Physics 231 Exam 2 (Ch 4 – 6) 2006 Problem 1 (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 DEthermal = 12000 J. (a) (4 pts) How much thermal transfer of energy Q (microscopic work) was there from the stove to the water? (b) (4 pts) By how much does its temperature rise? Problem 2 (16 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 221sks, neglecting Uo) the two curves crisscrossed each other, so, periodically K and Usp were equal. Consider a horizontal spring-mass system with spring constant 3 N/m, equilibrium spring length of 0.11m, that is initially stretched 0.04m and then released from rest. For what two spring lengths will K = Usp? Problem 3 (16 pts) A proton is sped up by a constant electric force < 3×10–12, –2×10–12, 4×10–12 > N. When the proton passes the location < 5, 2, 6 > m, its speed is 2.95×108 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, 4 > m, what is its kinetic energy? If you could not do part (a), call the answer to part (a) Ka and express your answer to part (b) in terms of Ka. Problem 4 (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 200 planets orbiting other stars (and still counting) and just shy of 20 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 = UX,s + UG,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. Be sure you label the curves to identify them! (b) (22 pts) If the space ship launches from Xena’s surface with speed vi and costs all the way how fast will it be going when arrives at Gabrielle in terms of vi, G, MG, MX, RG, RX and RG-X? (plug in no numeric values). Problem 5 (a)(6 pts) A person of mass 70 kg rides on a Ferris wheel whose radius is 4 m. The person’s speed is constant at 0.3 m/s. What is the magnitude of the net force acting on the person at the instant shown? Draw the net force vector on the diagram at this instant, with the tail of the vector on the person (shown as a dot on the diagram). Show your work clearly. r X GPhysics 232 Exam 2 (Ch 4 – 6) 2006 2 (b) (13 pts)You suspend a low-mass spring vertically in the lab. Its length initially is 16 cm. You hang a 300 gram mass from the spring and find that when oscillations have damped out the length of the spring is 16.4 cm. Next you pull the mass down, so the length of the spring is 17 cm, and you release the mass. What is the period of the oscillations? Problem 6 (25 pts) A bar of metal 1.4 m long has a square cross section 8 cm by 8 cm. Young’s modulus for this metal is 3×1010N/m2 and its density is 2700 kg/m3. One mole of the metal has a mass of 70 grams. (a) (15 pts) Calculate the speed of sound in this metal. (b) (10 pts) Given these values, there are about 1.12 ×1016 atoms in one 8cm×8cm cross-section of the bar, therefore there are about 1.12×1016 bonds between layers of atoms. If the bar is completely submerged in water (density = 1000 kg/m3) while being hung vertically, by how much would the top layer of bonds lengthen due to the tension of holding the rod? Problem 7 (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 1.29 kg/m3. 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 1/2 be 0.5, not 0 Req = vector(0.5,0,0) # equilibrium position of spring Ro = Req + vector(0.2,0,0) # initial extension of the spring ks = 2.4 spring = cylinder(pos=vector(0,0,0), axis=Ro, radius=0.01) track = box(pos=vector(0,-.075,0), size=(1.0,0.05,0.10)) ball = sphere(pos=Ro, radius=0.05, color=color.green) ball.m = 0.025 ball.p = ball.m*vector(0,0,0) D= # that’s often denoted ρ, but VPython doesn’tknow greek. Ball.A = C = deltat = 0.001 t = 0 while t<3.0: rate(100) Fsp = -ks*(Ro – Req) Fair = Fnet = ball.p = ball.p + Fnet*deltat ball.pos = ball.pos + (ball.p/ball.m)*deltat spring.axis = ball.pos t = t + deltatPhysics 232 Exam 2 (Ch 4 – 6) 2006 3 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-226 is a radioactive nucleus that decays via a process called alpha decay into a radon-222 nucleus and a helium-4 nucleus. The atomic masses of radium-226, radon-222 and helium-4 are 226.025u, 222.017u and 4.002u, where u = 1.6603×10–27 kg. In 1 gram of radium there are 3.7×1010 decays per second (this is sometimes used as a unit of radioactivity and called 1 Curie). Consider a block of radium with a mass of 0.010 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 94 J/(kg