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)

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)

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)

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

(1 point)

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)

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)

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)

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)

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), 25⁄ M R2 (solid sphere),

13⁄ M L2 (stick from one end), 1

12⁄ M L2 (stick through middle),23⁄ 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 mvavg2

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