only
accelerate at 6.0 m/s2, about half what a good
human runner can achieve.
Humans are also better jumpers; the world record
broad jump for a human is about 9.0 m, while that
for a horse is only 7.5 m.
Multiple Choice Questions (3 points):
If a horse starts from rest and accelerates at the maximum value
until reaching its top speed:
1) How much time does this acceleration take, to the nearest
second?
A. 1 s
B. 2 s
C. 3 s
D. 4 s
2) How much distance does the horse cover during this time, to the
nearest 10 m?
A. 10 m B. 20 m C. 30 m D. 40 m
Short Answer Question (6 points)
When humans do a long jump, they get up to top speed and then
redirect their motion so that it has a vertical as well as a horizontal
component. Horses can’t do this nearly as well as humans. Suppose
a horse, running a top speed, could redirect its motion so that it took
off at a 30° angle with respect to the horizontal, moving in a
parabolic trajectory until landing. The horse could then do a jump
that is much longer than 7.5 m! For this theoretical jump,
• For how much time would the horse be in the air?
• At the high point of its motion, how high would the horse be?
• How much horizontal distance would the horse cover?
Next Time: Exam #1