Science One Physics Exam 1 - University of British Columbiascione/SOP2019/exams/exam1_2018.pdf ·...
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Name: Student Number:
Science One Physics Exam 1 December 7th, 2018
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
Formula sheet at the back (you can remove it)
Question 1: The above shows a motion diagram for an object. Which interval has the largest magnitude velocity in the y direction? A) Between 1 and 2. B) Between 2 and 3. C) Between 3 and 4. D) Between 5 and 6. E) Both C) and D).
Question 2: The graph above describes an aspect of the motion diagram used in Question 1. Which quantity does the graph best describe?
A) x B) y C) vx D) vy E) ax F) ay Question 3: Three different forces are used to drag a box horizontally across the ground. The vectors of each force are shown to the right. Which force does the most work?
A) F1 B) F2 C) F3 D) They all do the same amount of work.
Question 4: An object’s momentum is given by p = 12 - 6 t2. What can you say about the net force on the object?
A) The net force is causing the object to accelerate at a constant rate. B) The net force is causing the object to accelerate at an increasing rate. C) The net force is causing the object to decelerate at a constant rate. D) The net force is causing the object to decelerate at an increasing rate.
Question 5: A ball of given mass is travelling in the positive x-direction with constant velocity v, until it impacts on a spring. The figure below shows the spring potential energy V as a function of compression x.
This process is simulated with the Euler method. During the first couple of Euler time steps after impact, the Euler method
A) Generally underestimates the distance travelled B) Generally overestimates the distance travelled C) Gets the distance travelled exactly right, independent of the Euler step size Dt
Question 6: A bowling ball starts with a velocity of 5 m/s, and decelerates due to friction as shown in the graph to the right. The distance travelled by the ball during the first two seconds is
A) Larger than 10 m B) Between 8 m and 10 m C) Less than 8 m D) Insufficient data
Question 7: The diagram to the right shows a potential energy of a particle. If the particle is travelling to the right and has a maximum kinetic energy of 3 J, where is the turning point?
A) x = 2 m B) x = 2.5 m C) x = 3 m D) x = 3.5 m E) x = 4 m F) No turning point. G) Can’t have that much energy.
Question 8: Using the potential energy plot from the previous question, what is the force at x = 3 m
A) 4 N B) 2 N C) 1 N D) 0 N E) -1 N F) -2 N G) -4 N
Question 9: An isothermal process and an adiabatic process are drawn on the PV diagram to the right. Which process is adiabatic?
A) A B) B C) Impossible to tell without numbers.
In the pV-diagram shown above, three processes of expansion from an initial to a final state of an ideal gas (of a fixed number of moles) are shown. Process 1 is an isochoric increase of pressure followed by isobaric expansion. In process 2, pressure and volume increase in sync. Process 3 is an isobaric expansion followed by isochoric increase in pressure. All three processes begin in the same state of the gas (“intial” state above) and end in the same state of the gas (“final” state above). Which of the following statements is true? A) The heat Q flowing into the gas is the largest for path 1 and the smallest for path 3;
and the change in entropy of the gas is the largest for path 3 and the smallest for path 1.
B) The heat Q flowing into the gas is the largest for path 1 and the smallest for path 3; and the change in entropy of the gas is the same for all paths.
C) The heat Q flowing into the gas is the same for all paths; and the change in entropy of the gas is the largest for path 3 and the smallest for path 1.
D) The heat Q flowing into the gas is the largest for path 3 and the smallest for path 1; and the change in entropy of the gas is the same for all paths.
E) The heat Q flowing into the gas is the same for all paths; and the change in entropy of the gas is the largest for path 1 and the smallest for path 3.
F) Both the heat flowing into the gas and the change in entropy of the gas are the same for all three paths.
Question 11: Which of the following statements holds about the initial and the final temperature of the system considered in the previous question? A) The final temperature is independent of the path, and it equals the initial temperature
of the gas. B) The final temperature of the gas depends on the choice between the three above paths,
but in all cases the final temperature is higher than the initial temperature. C) The final temperature is independent of the path, and higher than the initial
temperature. D) The final temperature of the gas depends on the choice between the three above paths,
and whether or not the final temperature is higher than the initial temperature depends on the precise value of the volume and pressure ratios.
Question 12: Consider 10 marbles, numbered 1 – 10, distributed in a bi-partitioned container (a container with two parts). We denote the macrostate x by the configuration that has x marbles in the left part and 10-x marbles in the right part of the container. Which of the following statements is true? A) The above is an improper definition of macrostate, as every macrostate x contains
exactly one microstate. B) The macrostates with the highest entropy are x=0 and x=10, as they are extremal.
Every other macrostate can be generated from them by swapping marbles, but the reverse process is not possible.
C) The macrostates with the highest entropy are x=0 and x=10, as they contain the largest number of microstates.
D) The macrostate x=5 has the highest entropy, because once the system reaches it, it gets trapped in it.
E) The macrostate x=5 has the highest entropy as it contains the largest number of microstates.
Question 13: A high diver wants to impress the judges by doing a “tuck”, which is essentially folding yourself in half, as illustrated to the right. What can you say about the diver’s angular velocity after the tuck. Choose the best answer.
A) The angular velocity doesn’t change. B) The angular velocity is doubled. C) The angular velocity is halved. D) The angular velocity is quadrupled. E) The angular velocity is quartered.
Question 14: In class we discussed the different moments of inertia of an object spun about the x, y, and z axes. For the tennis racket to the right, rank the magnitudes of the moments of inertia when spun about each axes.
A) Ix > Iy > Iz B) Iy > Iz > Ix C) Ix = Iy > Iz D) Iz > Iy > Ix E) Iz > Iy = Ix
Question 15: Between classes you rush to Ike’s and buy a coffee at exactly 9:50am on your watch. An alien happens to be speeding by Earth at 0.75c. What time to they observe on your watch when you buy the coffee?
A) Earlier than 9:50am. B) Exactly 9:50am. C) Later than 9:50am. D) Relativity can’t answer this kind of question.
Question 16: An earth worm has 5 hearts that must beat simultaneously for the earthworm to live. If the earth worm travels at v = 4/5 c, what will happen to its beating hearts?
A) The hearts at the back will start beating at a different rate than the hearts at the front.
B) The length of the earthworm will get contracted and it will get squashed and die. C) The length of the earthworm will get stretched and it will die. D) We’ll measure the hearts will beat faster, but they’ll still all beat at the same time. E) We’ll measure the hearts will beat slower, but they’ll still all beat at the same time. F) The front of the worm will travel faster than the back of the worm and it will get
ripped apart. G) The front of the worm will travel slower than the back of the worm and it will get
Question 17: The Rudolph B-Line bus is full and passes your bus stop near the speed of light. As it passes you see a string of Christmas lights on the side of the bus all light up at the exact same time. What can you say about when the lights turn on for someone inside the bus?
A) They all turn on at the same time. B) The lights at the front of the bus turn on before the ones at the back. C) The lights at the back of the bus turn on before the ones at the front. D) Need to know the speed to determine the exact time dilation.
Question 18: It turns out that Newton’s equations F = dp/dt still work with the new definition of relativistic momentum we came up with in class p = γmv. Imagine you push two objects from rest for the same amount of time dt. According to the relativistic momentum, how hard to you have to push to make one object have twice the velocity as the other?
A) You have to push with slightly more than twice the force to get twice the velocity. B) You have to push with slightly less than twice the force to get twice the velocity. C) Because the definition of mass is when the object is as rest, you still just push with
twice the force.
Question 19: Two Happy Balls of mass m = 0.5 kg collide as shown above. They have the same initial velocity and the same incoming angle from the horizontal. Upon colliding they stick together, forming to So-So Balls, and travel horizontally at 5 m/s. The deformation of a Happy Ball to a So-So Ball results in 4 Joules of stored energy, much like a compressed spring.
What is the initial velocity v of the Happy Balls? Feel free to leave you answer in the form v = (vx, xy). (4 points)
Question 20: Mr. Zucchini-Man is swinging on a rope. What fun he’s having! The wind, caused by a drag force of magnitude FD = Cv2, is blowing in his face. He feels alive!
a) Draw a free body diagram for Mr. Zucchini-Man and determine the x and y components of the net force on him. (3 points)
part b on next page…
b) Write down the Euler method equations that would determine his velocity and position at some small time-step in the future. (1 point)
Consider a thermodynamic cycle as shown in the figure above. There are four processes in it, namely A to B: isobaric expansion, B to C: isochoric reduction of pressure, C to D: isobaric compression, and D to A: isochoric increase in pressure. Furthermore, it holds that the volume at B is 3 times the volume at A, and the pressure at A is 3 times the pressure at D. The work medium is an ideal gas.
a) [1 point] In which of the four processes does heat flow into the gas, and why?
b) [2 points] What is the efficiency of the cycle? (Recall that the efficiency is the ratio between the work extracted per cycle and heat injected per cycle.)
c) [1 point] What is the efficiency of a Carnot engine with the same highest and lowest temperature during the cycle? Which efficiency is higher, and why?
Question 22: Two containers filled with gas are in thermal contact with another, and otherwise isolated. The first container is filled with 1 mole of a monoatomic gas, at a temperature of 300K. The second container is filled with 1 mole of a diatomic gas, at a temperature of 500K.
a) [2 points] What is the equilibrium temperature of the system?
b) [2 points] What is the change in entropy of the combined system during the equilibration process?
Question 23: When Mr. Zucchini-Man is spinning at an angular velocity ω = 5 rad/s while he hangs from the ceiling. He doesn’t like it. No Sir! To stop himself he holds his arms out and turns on two tiny rockets that each provide a force
F = (5 N/s3) t3. Assume the rockets are positioned such that Mr. Zucchini-Man gets maximum torque and assume that he is a cylinder spinning about his center. How long does he have to turn on the rockets to stop himself from rotating? (4 points)
Question 24: In class we discussed the Twin Paradox. The paradox arises when we think of a set of twins, Amos and Clark. Amos stays on Earth and Clark travels on a rocket to a distant planet and back again. In the Earth frame Amos sees the Clark’s clock (clock C) tick slower than his (clock A), but in the rocket’s frame Clark sees Amos’s clock tick slower than his. When Clark returns, who is older, him or Amos? They can’t both be younger than each other. We will resolve the paradox.
a) If Clark is travelling at v = 3/4 c and the distance between planets in the Earth frame is 5 ly, how much time does Amos see pass on Clark’s clock? (2points)
b) In Clark’s frame the planets move away and towards him at speed v = ¾ c. Explain why the journey takes Clark a shorter amount of time in his frame than in Amos’s frame. (1 point)
c) In the Earth frame both the clocks A and B are synchronized. In the Earth frame
Clark arrives at clock B at 12:00 exactly. Assume that Clark turns around to return to Earth instantaneously when he gets to B. In Clarks frame, what can you say about the time on clock A compared to Clock B the instant before he reaches B and the instant after he reaches B and has turned around? What happens to poor Amos? (1 point)
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), 13, M L2 (stick from one end), 1 12, M L2 (stick through middle),2 3, M R2 (hollow sphere)
γ = (1 - v2/c2)-1/2 vγ = c (γ2 - 1)1/2
�⃗� = γ m �⃗� 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 S = nCV ln(T/T0) + nR ln(V/V0) 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