physics exam

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Auburn University *

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1600-001

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Physics

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Apr 3, 2024

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MIDTERM ANSWERS Under typical atmospheric conditions, there is an electric field near the earth's surface, directed downward, with a magnitude of 100 V/m Part A Part complete If we say that the potential at the earth's surface is 0 V V , what is the potential 1.3 km km above the surface? Express your answer with the appropriate units.V V =1.3×10 ^5 V Consider the wires shown in ( Figure 1 ). The upper wire carries the current I 1 = 20 A .What should the current I2 be in the lower wire such that the magnetic field at point P P is zero? Express your answer with the appropriate units. I2 = 40 A The three bulbs in (Figure 1) are identical. Rank the bulbs from brightest to dimmest. Rank the bulbs from brightest to dimmest. To rank items as equivalent, overlap them. A, BC, blank What is the magnitude of the electric field at the dot in the figure? (Figure 1) Express your answer in volts per meter. E= 1.0×10^4V/m What is the direction of the electric field at the dot in the figure? to the left

What is the time constant for the discharge of the capacitors in the figure (Figure 1)? Express your answer in milliseconds. τ =2.0 ms Draw a circuit diagram for the circuit of (Figure 1). —------------>

What is the equivalent resistance of group (a) of resistors shown in the figure? (Figure 1) Express your answer in ohms. Req = 11.0 Ω What is the equivalent resistance of group (b) of resistors shown in the figure? Express your answer in ohms. Req =9.0Ω ^^^ A scalloped hammerhead shark swims at a steady speed of 1.0 m/s with its 87-cm-wide head perpendicular to the earth's 58 μT magnetic field. What is the magnitude of the emf induced between the two sides of the shark's head? Express your answer in millivolts. E = 5.0×10^−2 mV What is the strength of the electric field 3.0 cm from a small glass bead that has been charged to + 7.0 nC ? Express your answer in newtons per coulomb. E =7.0×10^4 N/C What is the direction of the electric field 3.0 cm from a small glass bead that has been charged to 7.0 nC ? away from the bead As shown in (Figure 1), two protons are launched with the same speed from point 1 inside a parallel-plate capacitor. One proton moves along the path from 1 to 2, the other from 1 to 3. Points 2 and 3 are the same distance from the positive plate. Is ΔU1→2 , the change in potential energy along the path 1→2 , larger, smaller, or equal to ΔU1→3 ΔU1→2= ΔU1→3 Is the proton's speed v2 at point 2 larger than, smaller than, or equal to the proton's speed v3 at point 3? v2=v3

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The current in an electric hair dryer is 14A. How much charge flows through the hair dryer in 4.0 min? Express your answer in coulombs. Q=3400C How many electrons flow through the hair dryer in 4.0 min ? Ne =2.1×10^22 A copper loop hangs from two strings, as shown in (Figure 1). In which direction (toward or away from the magnet) does the loop swing if the magnet is stationary? The loop doesn't move. In which direction (toward or away from the magnet) does the loop swing if the magnet is moving toward the loop? away from the magnet In which direction (toward or away from the magnet) does the loop swing if the magnet is moving away from the loop? toward the magnet The wires in (Figure 1) are all made of the same material; the length and radius of each wire is noted. Rank in order, from largest to smallest, the resistances R1to R5 of these wires. Rank from largest to smallest. To rank items as equivalent, overlap them. R4, R5 and R1, R3, R2

What is the equivalent capacitance of the three capacitors in the figure? (Figure 1) Express your answer in microfarads. C=8.9 μF A current loop in a motor has an area of 0.75 cm2. It carries a 240 mA current in a uniform field of 0.62 T. What is the magnitude of the maximum torque on the current loop? Express your answer with the appropriate units. τ = 1.1×10^−5 N ⋅ m QUIZ QUESTIONS: A person's heart rate is given in beats per minute. Part A: Is this a period or a frequency? frequency If you want to play a tune on wine glasses, you'll need to adjust the oscillation frequencies by adding water to the glasses. This changes the mass that oscillates (more water means more mass) but not the restoring force, which is determined by the stiffness of the glass itself. Part A: If you need to raise the frequency of a particular glass, should you add water or remove water? remove water In 1831, soldiers marched across the Broughton Bridge in England in "lock step"-that is, marching in time together. As they marched, the bridge began to bounce in time with their footsteps; the amplitude of this bouncing became larger and larger until the bridge suddenly collapsed

Explain why the lock step of the soldiers caused this collapse and why afterward soldiers were ordered to "break step," or march at their own individual rates, as they crossed bridges. Match the words in the left column to the appropriate blanks in the sentences on the right. Make certain each sentence is complete before submitting your answer. FILL IN THE BLANK Every object has natural frequencies of oscillation with which they will respond when deflected from equilibrium. The marching soldiers appear to have been marching at a pace such that their stomping boots drove the oscillation of the bridge at the same frequency as its natural frequency Pushing an oscillating system at the same rate as it responds is like pushing a child on a swing at just the right time to drive the oscillations larger and larger. If the soldiers break step, the total driving force has no fixed frequency and will not drive the bridge into large-amplitude oscillations. When a guitar string plays the note "A," the string vibrates at 440 Hz Part A:What is the period of the vibration? Express your answer in seconds. T =2.3×10^−3 s In the aftermath of an intense earthquake, the earth as a whole "rings" with a period of 54 minutes. Part A:What is the frequency of this oscillation? Express your answer in hertz. f =3.1×10^−4 Hz An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t = 0 s. It then oscillates with a period of 1.5 s and a maximum speed of 60 cm/s . What is the amplitude of the oscillation? Express your answer in centimeters. A = 14cm What is the glider's position at t = 0.29 s? Express your answer in centimeters. x = 5.0cm Some passengers on an ocean cruise may suffer from motion sickness as the ship rocks back and forth on the waves. At one position on the ship, passengers experience a vertical motion of amplitude 1.6 m with a period of 16 s . What is the maximum acceleration of the passengers during this motion? Express your answer in meters per second squared. a max=0.25 m/s^2 What fraction is this of g? Express your answer in units of g. a max=2.5×10^−2g

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A 509 g mass oscillates with an amplitude of 10.0 cm on a spring whose spring constant is 25.0 N/m . Determine the period. Express your answer in seconds. T =0.897s Determine the maximum speed. Express your answer in meters per second. v max =0.701 m/s Determine the total energy. Express your answer in joules. W total =0.125J A mass on a string of unknown length oscillates as a pendulum with a period of 3.0 s. What is the period if the mass is doubled? Express your answer in seconds. T=3.0s What is the period if the string length is doubled? Express your answer in seconds. T =4.2s What is the period if the string length is halved? Express your answer in seconds? T =2.1s What is the period if the amplitude is doubled? Express your answer in seconds. T =3.0s Bottlenose dolphins (Figure 1) use echolocation pulses with a frequency of about 100 kHz, higher than the frequencies used by most bats. Why might you expect these water-dwelling creatures to use higher echolocation frequencies than bats? Drag the terms on the left to the appropriate blanks on the right to complete the sentences. FILL IN THE BLANK The speed of sound in water is greater than in air; hence for the same frequency the sound wavelength in water is greater than in air (for the given frequency the wavelength is in the direct proportion with the speed of sound). To "see" an object via the echolocation creature needs to use sound with the wavelength Smaller than the size of an object viewed. That means to "see" objects of the same size dolphin and bat need to use ultrasound of the same wavelength, hence dolphin needs to use higher frequency (for the given speed of sound the wavelength is in inverse proportion with the frequency).

Home professionals like realtors use ultrasonic measuring tools to quickly measure the size of rooms. These instruments work by sending out a pulse of ultrasonic sound, then measuring the time it takes for this pulse to reflect off a wall and return to the device. If you used such a device on a particularly hot day, would you measure the length of a given room to be longer or shorter than on a cool day? Construct the correct explanation. Drag the terms on the left to the appropriate blanks on the right to complete the sentences. FILL IN THE BLANK The speed of a sound wave in air increases with temperature vsound ∼ √T So on a hot day the sound pulse will strike the wall and return to the detector in a shorter time than on a cold day. Thus, the length of the room on a hot day will be measured to be shorter than on a cool day When in air, a waterproof speaker emits sound waves that have a frequency of 1000 Hz. When the speaker is lowered into water, does the frequency of the sound increase, decrease, or remain the same? The frequency remains the same. When the speaker is lowered into water, does the wavelength of the sound increase, decrease, or remain the same? The wavelength increases. The wave speed on a string under tension is 160 m/s . What is the speed if the tension is doubled? Express your answer in meters per second. v′ =230m/s The intensity of electromagnetic waves from the sun is 1.4 kW/m^ 2 just above the earth's atmosphere. Eighty percent of this reaches the surface at noon on a clear summer day. Suppose you model your back as a 28 cm × 49 cm rectangle. How many joules of solar energy fall on your back as you work on your tan for 1.5 h ? Express your answer in joules. E = 8.3×10^5 J A guitarist finds that the pitch of one of her strings is slightly flat - the frequency is a bit too low. The frequency of a vibrating string is determined by . So if the tension in the string increases, the rate at which it vibrates (the frequency) will also increase.

(Figure 1) shows a standing wave on a string. Point A on the string is shown at time t = 0. For t≥0 , what are the earliest times, in terms of the wave's period T , that points B , C, and D reach the positions shown? Express your answer in terms of T separated by commas. tB,tC,tD = T/2,0,T/4 You are listening to music from a loudspeaker. Then a second speaker is turned on. Is it possible that the music you now hear is quieter than it was with only the first speaker playing? yes Explain. Match the words in the left column to the appropriate blanks in the sentences on the right. Make certain each sentence is complete before submitting your answer. FILL IN THE BLANK The effect is easier to observe when the loudspeakers play a single frequency To observe it, you need to be at a location where compressions from one speaker will reach your ear at the same time as rarefactions from the other speaker. This can cause a reduction in the overall amplitude and the sound can be quieter, which is an example of destructive interference. The figure shows a standing wave oscillating at 100 Hz on a string. (Figure 1) What is the wave speed? Express your answer in meters per second. v =40m/s Two strings are adjusted to vibrate at exactly 190 Hz . Then the tension in one string is increased slightly. Afterward, three beats per second are heard when the strings vibrate at the same time. What is the new frequency of the string that was tightened? Express your answer in hertz to three significant figures.

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f= 193Hz The width of a particular microwave oven is exactly right to support a standing-wave mode. Measurements of the temperature across the oven show that there are cold spots at each edge of the oven and at three spots in between. The wavelength of the microwaves is 12 cm. How wide is the oven? Express your answer with the appropriate units. l =24 cm Rank in order the following according to their speeds, from fastest to slowest: (i) 425- nm -wavelength light through a pane of glass, (ii) 500- nm -wavelength light through air, (iii) 540- nm -wavelength light through water, (iv) 670- nm -wavelength light through a diamond, and (v) 670- nm -wavelength light through a vacuum. Rank from fastest to slowest. To rank items as equivalent, overlap them. fastest speed v V, ν ii , ν iii ,v i, ν iV How long does it take light to travel through a 2.0- mm -thick piece of window glass? Express your answer in seconds. t = 1.0×10^−11s Two narrow slits are illuminated by light of wavelength λ. The slits are spaced 40 wavelengths apart. What is the angle, in radians, between the central maximum and the m = 1 bright fringe? Express your answer in radians. θ = 2.5×10^−2 rad A 1.0-cm -wide diffraction grating has 1000 slits. It is illuminated by light of wavelength 590 nm . What are the angles of the first two diffraction orders? Express your answers in degrees separated by a comma. θ1, θ2 = 3.4,6.8 ∘∘ , Solar cells are given antireflection coatings to maximize their efficiency. Consider a silicon solar cell (n=3.50) coated with a layer of silicon dioxide (n=1.45). What is the minimum coating thickness (but not zero) that will minimize the reflection at the wavelength of 697 nm where solar cells are most efficient? Express your answer in nanometers. d=120nm The second minimum in the diffraction pattern of a 0.11- mm -wide slit occurs at 0.68 ∘∘ . What is the wavelength of the light? Express your answer in nanometers. λ =650nm

Can you see the rays from the sun on a clear day? Why or why not? How about when they stream through a forest on a foggy morning? Why or why not? Drag the terms on the left to the appropriate blanks on the right to complete the sentences. FILL IN THE BLANK You cannot see the sun's rays on a clear day. Rays of light are only visible if they reach your eye. For that to happen they have to be scattered off by something. When sunlight goes through treetops into a foggy forest the rays can be scattered off by the water vapor presented in the air. In that case, your eyes can detect light from regions where sunlight is shining in, so you Can effectively see the rays. Consider one point on an object near a lens. What is the minimum number of rays needed to locate its image point? 2 For each point on the object, how many rays from this point actually strike the lens and refract to the image point? Infinite number. An underwater diver sees the sun 57 ∘ above horizontal. How high is the sun above the horizon to a fisherman in a boat above the diver? Express your answer in degrees. ϕ =44 ∘ A light bulb is 60 cm from a concave mirror with a focal length of 20 cm. Use ray tracing to determine the location of its image. Express your answer to two significant figures and include the appropriate units. s′ =30 cm Is the image upright or inverted? inverted A 1.0-cm -tall object is 9.0 cm in front of a converging lens that has a 30 cm focal length. Calculate the image position. Express your answer with the appropriate units. Enter positive value if the image is on the other side from the lens and negative value if the image is on the same side as the object. s′ = -13 cm Calculate the image height. Express your answer with the appropriate units. h = 1.4 cm You are looking straight into the front of an aquarium. You see a fish off to your right. Is the fish actually in the direction you're looking, farther to the right, or farther to the left?

Drag the terms on the left to the appropriate blanks on the right to complete the sentences. FILL IN THE BLANK The light rays coming out of the water bend away from the normal Looking back along the line the light takes in the air gives you an image to the right from where the object really is, that means the fish is to the left from where you see it. If you hold a spoon in front of your face so that you see your image in the bowl of the spoon, your image is upright when you hold the spoon close to your face, but inverted when you hold the spoon far away. Construct the correct explanation why this change occurs. Drag the terms on the left to the appropriate blanks on the right to complete the sentences. FILL IN THE BLANK The spoon acts like a converging mirror. Light from your face is focused by the mirror. If you are very close to the spoon (within the focal length) then the light rays are converged somewhat . If you are farther from the spoon (beyond the focal length) then the light rays form an inverted image . You are using a converging lens to look at a splinter in your finger. The lens has a 9.0 cm focal length, and you place the splinter 6.0 cm from the lens. How far from the lens is the image? Express your answer to two significant figures and include the appropriate units. Enter positive value if the image is on the other side from the lens and negative value if the image is on the same side. s′ = -18 cm What is the magnification? Express your answer using two significant figures. Enter positive value if the image is upright and negative value if the image is inverted. m = 3.0 If you launch a projectile upward with a high enough speed, its kinetic energy is sufficient to allow it to escape the earth's gravity−it will go up and not come back down. Given enough time, hydrogen and helium gas atoms in the earth's atmosphere will escape, so these elements are not present in our atmosphere. Explain why hydrogen and helium atoms have the necessary speed to escape but why other elements, such as oxygen and nitrogen, do not. Drag the terms on the left to the appropriate blanks on the right to complete the sentences. FILL IN THE BLANK This is because hydrogen and helium, being lighter, move faster The root-mean-square speed of a particle is in Direct proportion with the square root of the temperature and in inverse proportion with the square root of its mass. Hence the lighter particles can escape the earth's gravity while havier cannot.

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You fill up a steel container with cool water to the very top. Now you place the container in the sun. As the container warms up, the water expands, but so does the container. Does the water overflow? Choose the correct explanation. Yes. Water has a significantly higher coefficient of thermal expansion than steel--about six times as much. As the water and steel get hotter, the water expands six times more than the steel. You may have noticed that latex helium balloons tend to shrink rather quickly; a balloon filled with air lasts a lot longer. Balloons shrink because gas diffuses out of them. The rate of diffusion is faster for smaller particles and for particles of higher speed. Diffusion is also faster when there is a large difference in concentration between two sides of a membrane. Given these facts, explain why an air-filled balloon lasts longer than a helium balloon. Drag the terms on the left to the appropriate blanks on the right to complete the sentences. FILL IN THE BLANK Since there is almost pure helium in a helium balloon and almost no helium in the outside air, helium tends to diffuse out of the balloon. Similarly, with almost no oxygen or nitrogen in the balloon initially and high concentrations of oxygen and nitrogen in the air, these molecules tend to diffuse into the balloon. However, since helium atoms travel about three times faster than oxygen or nitrogen molecules and since helium atoms are smaller, they diffuse much faster , so, gas leaves the balloon faster than it enters. An air-filled balloon has the same particles inside as outside and, therefore, the stated effect does not contribute to the deflation of such balloons. A common trick for opening a stubborn lid on a jar is to run very hot water over the lid for a short time. (Figure 1) Explain how this helps to loosen the lid. Drag the terms on the left to the appropriate blanks on the right to complete the sentences. FILL IN THE BLANK Thermal expansion will make the lid expand . The glass jar will also expand , but the coefficient of expansion of the glass is smaller than the coefficient for the metal, and this allows to open the lid.

The length of a steel beam increases by 0.79 mm when its temperature is raised from 22 ∘ C ∘ to 35 ∘ C. What is the length of the beam at 22 ∘ C? Express your answer in meters. L0 =5.1m A 1.9-cm-thick wood floor covers a 4.0m×5.5m room. The subfloor on which the flooring sits is at a temperature of 16.4 ∘ C , while the air in the room is at 19.5 ∘ C . What is the rate of heat conduction through the floor? Use 0.200 W/m ⋅ K for the thermal conductivity of wood. Express your answer in watts. P =720W END OF QUIZ QUESTIONS

physics exam

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