P131 S2022 Exam 1 TR solutions

Name __________________________ _ Physics 131 Spring 2022 Instructions: University of Maryland Department of Physics Exam lTR Do not open this examination until the proctor tells you to begin. D. Buehrle 3.111.2020 1. When the proctor tells you to begin, write your full name at the top of every page. This is es- sential since this exam booklet will be separated for grading . 2. Do your work for each problem on the page for that problem. You might find it convenient to do your scratch work on the back of the page before starting to write out your answer or to continue your answer on the back. If part of your answer is on the back, be sure to check the box on the bottom of the page so the grader knows to look for it! 3. On all the problems except the multiple choice questions in problem 1 or where it says not to ex- plain, your answers will be evaluated at least in part on how you got them . More than half the credit of the problem may be given for the explanation. YOU MAY EARN LITTLE OR NO CREDIT FOR YOUR ANSWERS IF YOU DO NOT SHOW HOW YOU GOT THEM . Partial credit will be granted for correct steps shown, even if the final answer is wrong. Explanations don 't need to be long, but they need to show what physics you are using and assumptions you are making. (This means words.) 4. Write clearly and logically so we can understand what you are doing and can give you as much paiiial credit as you deserve. We cannot give credit for what you are thinking - only for what you show on your paper. 5. If you try one approach and then decide on another, cross out the one you have decided is wrong. If your paper contains both correct and incorrect approaches the grader will not choose between the two. You will not receive any credit when contradictory statements are present, even if one is correct. 6. All calculations should be done to the appropriate number of significant figures. 7. At the end of the exam , sign the honor pledge in the space below I pledge on my honor that I have not received or given any unauthorized assis- tance on any part of this examination in its whole duration. Signature ______________ _ You may find some of the following values useful (or not). kc = 9 x 10 9 N-m 2 /C 2 ks = 1.38 x 10 - 23 J/K NA= 6.02 x 10 23 molecules/mo! Nw = 7 x 10 9 ppl C = 3 X 10 8 m/s Vo max = 55 mi/hr kBT= 1/40 eV/molecule* RT = 2.5 kJ/mol * g = 10 N/kg e = 1. 6 x 10- 19 C NusA = 3 x 1 0 8 peeps Vs = 343 m/s *@300 K *** Good Luck ***

NAME _________________ _ POINTS ---- Physics 131 Spring 2020 D. Buehrle Exam lTR 1. (25 points) Place your answers in the box on the right side of the paper for each question. 1.1 Kinetic energy is defined as½ mv 2 , where mis the mass of the object, and vis the velocity (or speed). Which of the following could NOT be a unit for energy? (5 pts) . meter A. kilogram ctz secon B nanometer 3 gram · week-hour - foot kilometer -kilogram ·cm C. . d mmute· ay D centimeter 2 gram · second 2 . mile 2 E. kilogram - 1 - 2 10ur F. None of these could be units of energy G. All of these could be units of energy 1.2 You know that one cubic centimeter of biomaterial has a mass of 1 gram. What's the mass of I cubic meter of biomaterial? (5 pts) A. 100 g B. 1 kg C. 10 kg D. 10 2 kg E. 10 3 kg F. 10 4 kg G. You can't answer without knowing the density. 1.3 A ball, starting from the position shown, is roll- ing horizontally at a constant speed. It comes to a hill and rolls over it. Which of these graphs could represent the horizontal (x) component of the ball's position? (3 pts) X X (2) X X (4) (5) (7) None of these r- - - ----+--- -- - - ---- .;::,,i. x 0 X (3) X (6) If you need more space, continue on the back and check here. □

NAME _______________ _ Physics 131 Spring 2020 2. (10 points) In physics, we often focus on highly simplified sys- tems in order to help us understand how a basic principle or equa- tion applies in a physical situation - "toy models". In this class, two of the toy models we have considered so far are a ball thrown straight up ignoring air resistance and a goat sliding on ice, as- sumed to be frictionless. Did either of these models help you un- derstand a basic principle, idea, or equation? If so, explain which and how it helped. If not, explain why you did not find these exam- POINTS ---- D. Buehrle Exam lTR ples useful. Note: This is an essay question. Your answer will be judged not solely on its cor- rectness, but for its depth, coherence, and clarity. I If you need more space, continue on the back and check here. □

NAME POINTS ----------------------- ---- Physics 131 Spring 2020 D. Buehrle Exam lTR 3. (15 points) I saw a commercial for a health care product that said, "There are 1 Os of trillions of cells in the human body." This seems like a lot! A trillion is l 0 9 . Estimate the number of cells in the human body to see if the statement is approximately correct or not. Be sure to clearly state your assumptions and how you came to the numbers you estimated, since grading on this problem will be mostly based on your rea- soning, not on your answer. t>-G<-o c.\.n:J-- \ . ., c Y \ ,- "'~-(.' ( l (A; -r '2, ~ c%, t-o ~ S' o..y '-'"'~" ~ b-t '"" '\ J ~ \ IIJJ \\ c. ~Vt\ 0 h S Q~G. e, ,"""' fd,e.,) ,t't/\(/\W".,..,..~ icsV\. n ~ t · (l V ~ ,\\-<ck_ ~ ¼A \ ..... ,o.\-.~ .\''3 A~f tA.• \ ~d,v. \ t , .... , (./\JV\, 1-d 's {,f. \ \ j \j l 6-t.rM~ fl I>.', ~~lt, ~~j ? ) i. ~ \<\ d 4i p<X 1\ ~ -so I\_, Joe.,"'\ °' \."}\,\--! ~, .. 1h (plv,S - It.\ \ 0 \ 1"'-6J•~ I tl o {-r ;,r,cM If you need more space, continue on the back and check here. □

POINTS NAME _________________ _ ---- Physics 131 Spring 2020 D. Buehrle Exam lTR 2. (25 points) Various components in a cell are moved through the cell by motor proteins such as kinesin. The kinesin attaches itself on one end to the packet it is moving (the "cargo" shown here as a big sphere) and the other end to a tubule (at the bottom of the picture). The kinesin has two "feet" at the bottom that detach, swing forward, and attach again alternately, "walking" the kinesin along the tubule. The cargo it's dragging is not mov- ing in a vacuum but is moving through a storm of wildly fluctuating fluid molecules (the water and other chemicals of which the fluid in the cell is made). This means that to drag the object through the fluid - even at a con- stant speed - the kinesin has to exert a force to counteract the resistive force of the fluid. (It does so by burning ATP into ADP.) A. Suppose the packet being dragged through the cell's fluid has a mass, m, a radius, R, and, when it is moving through the fluid with a speed, v, experiences a viscous force of magnitude Fvisc = 6rrμRv. The parameter/tis the viscosity of the fluid. If the kines in is exerting a constant force, Fk , on the cargo, which of the following expresses the condition on the two forces in order that the cargo move at a constant velocity? (5 pts) a) Fk > Fvisc b) Fk = Fvisc c) Fk < Fvisc d) There is not enough information to tell. (Write a brief note saying what additional information is needed.) B. What is the dimensionality of ~t? (Express your answer in terms of the standard dimensions of mass, M, length, L, and time, T.) Show your work in the space be- low. (5 pts) [μ] = tt.01 ~-r J.. --.ir"°'"'cf L.- L.i- -t2- tXfttA -------"""'! ~- ,·~ >.'ffl M C. If a small object like the cargo package above is not being actively driven by a kinesin molecule, it w II I .,l,)W f.S•'lr\ wander around at random due to the sometimes-unbalanced collisions it is feeling from the water and pf- N\ other molecules in the fluid. After a time interval M , the average distance the package wilJ be from its starting point is given by the equation rJv = DM .,-1... e,~ J.r~wv>tw.l where D is calJed the Diffusion constant. What is the dimensionality of D? ~ CJ? l, -¥1- (5 pts) [c-._,.,1- 1 -:: to]~-\.] '[n J =- [ r .. ~ .,_ ~-i, [DJ = ? < o-tJ " (,( ~Q,1, --------- o+- r D. Suppose a cargo package of radius Rand mass m i~"'bserved to be traveling at a constant velocity, and moves a distance l:lx in a time M. Find an equation for the force Fk exerted by the kinesin on the ;-,f CIJWY¢tr package in terms of the parameters m, R, andμ, and the observed data l:lx and M. Show your reasoning D ;~"'~ of" in the space below. (10 pts) M S' i ,c. _, j 4,-- f', y'\/\ 0 V a ~ ~ N 2. sd.. ... , ~ r "'" t : o ~"'-\-- ~ ~UV' (-( <; f \( : (g trr'1..v V..f \(.)6 ;~ (.OW'l,J.,·k""' I pk = &rr fJ.-~~>r 0~ ..._ _____________ _. - & Kt"- R ~'>< -r-S e1V\ At: If you need more space, continue on the back and check here. ~ .\- c. fN. ~ r '"'~ ..f. '7 \'-'.,~ ,,·ve~ -f'\.,..<. \,~\o."U .