BYU IS Physics 123 Final Exam Review
8.3 According to a stationary observer, a moving object is (a) shorter or (b) longer than an identical stationary object.
(A) 8.3 This is yet another consequence of Einstein's special theory of relativity. It is called length contraction
*2.2 If we increase the tension on a string, the velocity of waves traveling along the string will (a) increase, (b) decrease, or (c) remain the same.
2.2 From v = pT /µ, we see that if we increase the tension T, the velocity v must also increase. Also T and wavelength are directly proportional. Since wavelength and v are also proportional, v and T are also proportional.
7.4 Consider an interference pattern produced by a diffraction grating. If we use a grating with lines closer together, the distance between the points of maximum intensity in the pattern will (a) increase, (b) decrease, or (c) remain the same.
7.4 From d sin θbright = mλ, we see that if the distance d between lines is decreased, the angle θbright must increase, as will also the distance between the points of maximum intensity. (A)
9.l In the photoelectric effect, no electrons are emitted if the frequency of the light is (a) greater or (b) less than the cutoff frequency
9.1 The energy of a photon is equal to hf. At frequencies f greater than the cutoff frequency fc, the photons have more than enough energy to cause an electron to be emitted. (B)
1.4 An object is submerged in water 10 m below the surface. If I move the object to 20 m below the surface, the buoyant force of the water on the object will (a) increase, (b) decrease, or (c) remain the same. Consider the density of the water and the volume of the object to not be affected by the change in depth.
1.4 From B = ρfluidgV , we see that the buoyant force B depends only on the density ρfluid of the fluid, not the depth.
*1.5 A container of water is sitting on a scale. I dip my finger into the water without touching the sides or bottom of the container. The force exerted on the scale by the container will (a) increase, (b) decrease, or (c) remain the same
1.5 The water produces an upward buoyant force on the finger. By Newton's third law, the finger therefore produces a downward force on the water.
1.6 A block of balsa wood is floating in water. (Balsa wood has a very small density.) A stone is tied to the top of the block. The weight of the stone is chosen so that exactly half the wooden block is below the surface of the water. When the block is turned over so that the stone is underneath and submerged, will the amount of the wooden block below the surface of the water be (a) less than half, (b) still equal to half, or (c) more than half? Be sure to indicate the answer for the amount of the block below the surface, not above the surface.
1.6 When the block and stone are turned over, they still have the same total weight. Therefore the buoyant force keeping them afloat must be the same. This means that the submerged volume must be the same. When the block and stone are turned over, the submerged volume now includes the volume of the stone, so the submerged volume of the block will be less. (G)
1.7 Air is flowing through the tube shown in the figure. The velocity v2 (smaller tube section) is (a) greater than, (b) less than, or (c) equal to the velocity v1 (larger tube section).
1.7 From A1v1 = A2v2, we see that if A2 is less than A1, then v2 must be greater than v2 (A)
1.8 In the previous problem, the pressure in the small tube is (a) greater than, (b) less than, or (c) equal to the pressure in the large tube
1.8 From P +0.5ρv^2 + ρgy = constant, we see that if the velocity v of the fluid increases, then its pressure P must decrease (B)
1.9 A small tunnel is dug near the edge of a cliff. One end of the tunnel is on top of the cliff where the wind is blowing. The other end comes out the side of the cliff where there is no wind. In which direction will the air in the tunnel move? (a) out the top (b) out the side of the cliff.
1.9 The pressure will be less at the top because the air is moving there. Therefore, air willflow out the top. Velocity and Pressure in Venturi tubes are inversely proportional. Pressure +KE + PE = Constant.
10.1 All isotopes of a given element have the same (a) atomic number, (b) neutron number, (c) mass number, (d) atomic number and neutron number, (e) atomic number and mass number, (f) neutron number and mass number, or (g) atomic number, neutron number, and mass number.
10.1 Two different isotopes of the same element have the same number of protons (atomic number Z) but different number of neutrons (neutron number N). This means that the mass number A = Z + N must also be different. (A)
10.10 The sun produces energy using nuclear (a) fusion or (b) fission.
10.10 The energy of the sun is generated by the proton-proton cycle, where hydrogen nuclei essentially combine to form helium nuclei.
10.2 Stable isotopes of the heavier atoms have (a) more protons than neutrons or (b) more neutrons than protons in their nuclei.
10.2 As the number of protons increases, the strength of the Coulomb force increases, which tends to break the nucleus apart. As a result, more neutrons are needed to keep the nucleus stable because neutrons experience only the attractive nuclear force. (B)
10.3 A deuteron is a particle composed of a proton and a neutron bound together. Which of the following is greater? (a) mass of deuteron (b) mass of proton plus mass of neutron (c) equal
10.3 The total energy of nucleons bound together in an atomic nucleus is less that the combined energy of the separated nucleons. From E = mc2, we see that this same statement is true for mass as well. The total mass of nucleons bound together in an atomic nucleus is less that the combined mass of the separated nucleons. (B)
10.4 A radioactive sample of 128 53 I emits 256 beta particles per second. After how many half-lives will this sample emit 1 beta particle per second? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 (f) 6 (g) 7 (h) 8 (i) 9 (j) 10
10.4 After each half-life, the sample will emit half as many particles per second. So after 1 halflife, the sample will emit 128 particles per second; after 2 half-lives, 64 particles; 3 half lives, 32; 4 half-lives, 16; 5 half lives, 8; 6 half lives, 4; 7 half lives, 2; and 8 half lives, 1
10.5 Consider the alpha decay: 238 92 U → 4 2He + 234 90 Th. Which is greater? (a) mass of 238 92 U (b) mass of 4 2He plus mass of 234 90 Th
10.5 In spontaneous decay, energy must be released, so the combined energy of the products must be less than the energy of the parent nucleus. From E = mc2, we see that this same statement is true for mass as well. The combined mass of the products must be less than the mass of the parent nucleus (B)
10.6 Identify X in the following decay: 95 36Kr → X + e− + ¯ν. (a) 94 35Br (b) 95 35Br (c) 96 35Br (d) 94 36Kr (e) 96 36Kr (f) 94 37Rb (g) 95 37Rb (h) 96 37Rb
10.6 From conservation of nucleons (mass number), we have 95 = M. From conservation of charge, we have 36 = Z − 1. Thus, Z = 37 (Rb), and M = 95
10.7 In beta decay, the beta particle carries off only part of the energy released by the decay. Name the particle that carries off most of the remaining energy. (a) electron (b) proton (c) neutron (d) neutrino (e) positron
10.7 In 1930, Pauli proposed that a third particle must be present in the products of beta decay to carry away energy that could not be accounted for by the daughter nucleus and the electron alone. This particle was named the neutrino (D)
10.8 In a nuclear reaction that produces heat, the mass of the products is (a) greater or (b) less than the mass of the reactants.
10.8 If the reaction produces heat, it must release energy. This means that combined energy of the products must be less than the combined energy of the reactants. From E = mc2, we see that this same statement is true for mass as well. The combined mass of the products must be less than the combined mass of the reactants. (B)
10.9 Identify the nuclide X in the following fission event: 235 92 U + n → 100 40 Zr + X + 2n. (a) 132 51 Sb (b) 133 51 Sb (c) 134 51 Sb (d) 135 51 Sb (e) 132 52 Te (f) 133 52 Te (g) 134 52 Te (h) 135 52 Te
10.9 From conservation of nucleons, we have 235 + 1 = 100 + M + 2. From conservation of charge, we have 92 = 40 + Z. Thus, Z = 52 (Te), and M = 134. (G)
2.1 If we increase the velocity of a wave, keeping its frequency constant, its wavelength will (a) increase, (b) decrease, or (c) remain the same
2.1 From v = λf, we see that if we increase the velocity v, the wavelength λ must also increase.
2.3 What kind of wave is sound? (a) longitudinal (b) transverse
2.3 In a sound wave, the fluid moves back and forth in a direction parallel to the direction of propagation (longitudinal, like a compressed spring) (A)
2.4 When a frequency source and an observer are moving toward each other, the frequency heard by the observer is (a) higher than, (b) lower than, or (c) equal to the frequency of the source.
2.4 This is the Doppler effect. (a?)
2.5 If some source of light travels away from us, the Doppler effect causes the wavelength of the light we receive from that source to (a) increase, (b) decrease, or (c) remain the same. Note: Although the equations for the Doppler effect are not the same for light as for sound, you may use the same reasoning as for sound.
2.5 For a source moving away from us, the Doppler effect causes the frequency to decrease, both for sound waves and for light waves. From v = λf, we see that if the frequency f decreases, then the wavelength λ must increase.
2.6 A bat is flying at velocity vb. The bat emits a sound wave with frequency f. The sound wave reflects from a stationary object, and the bat hears the reflected sound. What frequency f 0 does the bat hear? In the expressions below, vs is the speed of the source, vo is the speed of the observer, and v is the speed of sound. (In this case, the bat is both the source and the observer, so that |vs| = |vo| = |vb|.)
2.6 This is analogous to a source and observer moving toward each other. (The source is moving in the same direction as the sound it's emitting, and the observer is moving in the opposite direction as the sound it's hearing.) In this situation, both the motion of the source and the motion of the observer cause an increase in frequency. This means that the numerator must increase for increasing |vo| (plus sign), and the denominator must decrease for increasing |vs| (minus sign).
3.1 Standing waves are caused by the superposition of (a) two waves with the same frequency, traveling in the same direction but out of phase with each other, (b) two waves with the same frequency, traveling in opposite directions, or (c) two waves with slightly different frequencies.
3.1 For example, we can produce standing waves with two speakers facing each other. (b) See p. 550
*3.2 Consider a two-loop standing wave on a string. If we increase the tension without changing the frequency, what kind of standing wave can we obtain? (a) one-loop (b) three-loop
3.2 From v = p T /µ, we see that if we increase the tension T, the velocity v will also increase. From v = λf, we see that if we increase the velocity v, the wavelength λ will also increase. Finally, from λn = 2L/n, we see that λ1 > λ2 > λ3, so an increased wavelength must take us from λ2 (two loops) to λ1 (one loop). We also see this from the increased distance between nodes as we go from two loops to one loop.
3.3 What is the wavelength of the wave which is generating the standing wave shown in the figure? (a) 1/3 L (b) 2/3 L (c) L
3.3 The distance between adjacent nodes is equal to a half-wavelength. This is the length of each loop in the figure. Therefore, the length of two loops is one wavelength, which is 2L/3
3.4 Consider standing waves in an air column inside a pipe. One end of the pipe is open, and the other end is closed. (a) Only even harmonics are present. (b) Only odd harmonics are present. (c) Both even and odd harmonics are present
3.4 This happens because there is a displacement node at one end of the tube and a displacement antinode at the other end. (B) See Pages 560-561
3.5 Beats are caused by the superposition of (a) two waves with the same frequency, traveling in the same direction but out of phase with each other, (b) two waves with the same frequency traveling in opposite directions, or (c) two waves with slightly different frequencies.
3.5- 3.5 For example, we can produce beats by striking two tuning forks of slightly different frequencies (C) See page 564
4.1 Which is the greater change in temperature? (a) ∆T = 1◦C (b) ∆T = 1 K (c) They are equal.
4.1 The size of one degree is the same on the Celsius and Kelvin temperature scales. (C)
4.2 If we heat up a piece of metal with a hole in it, the diameter of the hole (a) increases, (b) decreases, or (c) remains the same
4.2 Thermal expansion is like photographic enlargement. Everything is larger, including holes. (A)
4.3 The amount of heat required to melt ice is called (a) specific heat or (b) latent heat.
4.3 Latent heat is the quantity of heat required to change the phase of some substance. (B)
4.4 We drop 100 g of aluminum at 100◦C into 100 g of water at 20◦C. When the aluminum and water come to thermal equilibrium, will the final temperature be (a) greater than, (b) less than, or (c) equal to the average temperature 60◦C? c = 900 J/kg· ◦C for aluminum c = 4186 J/kg· ◦C for water
4.4 From Q = mc∆T, we see that when two substances of equal mass exchange heat Q, the substance with the greater specific heat c will experience the smaller change ∆T of temperature. (B)
4.6 In the path shown in the P V diagram (P increase, V is constant), the work done on the gas is (a) positive, (b) negative, or (c) zero. The path in the figure is vertical.
4.6 No work is done when there is no change in volume. (C). Isovolumetric = No Work; Isobaric = work
4.7 Two paths, A and B, from point i to point f are shown in the P V diagram for an ideal gas. Which path requires putting the most heat into the gas? (refer to figure) (a) A (b) B
4.7 The initial and final states of the gas are the same for both paths, so the change ∆Eint of internal energy is also the same along both paths. The work done on the gas is given by W = −int (P dV) . Since Vf > Vi , we see that the work W done on the gas is negative along both paths. Since there is more area under path A, the work W done along path A is more negative. From the first law of thermodynamics, ∆Eint = Q+W, a larger negative work W requires a larger positive heat Q. (A)
5.1 Consider an ideal gas contained in a sealed jar. The average translational kinetic energy of a molecule in that gas depends on (a) the number of molecules, (b) the mass of the molecule, (c) the pressure of the gas, or (d) the temperature of the gas
5.1 From 0.5m0v^2 =3/2*T, see we that the average translational kinetic energy, 0.5m0v^2, depends only on the temperature T. (D)
5.10 The net heat Q absorbed by a heat engine is (a) positive, (b) negative, or (c) zero
5.10 A heat engine turns heat into work (C)
5.11 A heat pump (a) moves heat from a hot object and puts it into a cold object or (b) moves heat from a cold object and puts it into a hot object.
5.11 The nature of a "pump" is to move something in a direction opposite to how it would naturally flow. In this case, heat flows naturally from a hot object to a cold object. A heat pump moves heat in the opposite direction. (A)
5.12 Two cyclic processes are shown in the P V diagrams for an ideal gas. Which cycle has the greatest thermal efficiency e = Weng/|Qh|? (a) cycle A (rectangle) (b) cycle B (triangle) (c) Both cycles have the same thermal ef- ficiency.
5.12 The work Weng is the area enclosed by the path, so cycle A produces more work. Heat is extracted from the hot reservoir along the paths which are increasing in pressure and increasing in volume. Since these paths are the same for both cycles, |Qh| is the same for both cycles. From e = Weng/|Qh|, we see that the cycle producing the greater amount of work Weng has the greater thermal efficiency e
5.13 In an irreversible process, the change in entropy of the system plus its surroundings is (a) always positive, (b) always negative, (c) always zero, or (d) sometimes positive and sometimes negative, depending on the details of the process
5.13 The second law of thermodynamics states that the total entropy cannot decrease. For reversible processes, the entropy remains constant. For irreversible processes, the entropy increases. (A)
5.2 Consider molecules of N2 and molecules of CO2 in a sample of air. A molecule of CO2 has more mass than a molecule of N2. Which type of molecule has the highest average speed? (a) N2 (b) CO2 (c) Both have the same average speed.
5.2 From 0.5m0v^2 =3/2T, we see that both kinds of molecules have the same average kinetic energy 1/2m0v^2 since they are both at the same temperature T (molecules in the same sample of air). Therefore, the molecule with less mass m0 will have more speed v (A).
5.3 If I raise the temperature of an ideal gas, its internal energy (a) always increases, (b) always decreases, or (c) sometimes increases and sometimes decreases, depending on the method of raising the temperature.
5.3 For an ideal gas, the internal energy is just the kinetic energy of the molecules and is proportional to the temperature. (A)
5.4 Suppose we add heat Q to an ideal gas, holding its volume constant. Which of the following is true about the change of internal energy of the gas? (a) ∆Eint > Q (b) ∆Eint < Q (c) ∆Eint = Q
5.4 The work W done on the gas is zero since ∆V = 0. From the first law of thermodynamics, ∆Eint = Q + W, we see that for W = 0, we have ∆Eint = Q. (C)
5.5 Consider a mole of an ideal gas. We add heat in order to raise its temperature from 20◦C to 100◦C. For which case will the change of internal energy be the greatest? (a) constant volume (b) constant pressure (c) both the same
5.5 The change of internal energy of an ideal gas only depends on the change of temperature. (C)
5.6 The figure show a P V diagram for an ideal gas. The path is isothermal (∆T = 0). The change of internal energy of the gas is (a) positive, (b) negative, or (c) zero.
5.6 The change of internal energy of an ideal gas only depends on the change of temperature. If the temperature doesn't change, then the internal energy doesn't change either.
5.7 The figure show a P V diagram for an ideal gas. The path is adiabatic (Q = 0). The change of internal energy of the gas is (a) positive, (b) negative, or (c) zero.
5.7 Adiabatic expansion causes a gas to cool down. The change of internal energy of an ideal gas only depends on the change of temperature. If the temperature decreases, so does the internal energy.
5.8 The figure shows a P V diagram for an ideal gas. Along the path, the gas returns to its original state. The change of internal energy of the gas is (a) positive, (b) negative, or (c) zero.
5.8 The change of internal energy of an ideal gas only depends on the change of temperature. If the gas returns to its original pressure and volume, it also returns to its original temperature and internal energy (C)
5.9 Consider a mole of an ideal gas at 300 K. If we compress the gas to half its volume, which process requires the most work? (a) isothermal (b) adiabatic (c) both the same
5.9 Adiabatic compression causes the temperature of the gas to increase, and therefore the pressure increases more rapidly than in an isothermal compression. More pressure results in more work done. (Isothermal is a steeper PV curve than adiabatic; therefore adiabatic requires more work)
6.1 When light travels from air into glass, it (a) speeds up or (b) slows down.
6.1 From n = c/v, we see that the velocity v of light is smaller in the medium with the greater index of refraction n. (B)
6.10 Consider a real image formed by a converging lens. If we block out the top half of the lens, what happens to the image? (a) top half disappears (b) bottom half disappears (c) none of the image disappears
6.10 Consider a real image formed by a converging lens. If we block out the top half of the lens, what happens to the image? (a) top half disappears (b) bottom half disappears (c) none of the image disappears (C)
6.11 In the figure are shown an object O, an image I, and the location of some optical element which is a lens or mirror. The location of the focal point(s) is not shown. Identify the optical element. (a) concave mirror (b) convex mirror (c) converging lens (d) diverging lens (e) Cannot be determined from the information given.
6.11 If the optical element were a lens, then a ray from the tip of the object passing through the center of the lens would pass through the tip of the image, as shown in figure (a). This means that the image would be inverted. Therefore, the optical element is a mirror. Now draw a horizontal ray from the tip of the object. It must reflect from the mirror in such a way that it appears to be coming from the tip of the image, as shown in figure (b). It must also appear to be coming from the focal point. This places the focal point behind the mirror, so the mirror must be convex.
6.12 How does the eye focus on objects? (a) changing the focal length of the lens (b) changing the distance between the lens and the retina
6.12 The eye focuses on an object by varying the shape of the pliable crystalline lens through a process called accommodation. (A)
6.13 The near point of my eyes is at 80 cm. I want a pair of reading glasses that allows me to read the newspaper at 25 cm. In the lens equation, what should be the value of q (the distance to the image)? (a) 25 cm (b) −25 cm (c) 80 cm (d) −80 cm
6.13 When I use reading glasses, I place the object at 25 cm. The lens forms an image at 80 cm, which is far enough away for my eyes to focus on it. Since the image is on the same side of the lens as the object, the image is virtual, and q is negative.
6.14 When viewing a distanct object with a telescope, the objective lens produces an image which is (a) larger than, (b) smaller than, or (c) the same size as the actual object. We are referring here to the actual size of the image, not the apparent or angular size.
6.14 "Distant object" means a large value of p. On the other hand, the value of q is approximately equal to the length of the telescope, so that |q|<<|p|. From M = h'/h =−q/p, we see that the magnification M will be very small so that the size h' of the image will be much smaller than the size h of the object.
6.2 Light passes through a glass prism. Which best represents the path of the light as it enters the prism? (a) A (up) (b) B (down)
6.2 As light passes from a medium (air) with a smaller index of refraction to a medium (glass) with a greater index of refraction, it bends toward the normal (direction perpendicular to the surface). (B) See diagram
6.3 Light passes through a glass prism. Red light travels faster in glass than violet light. Which color is bent the most as it leaves the prism? (a) red (b) violet
6.3 From n = c/v, we see that the index of refraction n is greater when the velocity v of light is smaller. Light with the greatest index of refraction will be bent the most. (B)
6.4 You are standing on the edge of a swimming pool. The water is clear and smooth. A fish is in the water. The fish shown in the figure is in its actual position and is stationary. You decide to spear the fish. Where would you need to aim in order to hit the fish? Assume that the spear travels in a straight line without changing its direction when it enters the water. (a) below the image (b) directly at the image (c) above the image By image, we mean the position where the fish appears to be
6.4 Light from the fish is bent away from the normal as itleaves the water, as shown in the figure. The dashed line shows the direction for which light appears to be coming from the fish. As can be seen, the image of the fish will be above the actual position of the fish. You want to aim toward the actual position of the fish. (A)
6.5 In the previous problem, suppose you wanted to "spear" the fish with a laser light. Where would you need to aim the light in order to hit the fish? (a) below the image (b) directly at the image (c) above the image Neglect the difference in the index of refraction for different colors of light.
6.5 The path of the light from the fish to your eye is the same as the path of the laser from your eye to the fish.
6.6 The image behind a flat mirror is (a) real or (b) virtual.
6.6 A real image is formed when light rays actually pass through the image. For a flat mirror, the image is behind the mirror, so no light actually passes through the image.
6.7 If I look into a convex mirror, the image of my face will (a) always be upright, (b) always be inverted, or (c) sometimes be upright and sometimes be inverted, depending on how far away the mirror is.
6.7 For convex mirrors, the focal length f is negative. From 1/p+1/q = 1/f, we see that if p is positive (real object) and f is negative, then q will always be negative. From M = −q/p, we see that if q is negative and p is positive, then M will be positive and the image will be upright
6.8 What kind of lens is this? ) (a) converging (b) diverging (c) It depends on which direction the light passes through the lens
6.8 If the lens is thicker in the middle than at the edges, it is converging (A)
6.9 If an image formed by a lens is on the same side of the lens as the object, the image is (a) real or (b) virtual.
6.9 A real image is formed when light rays coming out of the lens actually pass through the image. Therefore, an image can only be real if its position is on the opposite side of the lens as the object.
7.1 In the figure is shown a photograph of an interference pattern on a screen produced by light passing through two slits. The brightest maximum in this pattern is indicated by an arrow. Consider the dark minimum indicated by the second arrow. Let x1 be the distance from this minimum on the screen to one of the slits, and let x2 be the distance from this same minimum on the screen to the other slit. What is the value of |x2 − x1|? (a) 0 (b) 1/2 λ (c) λ (d) 3/2 λ (e) 2 λ (f) 5/2 λ (g) 3 λ
7.1 In the figure, we show a top view with the double slit on the left and the screen on the right. We get bright fringes when the difference in x1 and x2 is equal to a integer number of wavelengths so that the waves from the two slits constructively interfere, as shown in the figure. The dark minimum in this question is located between the bright fringe at x1 = x2 − λ and the bright fringe at x1 = x2 − 2λ.
7.2 Consider reflection of light from a thin film of MgF2 on a glass lens. Which reflected ray undergoes a 180◦ phase change upon reflection? (a) A (b) B (c) both A and B (d) neither A nor B In the figure is given the index of refraction n for air, MgF2, and glass.
7.2 A light ray undergoes a phase change of 180◦ upon reflection from a medium that has a higher index of refraction than the one in which the wave is travelling. Ray A is reflected from a medium that has a higher index of refraction (n = 1.38) than the one in which the wave is travelling (n = 1), so it undergoes a 180◦ phase change. Ray B is reflected from a medium that also has a higher index of refraction (n = 1.5) than the one in which the wave is travelling (n = 1.38), so it also undergoes a 180◦ phase change.
7.3 Consider diffraction of light through a narrow slit. Which color of light will spread out the most? (a) blue (b) red
7.3 Blue light has a shorter wavelength than red light. From sin θdark = mλ/a, we see that the light with the larger wavelength λ results in a larger angle θdark and will spread out more (B)
7.5 Using a sheet of polaroid to produce polarized light is an example of polarization by (a) selective absorption, (b) reflection, (c) double refraction, or (d) scattering.
7.5 Polaroid absorbs light with electric fields perpendicular to its transmission axis and transmits light with electric fields parallel to its transmission axis. (A)
7.6 In order to reduce the glare of sunlight reflection from the surface of a lake, the polaroid lens in sunglasses should be oriented so that the transmission axis is (a) vertical or (b) horizontal.
7.6 Light reflected from a horizontal nonmetallic surface will be polarized with the electric fields parallel to the surface. These electric fields will therefore be horizontal. We can block this light with polaroid by orienting is transmission axis to be vertical. (A)
8.1 Two events that are simultaneous in one reference frame (a) are or (b) are not simultaneous in a second frame moving relative to the first. Consider the two events to occur at two different locations.
8.1 This is one of the consequences of Einstein's special theory of relativity. It is actually only true for events that occur at two different locations. (B)
8.2 According to a stationary observer, a moving clock runs (a) faster or (b) slower than an identical stationary clock.
8.2 This is another consequence of Einstein's special theory of relativity. It is called time dilation. (B)
8.4 Consider traveling to a star which is 10 light years away in the earth's reference frame. If we travel with a speed near the speed of light, the time required to make the trip, according to the clock on the spaceship, (a) is always greater than 10 years, or (b) may be less than 10 years if our velocity is great enough.
8.4 As our velocity approaches the speed of light, the distance to the star is length-contracted so that it takes less and less time to make the trip.
8.5 Two objects are traveling in opposite directions in some reference frame. Their speeds are very near the speed of light. The speed of one object in the reference frame of the other object is (a) greater than the sum, (b) less than the sum, or (c) equal to the sum of their speeds in the original reference frame
8.5 Suppose the two objects are travelling at 0.9c. The sum of their speeds would then be 0.9c + 0.9c = 1.8c. But the speed of one object in the reference frame of the other object cannot be greater than c. (C).
8.6 If we apply a constant force on an object, the acceleration of the object, as it approaches the speed of light, will (a) decrease, (b) increase, or (c) remain constant.
8.6 From F~ = d~p/dt, we see that under a constant force F~ , the momentum ~p of an object increases at a constant rate, even when the object is travelling near the speed of light. However, from ~p = γm~u, we see that near the speed of light, small changes in the velocity ~u cause large changes in the Lorentz factor γ = 1/p1 − u2/c2 so that the change in the momentum ~p is mainly due to γ and not ~u. The acceleration d~u/dt actually goes to zero as u approaches c. (A) Constant force = constant momentum = approaching constant velocity = approaching zero acceleration = decreasing accel.
8.7 Consider an electron and a proton, each with a kinetic energy equal to 1 MeV. Which particle is moving at a relativistic speed? (a) electron (b) proton The rest energy of an electron is 0.511 MeV, and the rest energy of a proton is 938 MeV.
8.7 From K = (γ − 1)mc2 , we see that for K mc2 , we have γ ≈ 1, and the object is not moving at a relativistic speed
9.2 Consider the Compton effect. In the figure, in which case is the electron knocked out with more energy? (a) A (b) B
9.2 We can think of the Compton effect to be like a collision of billiard balls. The photon is like the cue ball which collides with another billiard ball initially at rest. Case A represents a "glancing" collision where the cue ball hardly changes direction at all. Case B represents a more direct hit where the cue ball rebounds in a direction nearly opposite to its initial direction. In case B, the ball initially at rest receives more kinetic energy. So it is with the Compton effect. This can also be seen from the equation λ 0 − λ0 = (h/m0c)(1 − cos θ). A larger angle θ causes a larger shift λ 0 − λ0 in the wavelength of the photon which means that the photon lost more energy, resulting in a larger kinetic energy for the electron. (B)
9.3 In the previous problem, in which case does the scattered photon have the longest wavelength? (a) A (b) B
9.3 In case B, the electron has more kinetic energy. Therefore the scattered photon has less energy. From E = hf and c = λf, we see that a photon with less energy has a larger wavelength
9.4 The de Broglie wavelength of a proton is (a) greater than, (b) less than, or (c) the same as that of an electron with the same velocity.
9.4 From λ = h/mv, we see that since a proton has more mass m, its de Broglie wavelength λ is smaller (B)
9.5 Four possible transitions for a hydrogen atom are listed below: A. ni = 2; nf = 5 B. ni = 3; nf = 5 C. ni = 5; nf = 2 D. ni = 5; nf = 3 Which transition will emit the shortest-wavelength photon? (a) A (b) B (c) C (d) D
9.5 First of all, photons are only emitted when the energy of the final state is lower than that of the initial state, i.e., nf < ni . Only transitions C and D meet this condition. Both of these transitions begin with the same energy (ni = 5), but transition C ends with a lower energy (nf = 2) and therefore emits a photon with more energy. From E = hf and c = λf, we see that a photon with more energy has a shorter wavelength.
9.6 Four possible transitions for a hydrogen atom are listed below: A. ni = 2; nf = 5 B. ni = 3; nf = 5 C. ni = 5; nf = 2 D. ni = 5; nf = 3 In the previous problem, for which transition will the atom gain the most energy? (a) A (b) B (c) C (d) D
9.6 First of all, the atom gains energy only when the energy of the final state is higher than that of the initial state, i.e., nf > ni . Only transitions A and B meet this condition. Both of these transitions end with the same energy (nf = 5), but transition A begins with a lower energy (ni = 2), causing the atom to gain more energy (A)
1.3 Two spheres have equal diameters. One sphere is made of wood and the other of steel. We hold both of them under water. For which sphere will the buoyant force be the greatest? (a) wood (b) steel (c) same for both spheres
From B = ρfluidgV , we see that the buoyant force B depends only on the volume V of the object, not on its density or mass.
1.1 An object is submerged in water. If we increase the pressure of the air above the water by an amount ∆P, the pressure on the object will increase by an amount (a) greater than ∆P, (b) less than ∆P, or (c) equal to ∆P. Consider the density of the water to not be affected by the change of pressure.
From P = P0 + ρgh, we see that if the pressure P0 of the air above the water changes by an amount ∆P, then the pressure P in the water changes by that same amount, no matter what the value of h is. (C)
1.2 The two containers shown in the figure are filled with water to the same height (container A is rectangular, container B is trapeoizdal). The bottom areas of the two containers are equal. In which container will the pressure at the bottom be the greatest? (a) container A (b) container B (c) same for both containers
From P = P0 + ρgh, we see that the pressure P in the water depends only on the depth h. (C)
4.5 A container of water is at room temperature. If I drop a hot piece of metal into the water, the temperature of the water rises. If the mass of the metal is 10 g and its initial temperature is 100◦C, which type of metal will cause the temperature of the water to rise the greatest? (a) lead (b) copper (c) Both lead and copper would cause the same rise in temperature. c = 128 J/kg· ◦C for lead c = 387 J/kg· ◦C for copper
From Q = mc∆T, we see that the metal with the greater specific heat c requires a greater amount of exchanged heat Q to lower its temperature, resulting in a greater rise in the temperature of the water. (B). C and delta T water are directly proportional.