Term 1 Exam - December 18, 2015

Name:

Student Number:

Bamfield Number:

Questions 1-20: Multiple Choice: 1 point each

Questions 21-26: Long answer: 24 points total

Multiple choice answers:

Formula sheet at the back

(you can remove it)

No droids are permitted during the

examination, except for Sharp EL-

series immobile calculational droids.

Your Jedi mind tricks will not work

on this examination.

Use The Force! (where appropriate)

Question 1: Yoda uses The Force to lift Luke’s

If the ship rises out of the water at a constant velocity, we can say that the net

force on the ship (including the force due to The Force) just before it leaves the

water is

a) upwards

b) downwards

c) equal to zero

d) cannot be determined

Question 2: The picture above represents the position of a

right to left at equal time steps. The arrow indicates the positive x direction. Which of

the graphs below best represents the object’s x

Yoda uses The Force to lift Luke’s X-wing fighter out of the swamp.

If the ship rises out of the water at a constant velocity, we can say that the net

g the force due to The Force) just before it leaves the

The picture above represents the position of a Tie Fighter

at equal time steps. The arrow indicates the positive x direction. Which of

the graphs below best represents the object’s x acceleration vs time?

wing fighter out of the swamp.

If the ship rises out of the water at a constant velocity, we can say that the net

g the force due to The Force) just before it leaves the

Tie Fighter moving from

at equal time steps. The arrow indicates the positive x direction. Which of

Question 3: A Storm Trooper starts at position -1 m

along the x-axis and moves with the x-velocity shown.

At what time is his position x=0?

A) 2 s B) 2.5 s C) 3 s

D) 3.5 s E) 4 s F ) 4.5 s

G) 5 s

Question 4: Two peas with the same mass and velocity fly through space. One

bounces off the Death Star with mass M and one bounces off a Tie Fighter with mass

m << M. When the peas bounce off they both have the same final velocity. What can

we say about the momentum transferred to the Death Star vs The Tie Fighter?

A) The peas transferred the same momentum the both the Death Star and the

Tie Fighter.

B) The pea transferred more momentum to the Death Star.

C) The pea transferred more momentum to the Tie Fighter.

Question 5: A rock is thrown off a cliff on a moon with no atmosphere (i.e. no

air drag). What can we say about the rock’s momentum in the x (horizontal) and y

(vertical) directions?

A) Its momentum is conserved in both the x and y direction.

B) Its momentum is conserved in the x direction, but not the y direction.

C) Its momentum is conserved in the y direction but not the x direction.

D) Its momentum isn’t conserved in either the x or the y direction.

Time Height y (m)

0.00s 1.3059

0.01s 1.2703

0.02s 1.2350

0.03s 1.2000

Question 6: An Ewok’s vertical position is shown in the table above. We can say

that the net vertical force on the Ewok

A) is positive B) is negative C) is zero

Question 7: An object of mass m has position x(t) and velocity v(t). If F denotes

the net force on the object, which of the following are true? In each case, b and C

are constants, independent of time.

A) F/m = - b t implies that v = C

B) F/m = - b x implies that v = C

C) F/m = - b v implies that v = C

D) Both A and B

E) All of the above

F) None of the above

Question 8: The potential energy for a particle in some region is shown in the

graph above. The particle has a turning point at x

kinetic energy of 3 J at x = 3 mm, what is the particle’s total energy?

A) 3 J

B) 2 J

C) 1 J

D) 0 J

E) -1 J

F) -2 J

G) -3 J

Question 9: Two identical springs sit next to each other. One is at its equilibrium

length, and the other is compressed. What can we say about the

the springs if the springs have the same temperature

A) The springs have the same mass.

B) The compressed spring is more massive than the uncompressed spring.

C) The compressed spring is less massive than the uncompressed spring.

D) You can’t say any of these for certain.

An object of mass m has position x(t) and velocity v(t). If F denotes

the net force on the object, which of the following are true? In each case, b and C

are constants, independent of time.

b t implies that v = C – b t2/2

s that v = C – b x2/2

b v implies that v = C – b v2/2

The potential energy for a particle in some region is shown in the

particle has a turning point at x = 6 mm. If the particle has a

kinetic energy of 3 J at x = 3 mm, what is the particle’s total energy?

Two identical springs sit next to each other. One is at its equilibrium

length, and the other is compressed. What can we say about the exact mass

if the springs have the same temperature?

The springs have the same mass.

ring is more massive than the uncompressed spring.

The compressed spring is less massive than the uncompressed spring.

t say any of these for certain.

An object of mass m has position x(t) and velocity v(t). If F denotes

the net force on the object, which of the following are true? In each case, b and C

The potential energy for a particle in some region is shown in the

= 6 mm. If the particle has a

Two identical springs sit next to each other. One is at its equilibrium

masses of

ring is more massive than the uncompressed spring.

The compressed spring is less massive than the uncompressed spring.

Question 10: Two Imperial Star Destroyers, each with proper length 1200m

pass each other with relative speed v = 3/5c. In the frame of reference of one of

these ships, how much time passes between the time when the fronts pass each

other and the time when the backs pass each other?

A) 1200 m/c B) 1500m/c C) 2000m/c D) 2100 m/c E) 3500 m/c

Question 11: In the previous question, we can say that for observers on the Star

Destroyer shown at the left, clocks at the front of the other Star Destroyer

A) are observed to tick slower than clocks at the back

B) are observed to tick at the same rate as clocks at the back

C) are observed to tick faster than clocks at the back

Question 12: Some comets travel on highly elliptical orbits, passing very close to

the Sun on one side of the orbit. Compared with the farthest point on the orbit,

we can say that at their closest point to the Sun, these comets have

A) more angular momentum but the same kinetic energy

B) more kinetic energy but the same angular momentum

C) the same angular momentum and kinetic energy

D) more kinetic energy and more angular momentum

E) more kinetic energy but less angular momentum

Question 13: Before it was destroyed by the Death Star, the length of a day on planet

Alderaan was 16 hours. If the debris from the planet’s destruction forms a solid sphere

10 times the radius of the original planet and if we assume the debris continues to

rotate together with some angular speed, how long does it take for the debris cloud to

rotate once around?

A) 4 hours B) 1.6 hours C) 16 hours D) 160 hours

E) 256 hours F) 1600 hours

Question 14: The rebel forces take down an At-At Imperial Walker by immobilizing

its legs with a cable. If the walker’s center of mass height changes by �� as it falls,

and the moment of inertia about the pivot point is I, we can say that the walker’s

angular velocity when it hits the ground is given by

A) ��� �� B) ��� ��

C) ��� �� D)

�� �� E)

�� ��

Question 15: Each of the light-sabers below has the same mass. If each is swung with

the same angular velocity (with the bottom end of the black handle fixed in place),

which will have the largest kinetic energy?

D) All will have the same kinetic energy.

Question 16: The pressure and volume of a

expands slowly from point 1 to point 2. During the process, the temperature of the gas

A) Remains constant

D) Increases then decreases

Question 17: During the process

gas is

A) zero B) positive

Question 18: The two pistons above are filled with a monatomic gas and a

diatomic gas and compressed adiabatically. I

amount, what can you say about Push A vs. Push B if

change in temperature?

A) Push A is with more force.

B) Push B is with more force.

C) Both A and B are the same f

pressure and volume of a gas are shown on the plot above as it

expands slowly from point 1 to point 2. During the process, the temperature of the gas

B) Increases C) Decreases

E) Decreases, then increases

process above, we can say that the net heat that flows into the

C) negative D) cannot be determined

The two pistons above are filled with a monatomic gas and a

and compressed adiabatically. If the pistons both travel the same

u say about Push A vs. Push B if both gasses have the same

Push A is with more force.

Push B is with more force.

Both A and B are the same force.

are shown on the plot above as it

expands slowly from point 1 to point 2. During the process, the temperature of the gas

heat that flows into the

D) cannot be determined

The two pistons above are filled with a monatomic gas and a

f the pistons both travel the same

both gasses have the same

Question 19: Consider a non-

two molecules in a gas that are a distance

the molecules are on average a distance of

freely expand until the average distance between molecules is

happens to the temperature of the gas?

A) It increases.

B) It decreases.

C) It stays the same.

Question 20: When two systems are placed in

thermal contact, energy will be observe

from the left system to the right system

A) if this increases the entropy of the system on the

left.

B) if this moves the system towards a configuration

where the energies are equal on the two sides.

C) if the heat capacity of the left system is

D) if this increases the total number of available

microscopic configurations for the combined

system.

E) if and only if all of the above are true.

-ideal gas in a box. The potential energy between

two molecules in a gas that are a distance x apart is given by the graph above. If

the molecules are on average a distance of 7mm apart, and the gas is allowed to

average distance between molecules is 14 mm apart

of the gas?

When two systems are placed in

thermal contact, energy will be observed to flow

from the left system to the right system

if this increases the entropy of the system on the

if this moves the system towards a configuration

where the energies are equal on the two sides.

if the heat capacity of the left system is larger.

D) if this increases the total number of available

microscopic configurations for the combined

E) if and only if all of the above are true.

ideal gas in a box. The potential energy between

apart is given by the graph above. If

, and the gas is allowed to

14 mm apart, what

Question 21: Explain why special relativity suggests that conservation of mass is not a

fundamental law. Give an example of a process where the total mass of objects in a

system increases and one where it decreases. (4 points)

Question 22: (4 points) Travelling with an initial speed of v = 30km/s, the Millenium

Falcon (mass 105 kg) gets caught in the tractor beam of an Imperial Star Destroyer.

The beam exerts a force proportional to the Falcon’s speed, in the opposite direction to

the velocity:

F = - C v

where C = 2 × 105 kg/s.

a) According to Euler’s method applied for a single step of δt = 0.1s, what is the

Falcon’s speed and displacement δx after 0.1s?

b) Determine the exact velocity as a function of time v(t) and use this to determine the

exact velocity after 0.1s. By what percentage was your result in part a) off?

Question 23: Deep within the hyperdrive engine of the Millenium Falcon, a pion

(an unstable particle with mass m1 =2.41x10-28

kg) decays into a positron and an

electron, each with mass m2=9.11x10-31

kg (and identical in every way but with

opposite charge.) If the pion is travelling at v1 = 3/5c, what is the angle θ that the

electron and positron travel relative to the pion’s initial direction? (4 points)

Question 24: Darth Vader orders that the Death Star

(mass 1018

kg, radius 60km) should destroy the

moon of Endor, home of the Ewoks. However, the

ship needs to be rotated by an angle of θ = 0.8 rad

before its weapon can fire on the moon. The ship is

initially rotating with angular velocity ω = 10-3

rad/s.

To speed up the rotation, a pair of thrusters located

at opposite sides of the ship fire, exerting forces in

the directions shown, each with time-dependent

magnitude

F(t) = (9.6 ×1016

N ) t .

If the thrusters turn off after 200s, how long after

that will the Death Star be able to destroy Endor (if

the rebels don’t intervene.) Assume the Deaths Star

is a solid sphere. (4 points)

Question 25: The PV diagram above shows a thermodynamic cycle being

performed on the cylinder of gas shown above

on the Wookie planet).

a) How is the net work done on the gas in the cycle related to properties of the

diagram above? (1 point)

b) For each process in the cycle

on the diagrams below. In space next to the drawing, explai

the cylinder to perform the process. Draw anything that might be helpful for your

explanation. In each case, say whether Q, W, and

zero, and explain your answers.

1 → 2

diagram above shows a thermodynamic cycle being

performed on the cylinder of gas shown above (used as part of a vehicle engine

a) How is the net work done on the gas in the cycle related to properties of the

b) For each process in the cycle, draw the final and initial positions of the piston

pace next to the drawing, explain what you must do to

to perform the process. Draw anything that might be helpful for your

In each case, say whether Q, W, and ΔE are positive, negative, or

zero, and explain your answers. (3 points)

diagram above shows a thermodynamic cycle being

(used as part of a vehicle engine

a) How is the net work done on the gas in the cycle related to properties of the

of the piston

n what you must do to

to perform the process. Draw anything that might be helpful for your

E are positive, negative, or

2 → 3

3 → 1

Question 26: Luke, Leia, Han, and Chewbacca are stuck

in a trash compactor on the Death Star. The compactor

works as a giant piston, with a moveable insulating wall

that compresses the trash (and any unlucky rebels) as heat

is added to the gas in the piston (cV = 5/2 R). If the graph

on the right shows the net outside force on the wall from

the trash and outside pressure as the trash is being

compressed, if the initial temperature of the gas in the

chamber is 300K, and if the initial chamber dimensions

are as shown in the diagram, how much heat needs to be

added to compress the trash by Δx = 3m? (4 points)

FORMULA SHEET

v = dx/dt a = dv/dt

p ≈ mv (if v ≪ c)

F = dp/dt

|F| = C v2, |F| = μ N, |F| = mg, |F| = kx Fx = -dU/dx F = G M m/R

2

E = mgh E = ½ mv2

E = ½ k (Δs)2 Δ = �� ∙ Δ��

L = I ω L = M vperpR = M vRperp ω = dθ /dt α = dω /dt

τ = dL/dt τ = FperpR = F Rperp E = ½ I ω2

a = v2/R ω = v/R

I = M R2 (ring, point mass), ½ M R

2 (solid disk, cylinder), 2 5� M R

2 (solid sphere),

1 3� M L2 (stick from one end), 1 12� M L

2 (stick through middle),2 3� M R

2 (hollow sphere)

γ = (1 - v2/c

2)

-1/2 vγ = c (γ2

- 1)1/2

�� = γ m �� E = γmc2 v/c

2 = p/E E

2= p

2c

2+ m

2c

4

PV = nRT = NkbT R = 8.31 J/(mol K) kb =1.38 × 10-23

J/K

ΔE = Q + W ΔE = n CVΔT CV = 3/2 R (ideal monatomic gas)

W = -∫ PdV

T = (2/3kb)Eavg P = (2/3)(N/V)Eavg

1 light year = c × 1 year c ≈ 3 × 108m/s NA = 6.02 × 10

23

G = 6.67 × 10-11

N m2/kg

2

vsound = 340 m/s g = 9.8 m/s2