Physics 231 Sample Exam 2 (Ch 5 8) Incorrect explanations mixed in with correct explanations will be counted wrong.

Transcription

1 Physics 3 Sample Exam (Ch 5 8) 009 Name Use correct notation for vectors and scalars. Read all problems carefully before attempting to solve them. Your work must be legible, and the organization must be clear. Correct answers without adequate explanation will be counted wrong. Incorrect explanations mixed in with correct explanations will be counted wrong. Make explanations complete but brief. Do not write a lot of prose. Include diagrams! Show what goes into a calculation, not just the final number: Give physical units with your results. If you cannot do some portion of a problem, invent a symbol for the quantity you can t calculate (explain that you re doing this), and do the rest of the problem. Problem Score (8 pts): (6 pts): 3 (6 pts): (30 pts): 5 (5 pts): 6 (5 pts): 7 (5 pts bonus): Total:

2 Physics 3 Exam (Ch 5-8) 006 Things you must know: () Definition of and approximation for average velocity (and the position update formula) () Definition of momentum v c (3) The Momentum Principle (also, the momentum update formula and derivative form) () Definitions of total energy, rest energy, and kinetic energy of a particle (5) The Energy Principle be able to apply to point particle systems and real systems EVALUATING SPECIFIC PHYSICAL QUANTITIES Projectile Motion: x f x i v xi t y f y i v yi t g t v xf v xi v yf v yi g t du F x F grav on by G m m dx Near the Earth s surface F grav mg 0 r ˆr U elec, and U grav mgy q F q elec on by 0 r ˆr U Gm m grav r U spring k s s U o k s m F k s spring s Y F / A L / L Ethermal cvm T Power = energy/time (watts = joules/second) k s, atomic d atomic q q r, opposite the stretch v sound d atomic k s, atomic m F air C Avˆv F buoyancy weight of displaced fluid K mv = p m for v c E pc mc dp m dp Circular motion at constant speed: rˆ, or m rˆ dt v / c dt r v T r F d p dt ˆp F p dˆp dt p v R ˆn W F for v << c r (for constant force) Where d dt T m Multiparticle Systems: r r m r cm Pcm Mvcm m m (v<<c) K tot K trans K rel K (v<<c) K rel K rot K vib trans Mv cm CONSTANTS G 6.7 N m /kg 8 g = 9.8 N/kg c 3 m / s 9 9 N m / C o Avogadro s number = 6 3 molecules/mole m electron = 9-3 kg m proton m neutron m hydrogen atom =.7-7 kg 5 Typical atomic radius r m Proton radius r m Specific Heat of water c v =. 3 J/(Kg K) 9 M Xena.86 kg M Gabrielle 5.63 kg Radius of Xena =.5 6 m Radius of Gabrielle =.9 5 m Distance from Sun to Xena =.0 3 m Distance from Xena to Gabrielle = m

3 Physics 3 Exam (Ch 5-8) Problem (8 pts) You use a beater to stir a pot of 600 grams of water on an electric stove, doing 3000 J of work on the water. From the observed temperature rise of the water, and the known heat capacity of water, you conclude that the rise in the thermal energy of the water was E thermal = 00 J. a) ( pts) How much thermal transfer of energy Q (microscopic work) was there from the stove to the water? b) ( pts) By how much does its temperature rise?

4 Physics 3 Exam (Ch 5-8) 006 Problem (6 pts) In lab you both experimented with and simulated a mass-spring system. When you plotted the kinetic energy and the spring potential energy (just s, neglecting U o ) the two curves crisscrossed each other, so, periodically K and U sp were equal. Consider a horizontal spring-mass system with spring constant 3 N/m, equilibrium spring length of 0.m, that is initially stretched 0.0m and then released from rest. For what two spring lengths will K = U sp? k s

5 Physics 3 Exam (Ch 5-8) Problem 3 (6 pts) A proton is sped up by a constant electric force < 3,, > N. When the proton passes the location < 5,, 6 > m, its speed is.95 8 m/s. (a) (8 pts) What is the kinetic energy of the proton at this point? (b) (8 pts) When the proton passes the location < 8, 0, > m, what is its kinetic energy? If you could not do part (a), call the answer to part (a) K a and express your answer to part (b) in terms of K a.

6 Physics 3 Exam (Ch 5-8) Problem (30 pts) Not so long ago, we knew of only 9 planets orbiting our sun and none orbiting other stars. Today, we know of over 00 planets orbiting other stars (and still counting) and just shy of 0 planets or plentoids (not officially designated planets ) around our own sun. Our local neighbors include Santa with the moon Rudolph and Xena with the moon Gabrielle (I m not making this up). Xena is actually half-again as large as Pluto and is probably over twice as massive! Say Xena-lings want to fly a rocket to their moon, Gabrielle (okay, I am making up the bit about the Xena-lings). (a) (8 pts) Fill in the plot of the combined gravitational potentials for the ship s interactions with Xena and Gabrielle, U = U X,s + U G,s. Also draw the K+U line for a ship that just makes it (doesn t come to a stop and fall back to Xena). Finally, draw what the K curve must look like for the trip. r Be sure you label the curves to identify them! X G (b) ( pts) If the space ship launches from Xena s surface with speed v i and costs all the way how fast will it be going when arrives at Gabrielle in terms of v i, G, M G, M X, R G, R X and R G-X? (plug in no numeric values).

7 Physics 3 Exam (Ch 5-8) Problem 5 (5 pts) You have a cold gas of atoms, and you observe that if you shine light consisting of photons with energy.5 ev through the gas, some free electrons are observed, implying that a photon of this energy is able to ionize an atom in the gas. You find that the emitted electrons have a kinetic energy of.3 ev. (a) ( pts) What is the ionization energy of these atoms, the energy required to remove an electron? (b) ( pts) What is the ground state energy K+U of one of these atoms? Next you shine light with a continuous energy distribution through the gas, and you observe absorption lines ( dark lines in the spectrum, corresponding to depletion of photons) at the following photon energies:. ev, 6.3 ev, 7.6 ev, and 8.7 ev. (c) ( pts) Using the information from the two experiments described above, draw a diagram of the energy levels of one of the atoms in this gas. Draw the diagram approximately to scale. Label the energy levels with their values of K+U. Do not draw a potential energy curve, because these data are insufficient to determine its shape. Finally, you run a beam of electrons through the gas. The kinetic energy of the electrons is 8.0 ev. Collisions of the electrons in the beam with the atoms of the gas excite gas atoms to states above the ground state. (d) ( pts) Draw and label with photon energies all possible transitions between levels as they would be detected by a photon detector that is sensitive to a wide range of photon energies. Arrows should start on initial states and end on final states.

8 Physics 3 Exam (Ch 5-8) Problem 6 (5 pts) Here is a program to model a mass oscillating on a spring. In lab you modified this to include a viscous drag force. For a mass-spring system oscillating in air, a better model for the drag would be that of air resistance. Add and modify necessary lines of code outside and inside the while-loop to include this force. Take the drag coefficient to be 0.3, and the density of air to be.9 kg/m 3. Recall that a sphere s cross-sectional area is simply the area of a circle of equal radius. from visual import * from future import division # makes / be 0.5, not 0 Req = 0.5 # equilibrium length of spring Ro = Req + vector(0.,0,0) # initial extension of the spring ks =. spring = cylinder(pos=vector(0,0,0), axis=ro, radius=0.0) track = box(pos=vector(0,-.075,0), size=(.0,0.05,0.)) ball = sphere(pos=ro, radius=0.05, color=color.green) ball.m = 0.05 ball.p = ball.m*vector(0,0,0) D= # that s often denoted, but VPython doesn tknow greek. ball.a = C = deltat = 0.00 t = 0 while t<3.0: rate(0) Fsp = -ks*(ball.pos Req*ball.pos/mag(ball.pos)) Fair = Fnet = ball.p = ball.p + Fnet*deltat ball.pos = ball.pos + (ball.p/ball.m)*deltat spring.axis = ball.pos t = t + deltat Problem 7 No longer covered in Ch 8; won t be on the 03 Exam (but appropriate for Exam 3) When I play with a yo-yo, I pretty quickly end up with it just dangling from my finger with the string all unwound. To rewind it, I set the yo-yo on the floor and pull the string forward as the yo-yo rolls forward it rewinds the string. Let s say I ve got a yo-yo of mass m with string length l. With a force F, I pull the yo-yo forward a distance d (which is less than l); meanwhile, a slightly weaker frictional force, f, pulls back in the other direction (thus the yo-yo rolls rather than slides). In terms of these parameters, what s the rotational energy of the yo-yo when it rolls into my hand?

9 Physics 3 Exam (Ch 5-8) BONUS (5 pts) Since this problem is only worth 5 bonus points, don t attempt it unless you have finished all the other problems and checked your work. Radium-6 is a radioactive nucleus that decays via a process called alpha decay into a radon- nucleus and a helium- nucleus. The atomic masses of radium-6, radon- and helium- are 6.05u,.07u and.00u, where u = kg. In gram of radium there are 3.7 decays per second (this is sometimes used as a unit of radioactivity and called Curie). Consider a block of radium with a mass of 0.0 kg. If the radium is perfectly isolated from the environment, and all the radioactive decay energy is deposited inside the material, by how much does the temperature of the radium block increase in one second? The heat capacity of radium is 9 J/(kg K).