TFY4102 Exam Fall 2015

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Cameron Lenard Barnett
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1 FY40 Eam Fall 05 Short answer (4 points each) ) Bernoulli's equation relating luid low and pressure is based on a) conservation o momentum b) conservation o energy c) conservation o mass along the low lines d) conservation o entropy ) What is the dierence between the "plot" and "igure" commands in MALAB? "igure" opens a window with aes that can be used or a plot "plot" taes two variables and produces a graph o the second as a unction o the irst 3) Why does the conductivity o semiconductors increase at high temperature? there are more ree carriers, either rom impurity ionization or rom ecitation across the energy gap. 4) Which charged particles contribute to the electric ield on the Gaussian surace shown? a) Only q and q b) Only q3 and q4 c) All our contribute d) Some other combination o particles contribute e) he number o charged particles that contribute depends on the shape o the Gaussian surace 5) Does the woring luid (gas) an air conditioner epand inside the house or outside? Eplain why. he epansion is done inside the house; this reduces the temperature o the woring luid and allows it to absorb heat rom the inside o the building.

Problems: j μ i A) MECHANICS wo blocs are staced on top o one another on a rictionless inclined plane, and are attached to each other with a massless string that runs through a rictionless pulley, as

Consider the case where the blocs are moving and are still in contact, and the inetic coeicient o riction between the two blocs is μ, and the acceleration due to gravity is g.

2 Problems: j μ i A) MECHANICS wo blocs are staced on top o one another on a rictionless inclined plane, and are attached to each other with a massless string that runs through a rictionless pulley, as shown. Bloc is lighter than Bloc (m < m ). Consider the case where the blocs are moving and are still in contact, and the inetic coeicient o riction between the two blocs is μ, and the acceleration due to gravity is g. a) 4 In what direction (vector ormat) does Bloc move? the displacement is a multiple o the vector dˆ ( cos iˆ sin ˆj ) b) 4 Draw ree-body (orce) diagrams or the two blocs. Show your choice o coordinate system. deine ˆ parallel to the inclined plane and ŷ perpendicular to it. hen all motion will be parallel to. N N ˆ ŷ mg Np mg c) 8 Solve or the acceleration o each bloc in terms o m, m, μ,, and g. Bloc ˆ : m g sin m a Bloc yˆ : N m g cos 0 m g cos m g cos m g sin m a a a a ˆ : m g sin m a m g cos m g sin m a

m g cos m g sin m a m g cos m g sin m a subtract thebottom equation and divide by sum o masses ( m g cos ) ( m m ) g sin a m m d) How will the equations change when /3 o Bloc is no longer in contact

3 m g cos m g sin m a m g cos m g sin m a subtract thebottom equation and divide by sum o masses ( m g cos ) ( m m ) g sin a m m d) How will the equations change when /3 o Bloc is no longer in contact with (o the top end o) Bloc? It will not change because the riction depends only on the normal orce, and the weight o Bloc is still supported entirely by Bloc. (Friction is not area dependent) B) HERMODYNAMICS he speciic heat o copper at low temperatures is approimated by c = 3(/34) 3 J/g.K. a) 6 Find the entropy change when a 50g ingot o copper is cooled rom 5K to 0K. b) 4 What is the sign o the change, and why? he entropy change is negative because cooling the bloc decreases the entropy. dq ds 3 mc m3( ) 3m 3 34 S d d dt 34 3m g K.88 0 J/g C) ELECROSAICS A thin dis with a circular hole at its center, called an annulus, has an inner radius R and and outer radius R. he dis has a uniorm positive surace charge density on its surace. a) 4 determine the total electric charge on the annulus ( R R ) b)8 or an arbitrary point on the -ais (using the coordinates shown), ind the electric potential, U. b R r dr V dv r R R r R a c)6 Show that the electric orce on a negatively charged particle, -q with mass m placed on the ais at a distance 0= 0.0 R is a linear unction o. here are two ways to do this; either dierentiate V(), or use superposition and Coulomb's law to develop an epression or the E-Field., then use F=qE. E( ) / ( R ˆ / ) / ( R/ ) i. 0

he distance to the plane o the ring is much less than the ring diameter. You need to approimate the ield without eliminating it completely / ( R / ) ( ( / ) ) / R R R ˆ E( ) i i ˆ.

4 he distance to the plane o the ring is much less than the ring diameter. You need to approimate the ield without eliminating it completely / ( R / ) ( ( / ) ) / R R R ˆ E( ) i i ˆ. 0 R R 0 R R q F qe 0 R R d)6 Write down the equation o motion or this particle and ind the oscillation requency. q m 0 R R his is just Hooe's law with q 0 R R q m 0m R R D) WAVES In the optical setup shown, intererence occurs between the light coming directly rom the source, and light relected rom the silicon mirror (n=3.4). a)6 Find an epression or the separation o bright ringes on the screen, in terms o d, D and the wavelength o the light,. Because o the etra 80 phase change, the direct and relected beams o light will constructively interere when their path lengths are an odd-integer multiple o hal-wavelengths: dsin m m. hereore, the separation between ringes on the screen will be 3 D y Dsinm Dsinm Dm m d d b)4 How will the result change i the entire eperiment is perormed underwater (n=.33)? he wavelength will be replaced by ' /.33 he inde o the silicon is still higher than the water, so the phase shit on relection will not be changed; however the amplitude o the relected light would be reduced a little.

5 E) CIRCUIS In circuit diagram A, the resistors all have the same value, and the two capacitors are dierent. I the capacitors are initially uncharged, a) 4 Give an epression or the current through R immediately ater the switch is closed. he capacitors act lie short circuits and no current lows through R ; I=0 b) 4 Give an epression or the current through R ater the switch has been closed or a long time. When the switch has been closed or a long time, C and C are ully charged. No current will low through them and the circuit is equivalent to R and R in series. I= ɛ/(r +R ) B A c) 6 In circuit diagram B, the batteries and meters are all ideal. With the switch open, the voltmeter reads 7.0 V. What is the em,, o the battery? Find the current through the unnown battery using Ohm s law. hen use the equivalent resistance o the circuit to ind the em o the battery. I50 (7.0 V)/(50.0 ) 0.34 A I30. he potential drop across the resistor is the same as the potential drop across the series combination. We can use this act to ind the current through the resistor using Ohm s law: V75 V80 (0.34 A)(80.0 ) 7. V I (7.V)/(75.0 ) A. I 75 tot A he equivalent resistance o the resistors in parallel is / R =/(75.0 ) /(80.0 ). Rp 387. then the total resistance seen by the voltage p source is Requiv Requiv Iotal (58.7 )(0.703 A) 4.3 V. d) 6 In Circuit diagram B, what will the ammeter reading be when the switch is closed? With the switch closed, the 5 V battery is connected across the resistor. ae a loop around the right part o the circuit; the voltage drop across the resistor must be 5 V. Ohm s law gives I (5.0 V)/(50.0 ) A.

Lesson 6: Apparent weight, Radial acceleration (sections 4:9-5.2)

Lesson 6: Apparent weight, Radial acceleration (sections 4:9-5.2) Beore we start the new material we will do another Newton s second law problem. A bloc is being pulled by a rope as shown in the picture. The coeicient o static riction is 0.7 and the coeicient o inetic