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Name: Student Number: Bamfield Number: Science One Physics Exam 1 December 14 th , 2016 Questions 1-18: Multiple Choice: 1 point each Questions 19-24: Long answer: 22 points total Multiple choice answers: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Bonus Bonus Formula sheet at the back (you can remove it) solutions A CA BA A B D B D C A A F B B B E

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Name: Student Number:

Bamfield Number:

Science One Physics Exam 1 December 14th, 2016

Questions 1-18: Multiple Choice: 1 point each Questions 19-24: Long answer: 22 points total

Multiple choice answers: 1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 Bonus Bonus

Formula sheet at the back (you can remove it)

solutions

A CA BA

A B D B D

C A A F B

B B E

Time Position 0.000s 4.123512 m

0.001s 4.124678 m 0.002s 4.125865 m

Question 1: Given the position data above, to how many decimal places can we be certain of the velocity between the times 0.00 s and 0.002 s? A) 1 decimal place. B) 2 decimal places. C) 3 decimal places. D) 4 decimal places. E) 5 decimal places. F) 6 decimal places.

Question 2: What can we say about the data shown in the graph above? A) The instantaneous velocity at 2 seconds is positive. B) The average velocity at 1 second is positive. C) The average velocity between 1 and 2 seconds is positive. D) More than one of the above is true.

Question 3: Two space salmon are travelling as shown above. Each has a mass of 1 kg. One is travelling at 3 m/s and the other at 4 m/s and they stick together. What can you stay about the magnitude of the final momentum? a) The final momentum is less than 7 kg m/s. b) The final momentum is equal to 7 kg m/s. c) The final momentum is greater than 7 kg m/s. d) Can’t tell because we don’t know if energy is conserved or not.

Question 4: Two pea shooters shoot peas at the same rate and velocity against two incoming space salmon with masses M > m. The peas all bounce off the space salmon with the same velocity. If v1 > v2, what can we say about the force that the peas exert on the space salmon? A) The force on salmon M is less than the force on salmon m. B) The force on salmon M is equal to the force on salmon m. C) The force on salmon M is greater than the force on salmon m.

Question 5: A small spaceship pulls a bigger, heavier spaceship, as shown above. What can you say about the net force exerted on each spaceship? A) The net force on the larger spaceship is greater than on the smaller spaceship. B) The net force on each spaceship is equal. C) The net force on the larger spaceship is smaller than on the smaller spaceship.

Question 6: The graph above shows the velocity as a function of time. If you were to use the Euler method starting from t = 0 with a time step of 1 seconds, what can you say about the estimate of your velocity at time t = 6 seconds? A) The estimated velocity will be higher than the actual velocity. B) The estimated velocity will be the same as the actual velocity. C) The estimated velocity will be lower than the actual velocity. Question 7: In outer space, a bullet is shot into a block of wood such that it gets stuck inside. What quantities are conserved in this collision? A) Linear momentum is conserved. B) Linear momentum and angular momentum are both conserved. C) Linear momentum, angular momentum, and mechanical energy are all

conserved.

Question 8: A particle moving to the right has a kinetic energy of 3 J at x = 3 mm. What is the particle’s turning point?

A) 13 mm B) 12 mm C) 8 mm D) 6 mm E) 1 mm

Question 9: When you catch a ball in your hand, what can you say about the work done by the force from your hand on the ball? A) The work is positive. B) The work is negative. C) The work is zero because of the equal and opposite force from the ball on your

hand.

Question 10: In order to reach all the houses on Christmas Eve Santa must travel at relativistic speeds. If the above picture represents how we see Santa, which of the following pictures best represents Santa in his frame? A) B) C)

D) E)

Question 11: The 12 days of Christmas takes 12 Earth days (1037000 seconds). Aliens on a spaceship passing through our solar system near the speed of light also want to partake in the 12 days of Christmas. How much time passes on a clock on their ship as they watch us celebrate the 12 days of Christmas? A) Less than 12 Earth days. B) 12 Earth days. C) More than 12 Earth days.

Question 12: If you lift a ball higher off the Earth’s surface, what can you say about the mass of the system that includes the ball and the Earth (and not you)? A) The system of the ball and the earth gets more massive. B) The system of the ball and the earth stays the same mass. C) The system of the ball and the earth gets less massive.

Question 13: Two cylinders with a small protrusions spin around at angular velocity ω. They hit the protrusions on two stationary cylinders, causing each of them to spin. If all of the cylinders have same mass, what can we say about the final angular velocities ω1 and ω2 of the cylinders? A) ω1 < ω2 B) ω1 = ω2 C) ω1 > ω2

Question 14: The graph above shows the angular acceleration of you spinning in a chair. If you are originally spinning at ω = 1 rad/s, at what time do you have zero angular velocity? A) 1 s B) 2 s C) 3 s D) 4 s E) 5 s F) 6 s G) 7s

Question 15: A wheel is attached to a spring with equilibrium length L, as shown above. To the right of the spring’s equilibrium position the floor has zero friction, so the wheel is free to slide. To the left, the floor has infinite friction, meaning the wheel is unable to slip and must rotate. If the spring stretched to a length 1.5L, then released, to what length will the spring compress? A) To a length less than 0.5L B) To a length equal to 0.5L C) To a length greater than 0.5L

Question 16: You want to compress a gas from 10 litres to 1 litre. What requires more work, doing it very fast (adiabatically), or very slow (isothermally)? A) Slow (isothermal) B) Fast (adiabatic) Question 17: Two containers each holding 10 mol of gas are brought in thermal contact. The gas in the first container is helium (a monatomic gas) and is initially at 0 degrees C. The gas in the other container is hydrogen (a diatomic gas), and is initially at 80 degrees C. What is the equilibrium temperature of the two gases? A) Less than 40 C. B) Greater than 40 C. C) Equal to 40 C. Question 18: You roll two dice and take the sum. What is the entropy of the most likely result? A) 𝑘B ln(2) B) 𝑘B ln (3) C) 𝑘B ln (4) D) 𝑘B ln (5) E) 𝑘B ln (6) F) 𝑘B ln (7)

Written Question 19: On the midterm you were given the question with two rotating spools. The rotation in one was caused by a mass m attached to a string (case (a) below). The other was spun by pulling directly on the rope with a force F = mg.

Explain why (b) spins faster than (a)? (4 points)

F=maF

(a) (b)

In case a the farce rotating the spool is T

0ft T ngs o

aaed.FM jto mg T

Iv drug

In case b the farce rotatingthe spool is

equal to mg

0ft ing Sa Ta mg 7T

to Tx T

Since they're both the same spool theone with the greater force rotates faster

Written Question 20: Bamfield has designed a squid launcher consisting of a spring with k = 2 N/m to test how fast you can launch a squid under water. You have a feeling that you could probably save some squid from unnecessary stress by doing the calculation for them. A typical squid plus launching platform has a mass of 25 grams and experiences a force |F| = (0.02 Ns2/m2) v2. a) If the spring is compressed by 0.5 meters and then released, estimate the velocity of

the squid after t = 0.01 seconds after it is released (i.e., the squid is still on the platform being accelerated). (3 points)

Foras Fspjms Fnet Fspring Fdras

Kx cuz

a 1 of xp D Smv 3 0 Vs

VK.ms Vds tacos ato ftp.I o.oz.IJK.nl0.40 Ms

b) Estimate the position of the squid at t = 0.01 seconds and t = 0.02 seconds. (1 point)

X alls i x Kos ofa Sm t 010.01O Sm

0.02 s x b t VI oldest

o Sm t 0.4074010.496 m

Written Question 21: The Runner King and Pearl race towards their home planet 5 light years away. The Runner King travels at 3/5c and Pearl travels at 4/5c. In the frame of the home planet, how much time is seen to pass on the Runner King’s clock from the beginning if the race to when Pearl reaches the home planet? (4 points)

Time passed in planet frame

stplanet i

54,1 Yrs

The time that passes on the Runner

King's dock must be less

st stiganetes ritzyI4

2 yrsa 5 yrs

s

Written Question 22: 0.2 mol of oxygen gas (O2) is compressed to the left half of a cubic box of dimensions 20 cm x 20 cm x 20 cm, and separated from the right half of the container by a wall. The gas is at twice the atmospheric pressure (200 kPa). If the separation wall in the container is suddenly removed, the oxygen will equilibrate to a state where it uniformly fills the entire container. What is the time scale for this equilibration process? (i.e., estimate how long it takes for the gas to spread to the other side of the container.) The molecular weight of oxygen (O) is 16 g/mol. (4 points)

32 fer diatomi

We want the average y of the particlesso we need both ways of expressing temperature

T IRI Fe mvavi

N3Wars

Varg 311Name total mas

n MM thats ndaa

vows3 FENG2 10.032

866To get from one side to the other takes

stud 241866 9.2 ms

Written Question 23: A planet has a space tourism capsule attached to a tether that can be pulled in and let out. The space capsule is retracted such that it follows the equation

𝑅 = (500 km) ⋅ √1 −𝜃

4𝜋

which means that after two orbits (θ = 4π) the tether is fully retracted. How long does it take for the tether to be fully retracted? Treat the capsule as a point mass m = 1000 kg rotating about a fixed point at a distance R. The initial angular velocity before the cable is retracted is ω = π rad/hr. (4 points)

Ve know that angular momentum is

conserved

Li I w M132wet Mtwo

to M l d 1 date M two

c EE w

Sci da wastt

C 5 1 te tu

We set a D when t 0 so

Y 5 II c o

D c 2 it

so we gett 2 2 I 5

When A 4T we gett 2 2 hrs

Written Question 24: Photons (particles of light) are interesting in that their momentum is simply proportional to the energy they have. A photon with energy E has momentum p = E/c. The regular formula for momentum doesn’t hold because they don’t have mass. Mega electron-Volts (MeV) are a unit of energy like Joules, but much more convenient for particle physics. Masses then have units of MeV/c2. Just leave stuff in units of MeV. A photon with energy 100 MeV is incident on a stationary particle of mass 200 MeV/c2. If the photon is completely absorbed to form a new particle, what is the mass (in units MeV/c2) of this new particle and what is the speed of this new particle (as a fraction of the speed of light)? (2 points)

momentum

I to r Mv

energyE t mo t 8 ME

Isolate 8M to set

Eu Et in c

ve E100 Mer

K 0Meke E

I3C

The mass is

M Igi 100M

7300 Make8

E zoo Melfa

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/R2

E = mgh E = ½ mv2 E = ½ k (Δs)2 Δ𝑊 = �⃗� ∙ Δ𝑟 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 R2 (solid disk, cylinder), 2

5⁄ M R2 (solid sphere), 1

3⁄ M L2 (stick from one end), 112⁄ M L2 (stick through middle),2

3⁄ M R2 (hollow sphere) γ = (1 - v2/c2)-1/2 vγ = c (γ2 - 1)1/2

𝑝 = γ m 𝑣 E = γmc2 v/c2 = p/E E2= p2c2+ m2c4

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 Eavg = ½ mvavg

2 1 light year = c × 1 year c ≈ 3 × 108m/s NA = 6.02 × 1023 G = 6.67 × 10-11 N m2/kg2 vsound = 340 m/s g = 9.8 m/s2