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Physics 1A Winter 2020 Final Exam Cover Sheet
INSTRUCTIONS:
Right now, as soon as you get this part of the exam:
1. Fill in this cover sheet completely (which you should have). You need to upload this page separately.
2. Write your response to each problem on a separate paper.
3. Count the pages of the exam. There should be 11 pages in total with probelms and questions on page 2 -
9. If you find this is not the case, email me IMMEDIATELY. It is your responsibility to have a complete exam.
Remember:
* You are only allowed to consult your notes, homework, exams and textbook, and you are encouraged to do
so during the exam. Do not try to search for an answer online. Follow all instructions. If you are asked to
start your response in a certain way, you have to follow it. For multiple choice questions, you have to
explain. In general, an answer without an explanation or steps shown will not receive any credit. *
Don’t Cheat!
We automatically report anyone suspected of cheating to Student Judicial Affairs.
I certify by my signature below that I have read the above instructions and that I will abide by the UC Davis Code
of Academic Conduct. This includes
· not copying from anyone else’s exam
· not letting any other student copy from my exam
· not collaborating with anyone
· not consulting any unauthorized resource
· not discussing this exam with any student who has not yet taken it, nor providing any information, written or
oral, that might get to a student who has not yet taken it
Name (Print Clearly):
Last First
Student ID:
Signature:
| | | | page 2
Last Name First Name First three initials of last name
Grade:
1. (5 points) Mary has written an equation describing the torque (τ ) on an object. However, one factor, (?), is
missing from the equation,
τ = pa(?) ,
where p is the magnitude of the momentum of the object, and a is the magnitude of the acceleration of the
object. In order to have the dimensions/units to work out, (?) has to be: (There is only one answer. Show all
your work to explain your answer.)
I. t, the time since t = 0,
II. d, diameter of the object, or
III. v, speed of the object.
2. (5 points) A driver applies the brakes on a car traveling at 60.0 mph, which we will take it as 26.8 m/s. The
car then stops after traveling for 40.0 m under such a constant acceleration. What is its speed when it has
traveled for 20.0 m after applying the brakes?
26.8 m/s v = 0
20.0 m 20.0 m
v = ?
| | | | page 3
Last Name First Name First three initials of last name
Grade:
3. (5 points) Three identical rocks, rock X, rock Y, and rock Z are thrown with the same speed but in different
directions as shown. If the effect from air resistance is negligible, determine if the following statements are
true or false. Explain your choices.
I. They all hit the ground at the same time. True / False
II. They all hit the ground with the same speed. True / False
III. They all hit the ground with the same vertical component of their velocity. True / False
4. (5 points) Two blocks of masses, m and M, sitting one on top of each other are placed on a smooth frictionless
table as shown. However, the surface between m and M is not smooth. In a stunt, a person applies a force
(F~A) on M towards the right such that M is removed from the table while m remains on the table although
being slightly displaced. Draw two separate free body diagrams for m and M. Is the friction between m and
M kinetic or static? Hint: Look at Problem 4 on midterm 1. What is the difference here?
Free body diagram of m Free body diagram of M
Is the friction between m and M kinetic or static? Briefly explain.
| | | | page 4
Last Name First Name First three initials of last name
Grade:
5. (5 points) A person (mass = 70.0 kg) stands on an elevator which is acclerating upwards at 20.0 m/s2
. Draw a
free body diagram for the person and find the apparent weight he is experiencing. Hint: Look at L6.pdf about
apparent weight.
Free body diagram of the person
6. (5 points) A player throws a basketball straight up at 5.0 m/s from 2.0 m above the ground. It only reaches a
highest height of 3.0 m above the ground, indicating there is a presence of air resistance. From the moment
where the basketball leaves the player’s hand to the moment where the basketball is at the maximum height,
state whether the following quantities are negative, positive, or zero. Explain all your choices. “∆” is defined
as final minus initial.
I. ∆KE, the change of kinetic energy of the basketball: negative / positive / zero
II. ∆P EG, the change of potential energy of the basketball and the Earth: negative / positive / zero
III. WNC, the work done by non-conservative forces: negative / positive / zero
IV. WG, the work done by gravitational force: negative / positive / zero
| | | | page 5
Last Name First Name First three initials of last name
Grade:
7. (5 points) A solid disk of mass 10.0 kg and radius 50 cm is spun from rest by two forces (F~A and F~B) shown.
It is fixed at its center (x). (i) Find the net torque on the disk about its center taking the counter-clockwise
direction as positive. (ii) Find the angular acceleration of the disk. You can safely ignore the normal force and
the weight as they have no contribution to the net torque. Hint: Look at Problem 5 on midterm 2. Can you do
the same set of calculations for a solid disk?
8. (5 points) A table tennis ball moving to the North is also spinning such that it deviates to the West shown in the
top view (left). If we go into the table tennis ball’s rest frame, the wind will be flowing towards the ball as shown
on the right. On the figure to the right, (i) indicate the direction of the spin, (ii) draw at least three streamlines
on each side of the ball, and (iii) indicate which side of the ball has a higher/lower pressure. You may either
print this page or just draw your response on a paper.
Top View Top View (ball’s rest frame) Wind direction
Last Name First Name First three initials of last name
Grade:
9. Ball A traveling to the right at 5.0 m/s impacts a group of two identical balls (B and C) which are both initially
at rest (shown on the left). After the collision, all three balls are moving, and their speeds and directions are
shown on the right. All balls have the same mass of 1.0 kg. The +x and +y directions are defined for you.
a. (6 points) In terms of the quantities given, write down two momentum conservation equations; one for the
x-component and one for the y-component of the balls’ momenta.
b. (4 points) How many independent unknowns are there in part (a)? What are they? They should be very
obvious!
c. (6 points) Solve for the unknowns in part (a).
d. (4 points) Is the collision elastic? Justify your answer by calculating the total kinetic energy before and after
the collision.
| | | | page 7
Last Name First Name First three initials of last name
Grade:
10. These questions test your general understanding of the entire course.
a. (6 points) State three (and only three) distinctively different conservation laws you learned this quarter.
First state the of the conservation laws in words, then present it in a form of an equation (before) = (after).
Finally, write down the condition that needs to be satisfied for the quantity to be conserved.
Example:
xxx is conserved
xxxbef ore = xxxaf ter
This is true when ...
b. (8 points) What are the three important elements of the Newton’s Third Law? Draw two free body diagrams
of the same situation you find appropriate and demonstrate all three elements of the Newton’s Third Law
in that situation.
c. (6 points) Name one energy system we learned that cannot be negative. Explain why it cannot be negative.
Name one energy system we learned that can be negative. Explain why it is fine for it to be negative.
| | | | page 8
Last Name First Name First three initials of last name
Grade:
11. A ladder of mass mL = 15.0 kg and length L = 5.0 m, which we will assume it is a uniform beam, is leaning
against the wall on the ground. The wall is smooth and frictionless, but the ground is rough. A person
(mp = 40.0 kg) is standing at rest at a distance of 3.0 m above the ground on the ladder. The entire system
is at rest. This problem is very similar to the ladder problem on page 7 of L13.pdf. Follow the prompts and
you will find all the forces acting on the ladder. Recall the static conditions are ΣF~ = 0 and Στ = 0.
a. (8 points) Draw a free body diagram of the ladder+person directly on top of the above diagram.
b. (4 points) Find the vertical component of the force on the ladder by the ground. State which static condition
you are using.
c. (4 points) Find the horizontal component of the force on the ladder by the ground. State which static
condition you are using.
d. (4 points) Finally, find the normal force on the ladder by the wall. State which static condition you are
using.
| | | | page 9
Last Name First Name First three initials of last name
Grade:
12. Water from a water tank flows continuously through a pipe and eventually flows out of a horizontal cylindrical
pipe of 1.0 cm in radius that is placed 2.0 m above the ground. The water level inside the water tank is
assumed to be static and maintained at 30.0 m above the ground. Define point A at the water level inside the
tank, point B at the beginning of the cylindrical pipe, and point C at the end of the cylindrical pipe. Assume
no energy is lost due to non-conservative force. Report all pressure as the absolute pressure.
a. (5 points) Find the pressure at point B (PB). Explain. Hint: Point C is open to the atmosphere and the pipe
is unifom from point B to point C.
b. (5 points) Find the speed of the water at point B (vB). Hint: Find another point where you know the
pressure, fluid speed, and height to use the Bernoull’s equation.
c. (i) (5 points) By what percentage does one need to cover the area of the cylindrical pipe at point C such
that the speed of water at point C is five times than that at point B? That is vC = 5vB.
(ii) (5 points) Find the range of the water (R) if the pipe is covered at point C. Use only the kinematic
equations. Do NOT quote any results about the range in the available resource.
Useful Equations, Formulas, and Constants
Separate this sheet from the text packet. Do not turn it in.
Kinematics in 1D:
∆x = xfinal − xinitial = x − x0
average speed =
distance traveled
time elapsed
average velocity = ¯v =displacement
time elapsed =∆x∆t
instantaneous velocity = v = lim
∆t→0∆x∆t
average acceleration = ¯a =change in velocity
time elapsed =∆v∆t
instantaneous acceleration = a = lim
∆t→0∆v∆t
∆v = vfinal − vinitial = v − v0
v = v0 + at
x = x0 + v0t +12at2v2 = v20 + 2a(x − x0)v¯ =v + v02a = constant
Kinematics in 2D:
~r = x xˆ + y yˆ = (x, y)
~v = vx xˆ + vy yˆ = (vx, vy)
~a = ax xˆ + ay yˆ = (ax, ay)
~v = ~v0 + ~at
~r = ~r0 + ~v0t +12~at2~v2 = ~v02 + 2~ad(d = displacement in the direction of ~a)~a = constant
Forces:
gravity = weight = mg (downwards)
|F~
fr,s| ≤ µs|F~N |
|F~
fr,k| = µk|F~N |
F~
spring = −k~x
Circular Motion:
Energy:WF = Work = F~ · ~r
i = Wtotal
∆KE + ∆PE = Wnon-conservative
∆KE + ∆PE = 0
(When no non-conservative forces)
(1-dimensional elastic collision)
Angular Motion:
(Direction of ~τ given by right-hand rule)
L = Iω (Direction of L~ - right-hand rule)
Moments of inertia:
IPoint Mass = mr2
IHoop = mR2
ISolid Disk = ISolid Cylinder =12mR2
Physics 1A Winter 2020 Final Exam Cover Sheet
INSTRUCTIONS:
Right now, as soon as you get this part of the exam:
1. Fill in this cover sheet completely (which you should have). You need to upload this page separately.
2. Write your response to each problem on a separate paper.
3. Count the pages of the exam. There should be 11 pages in total with probelms and questions on page 2 -
9. If you find this is not the case, email me IMMEDIATELY. It is your responsibility to have a complete exam.
Remember:
* You are only allowed to consult your notes, homework, exams and textbook, and you are encouraged to do
so during the exam. Do not try to search for an answer online. Follow all instructions. If you are asked to
start your response in a certain way, you have to follow it. For multiple choice questions, you have to
explain. In general, an answer without an explanation or steps shown will not receive any credit. *
Don’t Cheat!
We automatically report anyone suspected of cheating to Student Judicial Affairs.
I certify by my signature below that I have read the above instructions and that I will abide by the UC Davis Code
of Academic Conduct. This includes
· not copying from anyone else’s exam
· not letting any other student copy from my exam
· not collaborating with anyone
· not consulting any unauthorized resource
· not discussing this exam with any student who has not yet taken it, nor providing any information, written or
oral, that might get to a student who has not yet taken it
Name (Print Clearly):
Last First
Student ID:
Signature:
| | | | page 2
Last Name First Name First three initials of last name
Grade:
1. (5 points) Mary has written an equation describing the torque (τ ) on an object. However, one factor, (?), is
missing from the equation,
τ = pa(?) ,
where p is the magnitude of the momentum of the object, and a is the magnitude of the acceleration of the
object. In order to have the dimensions/units to work out, (?) has to be: (There is only one answer. Show all
your work to explain your answer.)
I. t, the time since t = 0,
II. d, diameter of the object, or
III. v, speed of the object.
2. (5 points) A driver applies the brakes on a car traveling at 60.0 mph, which we will take it as 26.8 m/s. The
car then stops after traveling for 40.0 m under such a constant acceleration. What is its speed when it has
traveled for 20.0 m after applying the brakes?
26.8 m/s v = 0
20.0 m 20.0 m
v = ?
| | | | page 3
Last Name First Name First three initials of last name
Grade:
3. (5 points) Three identical rocks, rock X, rock Y, and rock Z are thrown with the same speed but in different
directions as shown. If the effect from air resistance is negligible, determine if the following statements are
true or false. Explain your choices.
I. They all hit the ground at the same time. True / False
II. They all hit the ground with the same speed. True / False
III. They all hit the ground with the same vertical component of their velocity. True / False
4. (5 points) Two blocks of masses, m and M, sitting one on top of each other are placed on a smooth frictionless
table as shown. However, the surface between m and M is not smooth. In a stunt, a person applies a force
(F~A) on M towards the right such that M is removed from the table while m remains on the table although
being slightly displaced. Draw two separate free body diagrams for m and M. Is the friction between m and
M kinetic or static? Hint: Look at Problem 4 on midterm 1. What is the difference here?
Free body diagram of m Free body diagram of M
Is the friction between m and M kinetic or static? Briefly explain.
| | | | page 4
Last Name First Name First three initials of last name
Grade:
5. (5 points) A person (mass = 70.0 kg) stands on an elevator which is acclerating upwards at 20.0 m/s2
. Draw a
free body diagram for the person and find the apparent weight he is experiencing. Hint: Look at L6.pdf about
apparent weight.
Free body diagram of the person
6. (5 points) A player throws a basketball straight up at 5.0 m/s from 2.0 m above the ground. It only reaches a
highest height of 3.0 m above the ground, indicating there is a presence of air resistance. From the moment
where the basketball leaves the player’s hand to the moment where the basketball is at the maximum height,
state whether the following quantities are negative, positive, or zero. Explain all your choices. “∆” is defined
as final minus initial.
I. ∆KE, the change of kinetic energy of the basketball: negative / positive / zero
II. ∆P EG, the change of potential energy of the basketball and the Earth: negative / positive / zero
III. WNC, the work done by non-conservative forces: negative / positive / zero
IV. WG, the work done by gravitational force: negative / positive / zero
| | | | page 5
Last Name First Name First three initials of last name
Grade:
7. (5 points) A solid disk of mass 10.0 kg and radius 50 cm is spun from rest by two forces (F~A and F~B) shown.
It is fixed at its center (x). (i) Find the net torque on the disk about its center taking the counter-clockwise
direction as positive. (ii) Find the angular acceleration of the disk. You can safely ignore the normal force and
the weight as they have no contribution to the net torque. Hint: Look at Problem 5 on midterm 2. Can you do
the same set of calculations for a solid disk?
8. (5 points) A table tennis ball moving to the North is also spinning such that it deviates to the West shown in the
top view (left). If we go into the table tennis ball’s rest frame, the wind will be flowing towards the ball as shown
on the right. On the figure to the right, (i) indicate the direction of the spin, (ii) draw at least three streamlines
on each side of the ball, and (iii) indicate which side of the ball has a higher/lower pressure. You may either
print this page or just draw your response on a paper.
Top View Top View (ball’s rest frame) Wind direction
Last Name First Name First three initials of last name
Grade:
9. Ball A traveling to the right at 5.0 m/s impacts a group of two identical balls (B and C) which are both initially
at rest (shown on the left). After the collision, all three balls are moving, and their speeds and directions are
shown on the right. All balls have the same mass of 1.0 kg. The +x and +y directions are defined for you.
a. (6 points) In terms of the quantities given, write down two momentum conservation equations; one for the
x-component and one for the y-component of the balls’ momenta.
b. (4 points) How many independent unknowns are there in part (a)? What are they? They should be very
obvious!
c. (6 points) Solve for the unknowns in part (a).
d. (4 points) Is the collision elastic? Justify your answer by calculating the total kinetic energy before and after
the collision.
| | | | page 7
Last Name First Name First three initials of last name
Grade:
10. These questions test your general understanding of the entire course.
a. (6 points) State three (and only three) distinctively different conservation laws you learned this quarter.
First state the of the conservation laws in words, then present it in a form of an equation (before) = (after).
Finally, write down the condition that needs to be satisfied for the quantity to be conserved.
Example:
xxx is conserved
xxxbef ore = xxxaf ter
This is true when ...
b. (8 points) What are the three important elements of the Newton’s Third Law? Draw two free body diagrams
of the same situation you find appropriate and demonstrate all three elements of the Newton’s Third Law
in that situation.
c. (6 points) Name one energy system we learned that cannot be negative. Explain why it cannot be negative.
Name one energy system we learned that can be negative. Explain why it is fine for it to be negative.
| | | | page 8
Last Name First Name First three initials of last name
Grade:
11. A ladder of mass mL = 15.0 kg and length L = 5.0 m, which we will assume it is a uniform beam, is leaning
against the wall on the ground. The wall is smooth and frictionless, but the ground is rough. A person
(mp = 40.0 kg) is standing at rest at a distance of 3.0 m above the ground on the ladder. The entire system
is at rest. This problem is very similar to the ladder problem on page 7 of L13.pdf. Follow the prompts and
you will find all the forces acting on the ladder. Recall the static conditions are ΣF~ = 0 and Στ = 0.
a. (8 points) Draw a free body diagram of the ladder+person directly on top of the above diagram.
b. (4 points) Find the vertical component of the force on the ladder by the ground. State which static condition
you are using.
c. (4 points) Find the horizontal component of the force on the ladder by the ground. State which static
condition you are using.
d. (4 points) Finally, find the normal force on the ladder by the wall. State which static condition you are
using.
| | | | page 9
Last Name First Name First three initials of last name
Grade:
12. Water from a water tank flows continuously through a pipe and eventually flows out of a horizontal cylindrical
pipe of 1.0 cm in radius that is placed 2.0 m above the ground. The water level inside the water tank is
assumed to be static and maintained at 30.0 m above the ground. Define point A at the water level inside the
tank, point B at the beginning of the cylindrical pipe, and point C at the end of the cylindrical pipe. Assume
no energy is lost due to non-conservative force. Report all pressure as the absolute pressure.
a. (5 points) Find the pressure at point B (PB). Explain. Hint: Point C is open to the atmosphere and the pipe
is unifom from point B to point C.
b. (5 points) Find the speed of the water at point B (vB). Hint: Find another point where you know the
pressure, fluid speed, and height to use the Bernoull’s equation.
c. (i) (5 points) By what percentage does one need to cover the area of the cylindrical pipe at point C such
that the speed of water at point C is five times than that at point B? That is vC = 5vB.
(ii) (5 points) Find the range of the water (R) if the pipe is covered at point C. Use only the kinematic
equations. Do NOT quote any results about the range in the available resource.
Useful Equations, Formulas, and Constants
Separate this sheet from the text packet. Do not turn it in.
Kinematics in 1D:
∆x = xfinal − xinitial = x − x0
average speed =
distance traveled
time elapsed
average velocity = ¯v =displacement
time elapsed =∆x∆t
instantaneous velocity = v = lim
∆t→0∆x∆t
average acceleration = ¯a =change in velocity
time elapsed =∆v∆t
instantaneous acceleration = a = lim
∆t→0∆v∆t
∆v = vfinal − vinitial = v − v0
v = v0 + at
x = x0 + v0t +12at2v2 = v20 + 2a(x − x0)v¯ =v + v02a = constant
Kinematics in 2D:
~r = x xˆ + y yˆ = (x, y)
~v = vx xˆ + vy yˆ = (vx, vy)
~a = ax xˆ + ay yˆ = (ax, ay)
~v = ~v0 + ~at
~r = ~r0 + ~v0t +12~at2~v2 = ~v02 + 2~ad(d = displacement in the direction of ~a)~a = constant
Forces:
gravity = weight = mg (downwards)
|F~
fr,s| ≤ µs|F~N |
|F~
fr,k| = µk|F~N |
F~
spring = −k~x
Circular Motion:
Energy:WF = Work = F~ · ~r
i = Wtotal
∆KE + ∆PE = Wnon-conservative
∆KE + ∆PE = 0
(When no non-conservative forces)
(1-dimensional elastic collision)
Angular Motion:
(Direction of ~τ given by right-hand rule)
L = Iω (Direction of L~ - right-hand rule)
Moments of inertia:
IPoint Mass = mr2
IHoop = mR2
ISolid Disk = ISolid Cylinder =12mR2