Name: Student Number:

Bamfield Number:

Science One Physics Exam 1 December 14th, 2017

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

πάθει µάθος

Formula sheet at the back (you can remove it)

Question 1: The actual position vs time of an object is plotted above. Starting at t1 we use the Euler method to determine the position at t2. What can we say about the velocity over this time interval? A) The Euler method overestimates the velocity between t1 and t2. B) The Euler method underestimate the velocity between t1 and t2. C) The Euler method estimate doesn’t concern velocity, so they’re the same

Question 2: Robert decides to hit James with a snowball when James isn’t looking. The ball explodes on impact covering James with snow. If we consider the system to be the snow ball and James, what can we say about James getting hit with the snowball? Assume they’re both in space. A) Momentum is conserved during impact, but mechanical energy is not conserved. B) Momentum is not conserved during impact, but mechanical energy is conserved. C) Neither momentum nor mechanical energy are conserved. D) It’s impossible to tell what is conserved with the provided information

Question 3: Four snowballs with masses (𝑀) are traveling at the same speed (𝑣) towards each other as shown above. What is the total mechanical energy of this system?

A) 0 B) 4Mv C) 4Mgv D) 2Mv2 E) 4Mv2

Question 4: What is the total momentum of the four snowballs as shown in the previous question? A) 0 B) 4Mv C) 4Mgv D) 2Mv2 E) 4Mv2 Question 5: Two cylindrical tins roll down a hill, one full of Christmas cookies (a full cylinder) and one empty (a hollow cylinder). They both starting from the same height. Assuming that no energy is lost to friction, which is rolling faster (has the linear velocity at the center of mass) when they get to the bottom? A) The final velocities of the two cylinders are the same. B) The final velocity of the tin with cookies (full cylinder) is higher. C) The final velocity of the tin without cookies (hollow cylinder) is higher D) Insufficient information. It depends on the ratio of the radii of the two tins.

Question 6: A rotationally symmetric object has a moment of inertia I = 0.6 m R2, where m is its mass and R is its outer radius. The mass density inside the object is uniform. Which of the above is the profile of the object? A) A B) B C) C D) It’s none of the above, because the maximum moment of inertia of a rotationally

symmetric object is I = m R2/2.

Question 7: Statistical definition of entropy. Consider a toy model of a gas, consisting of 20 molecules, and two macrostates thereof. Macrostate 1 has 5 molecules each of 4 boxes. Macrostate 2 has 10 molecules in each of two boxes. Which macrostate has the larger entropy? A) The entropy of the two macrostates is the same, because the four boxes of Macrostate

1 can be paired up to produce Macrostate 2. B) The entropy of Macrostate 1 is larger, because each microstate in Macrostate 2 is also

a microstate in Macrostate 1, but not the other way around. C) The entropy of Macrostate 2 is larger, because each microstate in Macrostate 1 is also

a microstate in Macrostate 2, but not the other way around.

view from the side

profiles

A B C

Macrostate 1 Macrostate 2

Question 8: Frosty sees Santa zip by him at relativistic speeds, as shown above in Frosty’s frame. Which of the following best represents what someone in Santa’s frame would see?

Question 9: Because of the time zone difference, kids on the East Coast open their presents before kids on the West Coast. If Santa wanted to be in a frame in which the kids opened their presents at the same time, what direction would he have to travel?

A) East B) West C) North D) South E) It’s impossible. That’s not how relativity works.

Question 10: In our frame it takes 1 minutes for a small child to open a Christmas present. Santa is zipping by us at 0.9c. In Santa’s frame, how much time does he see pass on his clock while the kid opens the present?

A) Longer that a minute B) Less than a minute

Question 11: The change in entropy of an ideal gas undergoing isothermal expansion is

A) Positive, because heat is injected into the system in isothermal expansion. B) Zero, because the process can be performed reversibly. By the second law, there

can be no change in entropy in reversible processes. C) Negative, because the argument in (A) is actually for the change in entropy of the

surroundings. To satisfy the second law, the change of the entropy of the gas must be the negative amount of the same magnitude.

Question 12: The velocity of an object is given by

𝑣 𝑡 = (3m/s,)𝑡- If the object has a position of x=1 at t=0, how long does it take for the object to reach a position of x=2m?

A) less than 0.7s B) between 0.7s and 0.9s C) between 0.9s and 1.1s D) between 1.2s and 1.3s E) more than 1.3 s

Question 13: Three identical blocks collide with three identical springs as shown above. All the springs compress by the same amount. What can you say about the incoming velocities of the blocks?

A) vA > vB > vC B) vA = vB = vC C) vA < vB < vC

Question 14: In the question above, what can you say about the mass of the spring when it is compressed versus when it is uncompressed?

A) The mass of the compressed spring is greater than the uncompressed spring. B) The mass of the compressed spring is less than the uncompressed spring. C) The mass of the compressed spring is the same as the uncompressed spring.

Question 15: Consider two gases, one monoatomic and one diatomic, of the same amount. They are both heated up by the same temperature difference ΔT. Which of the following two processes requires more heat? (i) The isobaric heating of the monoatomic gas. (ii) The isochoric heating of the diatomic gas. Possible answers:

A) Process (i) requires more heat. B) Process (ii) requires more heat. C) Both processes require the same amount of heat.

Question 16: Consider a Carnot process for a gas in contact with a hot reservoir at temperature TH and with a cold reservoir at temperature TC, where TH > TC > 0. Which of the following statements is true?

A) The work done in one cycle is larger than the heat drawn in isothermal expansion. B) The work done in one cycle is smaller than the heat drawn in isothermal expansion. C) The work done in one cycle equals the heat drawn in isothermal expansion. D) It depends on the number of degrees of freedom per molecule.

Question 17: Consider a fixed amount of gas, expanding at constant pressure P from volume V1 to volume V2. Then, it holds that

A) The change in entropy of the gas is larger if the expansion is carried out irreversibly as opposed to reversibly.

B) The change in entropy of the gas is smaller if the expansion is carried out irreversibly as opposed to reversibly.

C) The change in entropy is the same.

Question 18: The elves are playing with drills and balls. On one drill they have a solid ball. On the other drill they have a Jello ball that has the same mass and radius as the solid ball. However, when the Jello ball is spun using the drill, it deforms (flattens and stretches out as shown above). If both balls have the same torque applied to them using the drill, for the same time, what can we say about the angular velocity of each ball, ωsolid and ωjello?

A) The jello ball will have a lower angular velocity B) The jello ball will have a higher angular velocity C) Both balls with have the same angular velocity

Written Question 19 Santa is testing a new engine (powered by Rudolfium) for his sled. The thrust supplied by the engine is given by the graph shown above. Santa and his sled have a mass of 500 kg and snow has a coefficient of friction of 0.05. Assuming he starts from rest, how fast will he be going after 3 seconds? (4 points)

Written Question 20 Santa sometimes gets stuck sliding down chimneys. The force that stops him is given by

𝐹/012345 = 20N

m9:

𝑥</-

which takes an odd form due to his non-linearly elastic Santa belt snagging on the sooty inside of the chimney. If Santa is initially falling at 10 m/s right before his belt snags, estimate his velocity 0.2s after his belt snags and the chimney force kicks in. Use the Euler method with a time step of Δt = 0.1s. (4 points)

Written Question 21 In the spirit of Christmas, James decides to launch Jeff the grad student into a lake using a spring-loaded cannon that redirects the cannon ball downwards towards a teeter-totter. The cannonball collides and sticks to the end of the teeter-totter, causing it to rotate, launching Jeff skyward. Assume the cannon is 10 meters above the ground and that the teeter-totter is massless. The cannon ball is one tenth of Jeff’s mass, and is spring loaded a distance of 1 m from equilibrium with a spring constant of 220N/m. How high will Jeff the grad student be launched into the air? (4 points)

Written Question 22 Santa has been working on his Rudolfium engine. It working hinges on being able to determine the flash temperature at which the Rudolfium spontanouesly ignites. To test it he uses a cylinder similar to the one James and Robert used in class to light tissue paper on fire. The cylinder is 15 cm long and the piston has an area of 0.25 cm2. Room temperature is 300 K and atmospheric pressure is 100 kPa. Assume the air is nitrogen with CV = 5/2 R. Santa finds that applying a force of 100 N and moving the piston 14 cm causes the Rudolfium to ignite. What is the ignition temperature? (4 points)

Written Question 23 Consider the Ho-Ho shown above (which is like a Yo-Yo, but Christmas themed) with inner diameter of 1 cm and outer diameter of 7 cm. Starting from rest, and with the end of the string held in a fixed position, how long does it take the Ho-Ho to descend by 1 m? (4 points) (For its moment of inertia, model the Ho-Ho as a solid cylinder. Hence the contribution of the inner cylinder to the mass and the moment of inertia can be neglected. Also, the string winding around the inner cylinder has negligible thickness.)

Written Question 24: Earth is facing an energy crisis, and Santa Claus, known for having a special sled that can travel at relativistic speeds, has been tasked with saving it. His mission is to travel into the far reaches of space to collect the rare element, Rudolfium, which will presumably, somehow, solve our energy crisis. Santa leaves Earth travelling at 0.8c. When he reaches the Rudolfium deposit he will transmit a radio signal back to Earth telling us he has found it. We receive a signal from Santa after 6 years has passed on Earth. How far does Santa think he’s travelled to get to the Rudolfium deposit? (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/R2

E = mgh E = ½ mv2 E = ½ k (Δs)2 Δ𝑊 =𝐹 ∙ 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 5M R2 (solid sphere), 13M L2 (stick from one end), 1 12M L2 (stick through middle),2 3M 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 PVγ = const γ = κ+2/κ dS = dQrev/T S = kB ln ω 1/T = dS/dE 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