Physics 114 Practice Exam 1 PDF

PHYSICS 114 PRACTICE EXAM 1 Name (Print): PID: Honor Pledge: On my honor, I have neither given nor received unauthorized aid on this examination. Signature: Do no...

PHYSICS 114 PRACTICE EXAM 1 Name (Print): PID: Honor Pledge: On my honor, I have neither given nor received unauthorized aid on this examination. Signature: Do not open the exam until told to do so. You will have 50 minutes to complete the examination. NO CELL PHONES, TEXT MSG, etc. ALLOWED AT ANY TIME. Before the exam begins:  Print and sign your name, and write your student PID number in the spaces above. During the exam  When the exam begins, print your name on each page.  If you are confused about a question, raise your hand and ask for an explanation.  If you cannot do one part of a problem, move on to the next part.  This is a closed book examination. All equations and constants are provided.  You may use a calculator, but not a computer, or other Internet-connected devices (smart-phones, iPads, etc.).  Please write neatly and legibly in the spaces provided. Use of other scratch paper may be ignored.  Show your work in enough detail so that the grader can follow your reasoning. This means that you should solve each problem algebraically (before doing numerical calculations) with symbolic notation that the grader will be able to understand; use variable labels provided whenever possible.  Clearly identify your answers, include units where needed, and round final answers to an appropriate number of significant figures. End of exam:  Out of respect to other students, please remain seated for the last 10 minutes of the exam. At the end of the exam, please remain seated until all exams have been collected. PHYS 114 1. The heart rate (Hr) of birds varies with mass (m) as follows: Hr = 1990m-0.25. a. [4 pts] Which of the simplified graphs below is consistent with this data? Explain/show your work. A B C D 5 14 14 8 Log10 Hr Log10 Hr 12 12 4 6 ln Hr ln Hr 10 10 4 3 8 8 2 6 6 2 0 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 ln m Log10 m Log10 m ln m b. [2 pts] Which of the following statements correctly interprets the meaning of this relationship between heart rate and mass? Circle the correct answer. No explanation is necessary to receive full credit.  As mass increases, heart rate decreases.  As mass increases, heart rate also increases, but at a slower rate than mass  As mass increases, heart rate also increases, but at a faster rate than mass. Physics 114, Practice Exam 1 2 2. Maria walks north for 5 minutes at a constant speed of 2 m/s. She then walks 60o to the east of north for another 5 minutes at a rate of 3 m/s. a. [3 pts] What is Maria’s average speed (in m/s) over this 10-minute interval? Show your work. b. [5 pts] What is the magnitude of Maria’s average velocity (in m/s) over this 10-minute interval? Show your work. Physics 114, Practice Exam 1 3 3. [5 pts] Suppose one package of cookie dough is enough to make a single cookie that is 30 cm in diameter. If you used two packages of cookie dough to make a single cookie with the same thickness, then what diameter would it have? Show your work. Physics 114, Practice Exam 1 4 4. For birds, the feather shaft length (Lf) scales with body mass (m) according to the following relationship: Lf = 2.3 m0.34 a. [2 pts] Would the above relationship between Lf and m appear as a straight line on a linear, semilog, or log-log plot? No explanation is necessary to receive full credit. b. [4 pts] Determine the slope and y-intercept on the graph you chose in part (a). Show your work. Be sure to explicitly label which number is the slope and which is the y-intercept. c. [4 pts] Here is the scaling relationship between a bird’s mass (m) and cruising flight speed (v): m ~ v6.0 Use this relationship and the relationship between Lf and m to determine the value of the exponent (denoted by a) in the scaling relationship between Lf and v: Lf ~ va Show your work. Physics 114, Practice Exam 1 5 5. [9 pts] A child tosses a ball straight up into the air. At the instant the ball leaves the child’s hand, it is traveling at 2 m/s. Sketch a position vs. time graph, velocity vs. time graph, and acceleration vs. time graph for the ball from the instant it leave’s the child’s hand to the instant she catches it. Physics 114, Practice Exam 1 6 6. Imagine that you have an initial population of 2000 living red blood cells. These blood cells are no longer dividing, so as they die, the number of red blood cells in your population decreases. You find that the number of red blood cells as a function of time is described by the following mathematical relationship: () n t = 2000e ( -t/ 4 months) a. [2 pts] On what type of graph (linear, log-log, or semi-log) would this relationship appear as a straight line? b. [3 pts] Sketch the graph you indicated in part a. Label the axes appropriately (with correct units) and indicate the numerical values of the slope and y-intercept. Explain/show how you determined these values. 7. [4 pts] Two gift boxes need to be wrapped with paper. Box A is twice the volume of box B. How much more wrapping paper is needed for box A compared to box B? Show your work. Physics 114, Practice Exam 1 7 8. Two sprinters, A and B, train together on a horizontal, straight track. The table below shows the velocity vectors of the sprinters for instants 1-5, separated by equal time intervals. a. [4 pts] In the boxes at right, draw arrows to qualitatively represent the direction and magnitude of the average acceleration of each sprinter for the interval from instant 1 to instant 5. Briefly explain your reasoning. direction of average direction of average acceleration of Sprinter A acceleration of Sprinter B b. [6 pts] On the axes shown at right, sketch qualitatively correct graphs of velocity versus time for each sprinter in the interval from instant 1 to instant 5. Label your plots “Sprinter A” and “Sprinter B” as velocity appropriate. Take the positive direction to be to the right. Briefly explain why you drew the graphs as you did. time Physics 114, Practice Exam 1 8 9. [7 pts] A person ties a rope to a box and pulls the box to the right. The block slides along the floor at a constant speed. There is a friction force between the box moves to right box and the floor (the coefficient of kinetic friction is < 1). Draw the box’s free-body diagram. Label the types of forces (e.g., normal, friction, weight, etc.) and use appropriate subscripts to indicate the object exerting the force and the object feeling the force. The lengths of your arrows should be qualitatively correct (e.g., if two forces have the same magnitude, then their arrows should be the same length). No explanation is necessary to receive full credit. Physics 114, Practice Exam 1 9 10. [5 pts] An object is moving in one dimension and slowing down (it never speeds up). Sketch a position vs. time graph and a velocity vs. time graph that are consistent with the acceleration vs. time graph that is shown for the slowing object. No explanation is necessary to receive full credit. Make sure that there is no ambiguity as to whether a line you drew is straight or curved. x v a t t t Physics 114, Practice Exam 1 10 11. In 2013, a study published by Ryan and Shaw contained the graph at right, which shows the relationship between femoral trabecular bone number (Tb,N) and femur head height (FHH). a. [6 pts] Find the mathematical equation that relates Tb,N and FHH (not log(Tb,N) and log(FHH) – i.e., there should be no logarithms in your final answer). Show your work. b. [4 pts] In the same study, Ryan and Shaw reported the following relationship between the bone surface-area-to-volume ratio (BS/BV) and femur head height (FHH): 𝐵𝑆 ∝ 𝐹𝐻𝐻−0.62 𝐵𝑉 Use this result and your answer to part (a) to find the mathematical equation that relates Tb,N and BS/BV. Show your work. Physics 114, Practice Exam 1 11 12. Klipspringers (Oreotragus oreotragus) are African mammals that are renowned for their ability to jump high. Imagine a klipspringer jumps to the right, leaving the ground with a speed of 12.0 m/s at an angle of 40o above the ground. Assume the ground is perfectly flat. a. [10 pts] Sketch graphs of the x- and y-components of the klipspringer’s velocity. Let the +y-direction point up and the +x-direction point to the right. Each graph must include the following quantitative information labeled somewhere on the graph:  The numerical value of the slope of the line;  The initial value of the x- or y-velocity;  The time at which the klipspringer reaches its maximum height; and  The time at which the klipspringer lands on the ground. Show your work for any values you have to calculate. Physics 114, Practice Exam 1 12 b. [4 pts] Determine the maximum height above the ground that the klipspringer achieves during its jump. Show your work. c. [4 pts] Determine the total horizontal distance that the klipspringer travels as a result of its jump. Show your work. Physics 114, Practice Exam 1 13 13. A squirrel jumps off of a tree branch with a horizontal velocity of 3.0 m/s. The squirrel lands on a second tree branch. The two tree branches are separated by a horizontal distance of 2.0 m. a. [3 pts] Determine the magnitude and direction of the x- and y-components of the squirrel’s acceleration while it is traveling between the two branches. Explain/show your work. b. [6 pts] What is the magnitude of the squirrel’s final velocity when it lands? Show your work. c. [6 pts] What is the magnitude of the squirrel’s total displacement? Show your work. Physics 114, Practice Exam 1 14 g = 9.8 m/s2 kB = R/NA = 1.38 x 10-23 J/K 1 in. = 2.54 cm R = 8.31 J/mol-K 1 ft. = 0.305 m NA = 6.02 x 1023 mol-1 1 mi. = 1609 m 1 atm = 1.01 x 105 Pa 4 1 C circle  2r Acircle = p r 2 Asphere = 4p r 2 Vcylinder = p r 2 h Vsphere = p r 3 Atriangle = bh 3 2 dr dv v= a= vx, f = vx,i + axDt dt dt 1 ( ) vx,2 f = vx,i + 2ax Dx 2 x f = xi + vx,i Dt + ax Dt y = axb y = nakx 2 2 1 1 W + Q = DE = DK + DU + DEth K = mv 2 U g = mgy U s = kx 2 2 2 F Dℓ v2 stress = strain = Fr = DEth = fk Dx A ℓ gy 3 1 2p m L DEth = NkB DT f k = mk N f= w= = 2p f T = 2p T = 2p 2 T T k g x(t) = Acos(wt + f ) v(t) = -Aw sin(w t + f ), vmax = Aw a(t) = -Aw 2 cos(w t + f ), amax = Aw 2 F 3 A = A0e-t/t = A0e-dt S = kB lnW P= PV = nRT = NkBT Eth = NK avg = NkBT A 2 N N m n= (number of moles) (number density) r= (mass density) TK = TC + 273 NA V V 1 RT 1 d MFP = = D = vrms dMFP rrms 3D = 6Dt rrms 1D = 2Dt ( N /V )p (2r) 2 N A P p (2r)2 2 work done by the object as it relaxes 3kBT resilience = vrms = work done on the object as it is stretched or compressed m 3 K avg = kBT 2 Physics 114, Practice Exam 1 15