Download 006 Final: Question Outline Format

Student name:…………………………………………………
Student ID:……………………………..
Section:……………..
Teacher’s name:………………………………………………
Dawson College
Introduction to College Physics
912-017-94, 203-006-03, 203-005-03
FINAL EXAMINATION
Thursday, December 14, 2006, 2:00 pm – 5:00 pm
This exam is divided in three parts:
Part I: Problems. Please solve all six (6) problems. Show all your reasoning. If a formula is
not in the formula sheet, it must be derived. Answer directly on the question sheet. A second
blank page is provided with each page, if extra space is needed. 10 points each.
Part II: Multiple Choice Questions: Circle the appropriate answer (the letter only) for the
following quantitative multiple choice questions. You may answer 8 out of 10 questions. Space
is provided to carry out your work. Only the answer will be considered for marks, not the
reasoning. Clearly rule out the two questions you chose not to answer. 2.5 points each.
Part III: Conceptual questions. Circle the appropriate answer (the letter only) for the following
conceptual multiple choice questions. You may answer 10 out of 12 questions. Space is
provided to carry out your work. Only the answer will be considered for marks, not the
reasoning. Clearly rule out the two questions you chose not to answer. 2 points each.
Formulae and constants are given on the last page
INSTRUCTIONS
1. The time allotted for this examination is three hours.
2. Answer directly on the sheets of this package. If you need additional space
write on the back.
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3. Use g = 9.8 m/s .
4. You may detach the formula sheet from this package.
5. Write your name and the name of your teacher on the top of this page.
6. When finished, make sure this entire package and the formula sheet are
returned to your instructor.
Good luck! ☺
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Part I: Long Answer Questions
Part I: Please solve all six (6) problems. Show your reasoning to obtain full
marks. If a formula is not on the formula sheet, it must be derived.
1. Mr. Wilberforce is coasting to a stop on his skateboard. He travels from x0 = +83.00 m to
x = −37.00 m , where he stops, taking 60.0 s. His acceleration is constant.
(a)
(b)
(c)
(d)
(e)
What was the x-component of his average velocity?
What was the x-component of his initial velocity?
What was the x-component of his acceleration?
Draw the graph of v x as a function of time over the 60.0s interval.
From your graph in part “d”, determine ∆x . Does your answer agree with the given data? (It
must!)
2. A politician is launched horizontally at 1.80 m/s from the top of a 25.0 m tall building.
(a) How long after launch will the politician “arrive” at the ground?
(b) How far from the bottom of the building is his landing point?
(c) What is his final velocity? State magnitude and direction.
3. A 4.00 kg mass is hanging from the ceiling by a rope, as shown. You are holding the mass stationary
by a string. In this situation the rope makes an angle θ = 37.0o with the vertical.
(a) What is the vertical component of the tension in the rope?
(b) What force does the rope exert on the mass? State magnitude and direction.
(c) What is the tension in the string you are holding?
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4. Two gray boxes, one of mass m1 = 25 kg and the other of mass m2 = 40 kg, connected by a piece of
string, are pulled across a frictionless, level floor by a 120 N force acting at 35° above horizontal.
(a) Draw a free body diagram showing all of the forces
(b) Find the acceleration of the boxes
(c) Find the tension in the string joining the boxes.
5. Bruce the Shark is trying to steal a crate of tuna.
(a) The crate is moving with a constant speed to the right. What is the net force vector acting on the
crate?
(b) The crate has a mass of 200 kg, and Bruce is pulling with a force of 1000 N at an angle of 30°
above the horizontal. What normal force does the floor exert on the crate?
(c) Considering your answers to parts “a” and “b”, what is the coefficient of kinetic friction
between the crate and the floor?
(d) What net force does the floor exert on the crate? State magnitude and direction.
6. A 325 N force accelerates a 50.0 kg crate, initially at rest, along a horizontal frictionless surface for a
distance of 20.0 m as shown in the figure.
(a)
(b)
(c)
(d)
(e)
Draw a free-body diagram for the crate as it slides.
What is the final speed of the crate after the 20.0 m displacement?
How much work is done on the crate in this same interval?
What is the average power delivered by the applied force?
Suppose the surface now becomes rough, what coefficient of friction would be required to keep
the crate moving at constant speed under the action of the 325 N force?
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Part II: QUANTITATIVE MULTIPLE CHOICE
Please answer eight (8) out of the following 10 questions. Circle the correct
choice. Clearly rule out the two questions you chose NOT to answer.
Choose the ONE alternative that best completes the statement or answers the question.
1. The density of water is 1g/cm3. What is the density of water in kg/m3?
a)
b)
c)
d)
1 kg/m3
10 kg/m3
100 kg/m3
1000 kg/m3
2. A car starting from rest moves with a constant acceleration of 2 m/s2 for 10 s, then travels a certain
distance with constant speed for another 10 s, and then finally slows to a complete stop over a fnal
10 s interval with a constant acceleration of -2 m/s2. In total, how far does the car travel?
a)
b)
c)
d)
e)
300 m
100 m
400 m
200 m
500 m
G
G
G
G
G
G
3. In the figure, vectors B and C are shown. If D = B − C , the magnitude of D is closest to:
a)
b)
c)
d)
e)
8.0
3.2
9.2
5.3
6.6
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4. A net force F is required to give an object with mass m an acceleration a. If a net force 6F is applied
to an object with mass 2m, what is the acceleration on this object?
a)
b)
c)
d)
a
2a
3a
4a
5. A force of 86.6 N along East is applied on box placed on a frictionless surface. Two equal forces of
magnitude 50 N but acting in different directions are applied to keep the box in equilibrium. What is
the angle between the two equal forces?
a)
b)
c)
d)
1200
900
600
300
6. Two men together can exert a maximum force of 700 N on a box. However, when they pull the box in
the opposite directions, the net force is only 100 N. What will be the magnitude of the force if the
men apply their forces perpendicular to each other?
a)
b)
c)
d)
400 N
500 N
600 N
800 N
7. A 12 kg crate is pushed up an incline from point A to point B as shown in the figure. The height of
the points A and B from the ground are given in the figure. What is the change in the gravitational
potential energy of the crate?
a)
b)
c)
d)
e)
+ 590 J
- 590 J
+1200 J
- 1200 J
+ 60 J
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8. A 1.0 kg flashlight falls to the floor. At the point during its fall when it is 0.70 m above the floor, its
potential energy exactly equals its kinetic energy. How fast is it moving?
a)
b)
c)
d)
e)
45 m/s
3.7 m/s
9.8 m/s
6.9 m/s
14 m/s
9. A 4.0 kg box of fruit slides 8.0 m down a ramp, inclined at 300 from the horizontal. If the box slides
at a constant velocity of 5.0 m/s, the work done by gravity is
a)
b)
c)
d)
e)
zero
- 0.16 kJ
+ 0.16 kJ
+ 78 J
- 78 J
10. A roller-coaster car is moving at 20 m/s along a straight horizontal track. What will its speed be after
climbing the 15 m hill shown in the figure if the friction is negligible?
a) 17 m/s
b) 7 m/s
c) 5 m/s
d) 10 m/s
e) 14 m/s
Reminder: Did you indicate the two questions you chose not to answer?
I have omitted questions ................. and …………..
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Part III: QUALITATIVE MULTIPLE CHOICE
Circle the appropriate answer for the following conceptual multiple choice questions. You may
answer any TEN (10) of the 12 questions. Clearly rule out the
NOT to answer.
two questions you chose
Choose the ONE alternative that best completes the statement or answers the question.
1. Einstein's famous equation, E = mc2, describes the relationship between matter and energy. Given that “m” is mass
and “c” is the speed of light, the unit for “E” is
a)
b)
c)
d)
e)
m/N
kg.m/s2
m2/s2
N/m
N·m
2. A particle travels along a curved path between two points P and Q as shown. The displacement of the particle does
not depend on
a)
b)
c)
d)
e)
the location of P.
the location of Q.
the distance traveled from P to Q.
the shortest distance between P and Q.
the direction of Q from P.
3. A golf ball is hit at an angle of 300 from the horizontal with a speed of 20 m/s. There is no air resistance. Which of
the statements is true while the ball is in the air?
a)
b)
c)
d)
The net force on ball is always downward.
The net force on ball is upward when it is going up and downward when it is going down.
There is a horizontal force to keep the ball traveling horizontally.
The net force on ball is always upward.
4. The graph plots the velocity of two cars (A and B) along the same straight road. Which car reverses direction?
a)
b)
c)
d)
e)
both cars A & B
insufficient information
neither car A nor B
Car B
Car A
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5. Complete the following statement: The term net force most accurately describes
a)
b)
c)
d)
e)
the mass of an object
the inertia of an object.
the quantity that causes displacement.
the quantity that keeps an object moving.
the quantity that changes the velocity of an object.
6. Two forces act on a hockey puck. For which orientation of the forces will the puck acquire an acceleration with the
largest magnitude?
e) The magnitude of the acceleration will be the same in all four cases shown above.
7. An object moves in the eastward direction at constant speed. A net force directed northward acts on the object for
5.0 s. At the end of the 5.0 second period, the net force drops to zero newtons. Which one of the following
statements is necessarily true?
a)
b)
c)
d)
e)
The object will be moving eastward when the force drops to zero newtons.
The final velocity of the object will be directed north of east.
The change in the velocity of the object will be directed north of west.
The direction of the object's acceleration depends on how fast the object was initially moving.
The magnitude of the object's acceleration depends on how fast the object was initially moving.
8. In a plot of the displacement (x) vs. applied force (F) for an ideal elastic spring. The slope of the curve would be
a)
b)
c)
d)
the reciprocal of the spring constant.
the acceleration of gravity.
the reciprocal of the acceleration of gravity.
the spring constant.
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9. An apple of 1 kg, close to the surface of the earth, is falling on the surface of the earth. Which statement is true?
a)
b)
c)
d)
The force by the apple on the earth is less than 9.8 N.
The force by the apple on the earth is equal to 9.8 N
The force by the apple on the earth is more than 9.8 N
The force by the earth on the apple on is equal to 1.0 N
10. For the following situations, choose one in which there is zero net work done on the object in question?
a)
b)
c)
d)
e)
A ball rolls down an inclined plane.
A physics student stretches a spring.
A projectile falls toward the surface of Earth.
A box is pulled across a rough floor at constant velocity.
A child pulls a wagon across a rough surface causing it to accelerate.
11. You and your friend want to go to the top of the Eiffel Tower. Your friend takes the elevator straight up. You decide
to walk up the spiral stairway, taking longer to do so. Compare the gravitational potential energy (U) of you and your
friend, after you both reach the top.
a)
b)
c)
d)
Your “U” is greater than your friend's “U”, because you traveled a greater distance in getting to the top.
Your friend's “U” is greater than your “U”, because she got to the top faster.
Both of you have the same amount of potential energy.
It is impossible to tell, since the times and distances are unknown
12. You throw a ball straight up. Compare the sign of the work done by gravity while the ball goes up and with the sign
of the work done by gravity while it goes down.
a)
b)
c)
d)
Work up is negative, and the work down is positive.
Work up is positive, and the work down is negative.
Work up is negative, and the work down is negative.
Work up is positive, and the work down is positive.
Reminder: Did you indicate the TWO questions you chose NOT to answer?
I have omitted questions ................. and …………..
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Formulae Sheet
Introduction to College Physics
912-017-94, 203-006-03, 203-005-03
Differences
Definitions
Constant acceleration
∆ t = t − t0
∆x = x − x0
∆v = v − v0
s = d ∆t
v = ∆x ∆ t → x = x0 + v t
a = ∆v ∆ t → v = v0 + a t
x = x0 + v0 t + 12 at 2
Vectors
C = C +C
2
y
C x = C cosθ
vx2 = vx20 + 2ax ∆ x
x = x0 + v x 0 t + 12 a x t 2 & vx = v x 0 + ax t
G
C = C x xˆ + C y yˆ
2
x
v = (v + v0 ) 2
&
y = y0 + v y 0 t + 12 a y t 2 & v y = v y 0 + a y t
θ = tan (C y C x )
C y = C sin θ
−1
&
Two Dimensional Motion
Newton’s Laws
1st Law:
G
G
G G
Fnet = 0 N ⇒ a = 0 m/s 2
2nd Law:
G
G
∑F = ma
G
G
F1 on 2 = −F 2 on 1
Alternative notation:
kinetic: f k = µk
Friction (textbook notation)
kinetic: f k = µk N
static:
3rd Law:
i
FN
static: f s ≤ µs FN
f s ≤ µs N
Work & Energy
W = F||d = ( F cosθ ) d
1
2
m v 2 + U = 12 m v02 + U 0
K = 12 mv 2
Wnet = ∆K
E = K +U
U spring = 12 k x 2
(Fspring )x = −k x
U gravity = m g y
conservative : ∆E = ∆K + ∆U = 0 J
nonconservative : ∆E = ∆K + ∆U = Wnc
P = W t = F v cosθ
------------------------------------------------------------------------------------------------------------------------------------------------------------------
If
ax
2
(− b ±
+ bx + c = 0 , then x =
b 2 − 4ac
2a
)
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