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Sec 001, MWF 12:25 PM - 1:15 PM, Riddick 301, Dr. Fortner
PY205M
Test 1 (v1) Fall 2011
Start from a fundamental principle, and clearly show every step in your work (for the worked-out problems
only, NOT the multiple choice). Your score will be based on your reasoning. Answers without adequate
explanation will be counted incorrect.
Write out each calculation, showing the numbers you used: F = 6 · (0.5 − 0.7)
Include units in your final answer.
Cross out any incorrect work; otherwise, it will be counted wrong, even if later work is correct. If you
continue your work on a different page, note this.
I have neither given nor received unauthorized aid on this test.
Signature:
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Things you must know:
Definition of average velocity
Definition of momentum
Relationship between position, velocity, and time
The Momentum Principle
Other physical quantities:
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γ≡s
|~v | 2
1−
c
m1 m2
~
r̂
Fgrav = −G
|~r|2
~
Fgrav ≈ mg near Earth’s surface
~ F~spring = −ks sL̂, , where s = L
− L0
fˆ = hcos θx , cos θy , cos θz i unit vector from angles
Constant
Speed of light
Gravitational constant
Approx. grav field near Earth’s surface
Electron mass
Proton mass
Neutron mass
Electric constant
Proton charge
Avogadro’s number
milli
micro
nano
pico
m
µ
n
p
1 × 10−3
1 × 10−6
1 × 10−9
1 × 10−12
Symbol
c
G
g
me
mp
mn
1
4πǫ0
e
NA
kilo
mega
giga
tera
Approximate Value
3 × 108 m/s
6.7 × 10−11 N · m2 /kg2
9.8 N/kg
9 × 10−31 kg
1.7 × 10−27 kg
1.7 × 10−27 kg
9 × 109 N · m2 /C2
1.6 × 10−19 C
6.02 × 1023 atoms/mol
1 × 103
1 × 106
1 × 109
1 × 1012
K
M
G
T
DO NOT WRITE IN THIS TABLE
Problem
1-11
12
13
14
Total
Pts Score
55
15
15
15
100
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Problem 1 (5 pts): A camera on a timer takes snapshots of a bird in flight at serveral different times.
At time t = 2.0 seconds, the bird’s position is h−1.2, 6.0, 0.6i m. At time t = 4.0 seconds, the bird is at
position h8.4, 3.6, 0.6i m. At time t = 8.0 seconds, the bird is at position h6.4, 5.0, 1.2i m. Using the best
data available, what is the approximate velocity of the bird at time t = 3.0 seconds?
A. h1.27, −0.17, 0.10i m/s
B. h−0.50, 0.35, 0.15i m/s
D. h−0.6, 3, 0.3i m/s
E. h2.1, 0.90, 0.15i m/s
C. h4.8, −1.2, 0i m/s
Refer to the graphic below for problems 2 and 3
Problem 2 (5 pts): A cart on a track is attached to a fan which causes a constant net force on the cart
in the +x direction. You release the cart from rest. Which of the figures below best represents the graph
of the x-component of the cart’s velocity vs. time, from just after it leaves your hand to just before you
stop it?
CIRCLE YOUR ANSWER:
A
B
C
D
E
Problem 3 (5 pts): A cart on a track is attached to a fan which causes a constant net force on the cart
in the −x direction. You give the cart a push so that it initially moves in the +x direction. Which of
the figures belows best represents the graph of the x-component of the cart’s position vs. time, from just
after it leaves your hand to just before you stop it?
CIRCLE YOUR ANSWER:
A
B
C
D
E
Problem 4 (5 pts) A proton (mass 1.7 × 10−27 kg) is moving at a speed of 2.8 × 108 m/s. What is the
magnitude of the proton’s momentum?
A. 1.3 × 10−18 kg m/s
D. 7.8 × 108 kg m/s
B. 4.8 × 10−19 kg m/s
C. 4.7 × 10−27 kg m/s
E. 5.1 × 10−19 kg m/s
Problem 5 (5 pts) A soccer ball with a mass of 0.40 kg is moving with a velocity of h8.0, 0, 3.0i m/s
along the ground when a player kicks it. The player’s foot is in contact with the ball for a total time of
0.006 seconds. After the soccer ball leaves contact with the player’s foot, its new velocity is h−11.0, 2, 6.0i
m/s. What was the approximate net force on the soccer ball while it was in contact with the player’s foot?
A. h−7.6, 0.8, 1.2i N
D. h−200, 133, 200i N
B. h533, 0, 200i N
C. h−1267, 133, 200i N
E. h−3167, 333, 500i N
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Problems 6, 7, and 8, refer to the diagrams below.
sun
A.
B.
C.
D.
E.
Problem 6 (5 pts): A comet moves in a parabolic path around the sun. It moves from left to right on
the diagram, that is, from point A to B. You may assume that the comet has the same speed at A as it
has at B.Which arrow best indicates the direction of the comet’s instantaneous velocity at point B?
CIRCLE YOUR ANSWER:
A
B
C
D
E
Problem 7 (5 pts): Which arrow best indicates the direction of the Comet’s average velocity from
point A to point B?
CIRCLE YOUR ANSWER:
A
B
C
D
E
Problem 8 (5 pts): Which arrow best indicates the direction of the change in the comet’s momentum from point A to point B?
CIRCLE YOUR ANSWER:
A
B
C
D
E
Problem 9 (5 pts): You throw a ball to your friend (on Earth), and just after it leaves your hand, the
ball has a velocity of h3.0, 9.0, 0i m/s. The ball’s mass is 0.06 kg. Ignoring air resistance, what is the
velocity of the ball 0.4 seconds later?
A. h0, −3.92, 0i m/s
B. h0, −0.24, 0i m/s
D. h0.18, 0.31, 0i m/s
E. h3.0, 5.1, 0i m/s
C. h0, −0.59, 0i m/s
Problem 10 (5 pts): A cart on a long track has a fan attached to it, which causes a constant force on
the cart due to the air in the +x direction. At time t = 0, the velocity of the cart is h3, 0, 0i m/s. At time
t = 3.0 seconds, the velocity of the cart is h8, 0, 0i m/s. How far did the cart move during this 3.0 second
time interval?
A. 1.8 m
D. 24.0 m
B. 7.5 m
C. 9.0 m
E. 16.5 m
+y
+x
Problem 11 (5 pts)The diagram above shows a block attached to a spring with a stiffness of 3.4 N/m.
The relaxed length of the spring is 15 cm and its current length is 10 cm. What is the vector force that
the spring exerts on the block?
A. h−0.34, 0, 0i N
D. h0.17, 0, 0i N
B. h0.51, 0, 0i N
C. h−0.51, 0, 0i N
E. h−0.17, 0, 0i N
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Problem 12 (15 pts)A 0.035 kg block is attached to a vertically mounted spring with stiffness of 15 N/m
and a relaxed length L0 = 0.30 m. The length is L = 0.24 m, and the block is moving upward at 1.9 m/s.
(a, 5 pts) What is the net force acting on the block? Express your answer as a three-component
vector.
y
L0
L
x
z (out of page)
(b, 5 pts) What is the new velocity of the block 0.01 seconds after the instant shown in the diagram?You
may assume the net force is approximately constant during this time interval. Express your answer as
a three-component vector.
(c, 5 pts) What is the final position of the block 0.01 seconds after the instant shown? Express your
answer as a three-component vector. (Justify any approximations you make.)
Problem 13
planet of mass
2.0 × 1023 kg is in orbit
around a star of mass
7 × 1031 kg. The
(15 pts)A
planet is at 4.0 × 1012 , −7.0 × 1012 , 0 m and the star is at −3.0 × 1012 , 2.0 × 1012 , 0 m.
(a, 8 pts) What is the gravitational force vector on the planet due to the star? Show all steps in your
work and express your answer as a three-component vector.
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Problem 13, continued
(b, 7 pts) What is the vector change in momentum of the planet after 3 days (or 72 hours)? You may
assume the force is approximately constant. Start from a fundamental principle. Show all steps in
your work.
Problem 14 (15 pts) You throw a 0.6 kg rock into the air. At the instant it leaves your hand, it’s velocity
is h0.4, 3.5, 0i m/s and it’s position is h0, 1.2, 0i m. (the positive y-axis is vertical, the x-axis horizontal.
Ignore air resistance.)
(a, 8 pts) What is the rock’s momentum 0.30 seconds after it leaves your hand? Start from a fundamental principle or definition (or else you will not receive full credit). Express your answer
as a three-component vector.
(b, 7 pts) What is the rock’s position 0.30 seconds after it leaves your hand? Start from a fundamental
principle or definition (or else you will not receive full credit).
Express your answer as a
three-component vector.
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