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Physics 106 Homework Problems, Fall 2007 Sec. 1, Cheryl Davis These problems are adapted from Serway and Faughn, College Physics, and are used with permission from Harcourt Brace College Publishers. m from a −2.86-nC charge. Find the 1-1. A 4.51-nC charge is located [01] magnitude of the electrostatic force exerted by one charge on the other. 1-2. In the figure, q1 = 6.27 µC, q2 = [02] µC, q3 = −2.38 µC, r1 = 3.49 cm, and r2 = 3.22 cm. Calculate the magnitude and direction of the Coulomb force on (a) q1 , (b) q2 , and (c) q3 . Indicate a force to the right with a + sign and a force to the left with a − sign. 1-3. Three charges are arranged as shown in the figure. Find the (a) magnitude and (b) direction (angle with the x axis) of the electrostatic force on the 6.00-nC charge. In the figure, q = [03] nC. 1-4. Two small metallic spheres, each of mass 0.20 g, are suspended as pendulums by light strings from a common point as shown in the figure. The spheres are given the same electric charge, and it is found that the two come to equilibrium when each string is at an angle of [04] ◦ with the vertical. If each string is 30.0 cm long, what is the magnitude of the charge on each sphere? 2-1. (a) Determine the electric field at a point [01] cm to the left of the middle charge shown in the figure. Use a plus sign for a field pointing to the right, and use a minus sign for a field pointing to the left. (b) If a charge of −2.00 µC is placed at this point, find the force acting on it. Use a plus sign for a force pointing to the right, and use a minus sign for a force pointing to the left. 2-2. An electron is accelerated by a constant electric field of magnitude [02] N/C. (a) Find the acceleration of the electron. (b) Use the equations of motion with constant acceleration to find the electron’s speed after 1.54 × 10−8 s, assuming it starts from rest. 2-3. Positive charges are situated at three corners of a rectangle, as shown in the figure. Find the (a) magnitude and (b) direction (angle with the horizontal direction to the right) of the electric field at the fourth corner. In the figure, d = [03] 3-1. A proton moves [01] m. cm parallel to a uniform electric field with E = 223 N/C. (a) How much work is done by the field on the proton? (b) What change occurs in the potential energy of the proton? (c) Through what potential difference did the proton move? 3-2. Suppose an electron is released from rest in a uniform electric field whose strength is [02] V/m. (a) Through what potential difference will it have passed after moving 1.34 cm? (b) How fast will the electron be moving after it has traveled 1.34 cm? 3-3. Find the potential at point P for the rectangular grouping of charges shown in the figure, where d = [03] m. 3-4. Two point charges are on the y axis. One charge of 3.18 nC is at the origin and a second charge of 6.35 nC is at the point y = 29.2 cm. Calculate the potential at y = [04] cm. 4-1. An air-filled capacitor consists of two parallel plates, each with an area of 7.65 cm2 , separated by a distance of [01] mm. If a 23.2-V potential difference is applied to these plates, calculate (a) the electric field between the plates, (b) the capacitance, and (c) the magnitude of the charge on each plate. 4-2. A series circuit consists of a 0.056-µF capacitor, a [02] -µF capacitor, and a 400-V battery. Find the charge on (a) the first capacitor and (b) the second capacitor. If the capacitors are reconnected in parallel across the battery, find the charge on (c) the first capacitor and (d) the second capacitor. 4-3. Consider the combination of capacitors in the figure, where C = [03] ∆V = [04] µF and V. (a) What is the equivalent capacitance of the group? Determine the charge on (b) the 4.00-µF capacitor, (c) the 2.00-µF capacitor, (d) the 24.0-µF capacitor, and (e) the capacitor C. 4-4. A [05] -µF capacitor (C1 ) is first charged by being connected across a 10.0-V battery (see figure on left). It is then disconnected from the battery and connected across an uncharged 2.27-µF capacitor (C2 ) (see figure on right). Determine the resulting charge on (a) C1 and (b) C2 . 5-1. In a particular television picture tube, the measured beam current is [01] µA. How many electrons strike the screen every second? 5-2. A potential difference of 12 V is found to produce a current of [02] A in a 3.2-m length of wire with a uniform radius of 0.43 cm. What is (a) the resistance of the wire and (b) the resistivity of the wire? 5-3. A toaster is rated at [03] W when connected to a 120-V source. (a) What current does the toaster carry, and (b) what is its resistance? 5-4. A high-voltage transmission-line with a resistance of [04] Ω/km carries 1460 A, starting at 701 kV for a distance of 168 km. (a) What is the power loss due to resistance in the line? (b) What percentage of the initial power does this loss represent? 6-1. Three resisters are connected in series with a 24-V battery. Their resistances are R1 = 4.00 Ω, R2 = [01] Ω, and R3 = 12.00 Ω. (a) Find the equivalent resistance. Find the current in (b) R1 , (c) R2 , and (d) R3 . (e) Find the equivalent resistance if the three resisters are connected in parallel across the battery. Find the current in (f) R1 , (g) R2 , and (h) R3 for this case. 6-2. (a) Find the equivalent resistance between points a and b in the figure, where R = [02] Ω. (b) Calculate the current in the resister R if a potential difference of 34.0 V is applied between points a and b. 6-3. Find the current in the 12-Ω resistor in the figure, where R = [03] 6-4. If R = [04] Ω. Ω in the figure, find the current in the (a) top, (b) middle, and (c) bottom resistors. The algebra in this problem is challenging. Apply the loop rule to the top loop first and then to the bottom loop. 6-5. Extra credit activity: Connecting a light bulb to a battery. For this activity, you will need (1) a 1.5-V battery (the kind which is in a flashlight or TV remote control), (2) a small lightbulb (handed out in class, or, if you didn’t get one in class, remove one from a flashlight), and (3) a wire about 6 inches long (or anything metallic, such as a paper clip or strip of aluminum foil). Connect these three items together so that the lightbulb turns on. When you submit your homework answers, select “yes” if you were able to turn on the light bulb and select “no” if not. You must make this selection on the first try to receive credit. 7-1. If R = [01] Ω in the figure, find the current in the (a) top, (b) middle, and (c) bottom resistors. The algebra in this problem is challenging. Apply the loop rule to the top loop first and then to the bottom loop. 7-2. Find the values of (a) I1 , (b) I2 , and (c) I3 for the circuit in the figure if R = [02] Ω. The algebra in this problem is challenging. Apply the loop rule to the outer loop first and then to the left loop. 7-3. An uncharged capacitor and a resistor are connected in series to a source of emf. If E = 9.00 V, C = [03] µF, and R = 127 Ω, find (a) the time constant of the circuit, (b) the maximum charge on the capacitor, and (c) the charge on the capacitor after one time constant. 7-4. Consider the circuit shown in the figure, where R = [04] C = [05] kΩ and µF. Suppose that the switch has been closed for a length of time sufficiently long for the capacitor to become fully charged. Find the steady-state current in (a) the 12.0-kΩ resistor, (b) the resistor R, and (c) the 3.00-kΩ resistor. (d) Find the charge on the capacitor. 8-1. Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields in the figure, as shown. In each case, give one of the following answers: toward top of page, toward bottom of page, to the right, to the left, out of page, into page. 8-2. A wire carries a steady current of [01] A. A straight section of the wire is 0.752 m long and lies along the x axis within a uniform magnetic field of magnitude 1.68 T in the positive z direction. If the current is in the +x direction, what is the (a) magnitude and (b) direction of the magnetic force on the section of wire? 8-3. A circular coil consisting of a single loop of wire has a radius of 28.6 cm and carries a current of 25.4 A. It is placed in an external magnetic field of 0.293 T. Find the torque ◦ on the wire when the plane of the coil makes an angle of [02] with the direction of the field. 9-1. A 2.53-µC charged particle with a kinetic energy of 0.0929 J is fired into a uniform magnetic field of magnitude 0.147 T. If the particle moves in a circular path of radius [01] m, determine its mass. 9-2. The two wires in the figure carry currents of I1 = [02] and I2 = [03] A A, in a direction out of the page as shown. Find the (a) magnitude and (b) direction of the magnetic field at a point midway between the wires. Find the (c) magnitude and (d) direction of the magnetic field at point P , located 20.0 cm above the wire carrying the current I2 . 9-3. Find the direction of the current in the wire in the figure that would produce a magnetic field directed as shown, in each case. (a) Answer to the right or to the left. (b) Answer into or out of the page. 9-4. Two parallel wires are 12.3 cm apart, and each carries a current of [04] A. (a) If the currents are in the same direction, find the force per unit length exerted by one of the wires on the other. (b) Are the wires attracted or repelled? 10-1. A solenoid 4.29 cm in diameter and [01] cm long has 250 turns and carries a current of 15.7 A. Calculate the magnetic field through the circular cross-sectional area of the solenoid. 10-2. A magnetic field of strength 0.329 T is directed perpendicular to a plane circular loop of wire of radius [02] this loop. cm. Find the magnetic flux through the area enclosed by 10-3. The square loop in the figure is made of wires with total series resistance [03] Ω. It is placed in a uniform 0.115-T magnetic field directed perpendicular into the plane of the paper. The loop, which is hinged at each corner, is pulled as shown until the separation between points A and B is 3.00 m. (a) If this process takes 0.156 s, what is the average current generated in the loop? (b) What is the direction of the current? 10-4. When the current in the long, straight wire in the figure decreases rapidly to zero, a current is induced in the loop. Which direction will this induced current flow through the resistor? Answer to the right or to the left. 11-1. Consider the arrangement shown in the figure. Assume that R = 6.39 Ω and ` = 1.22 m, and that a uniform [01] -T magnetic field is directed into the page. At what speed should the bar be moved to produce a current of 0.576 A in the resistor? 11-2. In the figure, the rolling axle, 1.54 m long, is pushed along horizontal rails at a constant speed v = 3.39 m/s. A resistor R = 0.451 Ω is connected to the rails at points a and b, directly opposite each other. (The wheels make good electrical contact with the rails, and so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R.) There is a uniform magnetic field B = [02] T vertically downward. (a) Find the induced current I in the resistor. (b) What horizontal force F is required to keep the axle rolling at constant speed? (c) Which end of the resistor, a or b, is at the higher electric potential? (d) After the axle rolls past the resistor, does the current in R reverse direction? 11-3. A bar magnet is held above the center of a wire loop in a horizontal plane, as shown in the figure. The south end of the magnet is toward the loop. The magnet is dropped. Find the direction of the current through the resistor while the magnet is falling toward the loop. 11-4. A copper bar is moved to the right while its axis is maintained in a direction perpendicular to a magnetic field, as shown in the figure. If the top of the bar becomes positive relative to the bottom, what is the direction of the magnetic field? 12-1. A solenoid of radius 2.52 cm has [01] turns and a length of 19.2 cm. Find (a) its inductance and (b) the magnitude of the rate at which current must change through it to produce an emf of 75.7 mV. 12-2. A 25.5-mH inductor, and 8.13-Ω resistor, and a [02] -V battery are connected in series. The switch is closed at t = 0. Find the voltage drop across the resistor (a) at t = 0 and (b) after one time constant has passed. Also, find the voltage drop across the inductor (c) at t = 0 and (d) after one time constant has elapsed. 12-3. A 24.0-V battery is connected in series with a resistor and an inductor, where R = [03] Ω and L = 4.19 H. Find the energy stored in the inductor (a) when the current reaches its maximum value and (b) one time constant after the switch is closed. 13-1. An AC power supply produces a maximum voltage of Vmax = [01] V. This power supply is connected to a 24.8-Ω resistor, and the current and resistor voltage are measured with an ideal AC ammeter and an ideal AC voltmeter, as shown in the figure. (a) What does the ammeter read? (b) What does the voltmeter read? Recall that an ideal ammeter has zero resistance and an ideal voltmeter has infinite resistance. 13-2. What maximum current is delivered by a [02] -µF capacitor when connected across (a) a North American outlet having vrms = 120 V, f = 60.0 Hz; and (b) a European outlet having vrms = 240 V, f = 50.0 Hz? 13-3. A 2.42-µF capacitor is connected across an alternating voltage with an rms value of 9.18 V. The rms current in the circuit is [03] mA. (a) What is the source frequency? (b) If the capacitor is replaced by an ideal coil with an inductance of 0.165 H, what is the rms current in the coil? 13-4. An ac source with an rms voltage of 115 V and f = [04] Hz is connected between points a and d in the figure. Calculate the rms voltages between the points (a) a and b, (b) b and c, (c) c and d, (d) b and d. 14-1. A transmission line that has a resistance per unit length of [01] Ω/m is to be 5 used to transmit 5.13 MW over 400 miles (6.44 × 10 m). The output voltage of the generator is 4.50 kV. (a) What is the line loss if a transformer is used to step up the voltage to 539 kV? (b) What fraction of the input power is lost to the line under these circumstances? (c) What difficulties would be encountered on attempting to transmit the 5.00 MW at the generator voltage of 4.50 kV? (Do not turn in this part of the problem.) 14-2. A resonant circuit in a radio receiver is tuned to a certain station when the inductor has a value of 0.224 mH and the capacitor has a value of [02] pF. Find (a) the frequency of the radio station and (b) the wavelength sent out by the station. 14-3. An RLC circuit is used to tune a radio to an FM station broadcasting at [03] MHz. The resistance in the circuit is 11.8 Ω and the capacitance is 1.39 pF. What inductance should be placed in the circuit? 14-4. What is the wavelength of (a) an AM radio station broadcasting at [04] and (b) an FM radio station broadcasting at [05] kHz MHz? 14-5. An important news announcement is transmitted by radio waves to people who are 100 km away, sitting next to their radios, and by sound waves to people sitting across the newsroom, 3.0 m from the newscaster. Who receives the news first? Take the speed of sound in air to be 343 m/s. 15-1. A ray of light strikes a flat, h = [01] -cm-thick block of glass (n = 1.50) at an angle of 30.0◦ with the normal (see figure). When the light ray passes through the glass block, it is shifted laterally by a distance d. (a) Find the value of d. (b) Find the time required for the light to pass through the glass block. 15-2. A certain kind of glass has an index of refraction of 1.650 for blue light of wavelength 430 nm and an index of 1.615 for red light of wavelength 680 nm. If a beam containing these two colors is incident at an angle of [02] ◦ on a piece of this glass, what is the angle between the two beams inside the glass? (The incident angle is measured from the direction normal to the surface, as in Snell’s Law.) 15-3. A plastic light pipe has an index of refraction of [03] . For total internal reflection, what is the maximum angle of incidence to the wall of the pipe if the pipe is in (a) air? (b) water? Be careful: The problem asks for the angle with the wall of the pipe. This is not the angle in Snell’s law. Use n = 1.333 for the index of refraction of water. 16-1. A concave spherical mirror has a radius of curvature of 23.7 cm. Locate the image for an object [01] cm from the mirror. (a) What is the distance from the image to the mirror? (b) Is the image in front of or behind the mirror? (c) Is the image real or virtual? (d) Is the image upright or inverted? (e) Find the magnification. 16-2. A convex spherical mirror with a radius of curvature of [02] cm produces a virtual image one-third the size of the real object. Where is the object (distance from the mirror)? 16-3. A spherical mirror is to be used to form an image, five times as tall as an object, on a screen positioned [03] m from the mirror. (a) Is the mirror concave or convex? (b) Where should the mirror be positioned relative to the object? 16-4. A man standing 1.52 m in front of a shaving mirror produces an inverted image [04] cm in front of it. How close to the mirror should he stand if he wants to form an upright image of his chin that is twice the chin’s actual size? 17-1. The top of a swimming pool is at ground level. If the pool is [01] m deep, how far below ground level does the bottom of the pool appear to be located when the pool is completely filled with water? Use n = 1.333 for the index of refraction of water. 17-2. A convex lens of focal length 15.7 cm is used as a magnifying glass. At what distance from a postage stamp should you hold this lens to get a magnification of [02] + ? 17-3. Object O1 is 15.0 cm to the left of a converging lens of [03] -cm focal length. A second lens is positioned 10.0 cm to the right of the first lens and is observed to form a final image at the position of the original object O1 . (a) What is the focal length of the second lens? (b) What is the overall magnification of this system? (c) Is the image real or virtual? 17-4. A 1.92-cm-high object is placed [04] cm to the left of a converging lens of focal length 8.00 cm. A diverging lens of focal length −16.00 cm is 6.00 cm to the right of the converging lens. Find (a) the position (distance in front of the second lens) and (b) the height of the final image. (c) Is the image inverted or upright? (d) Real or virtual? 18-1. Light of wavelength 460 nm falls on two slits spaced 0.300 mm apart. What is the required distance from the slit to a screen if the spacing between the first and second dark fringes is to be [01] mm? 18-2. Interference effects are produced at point P on a screen as a result of direct rays from a [02] -nm source and reflected rays off the mirror, as in the figure. If the source is 141 m to the left of the screen, and 1.25 cm above the mirror, find the distance y to the first dark band above the mirror. 18-3. A Young’s interference experiment is performed with blue-green laser light. The separation between the slits is [03] mm, and the interference pattern on a screen 3.31 m away shows the first maximum 3.45 mm from the center of the pattern. What is the wavelength of the laser light? 19-1. Light of wavelength [01] nm falls on a 0.427-mm-wide slit and forms a diffraction pattern on a screen 1.46 m away. Find the distance on the screen from the central maximum to the first dark band on either side of it. 19-2. The hydrogen spectrum has a red line at 656 nm and a violet line at 434 nm. What is the angular separation between these two spectral lines in the first-order spectrum obtained with a diffraction grating that has [02] lines/cm? 20-1. A camera used by a professional photographer to shoot portraits has a focal length of 25.0 cm. The photographer takes a portrait of a person [01] m in front of the camera. (a) Where is the image formed (distance from the lens), and (b) what is the lateral magnification? 20-2. A person with a nearsighted eye has near and far points of 16.0 cm and [02] cm, respectively. (a) Assuming a lens is placed 2.0 cm from the eye, what power must the lens have to correct this condition? (b) Contact lenses placed directly on the cornea are used to correct the eye in this example. What is the power of the lens required in this case, and (c) what is the new near point? (Hint: The contact lens and the eyeglass lens require slightly different powers because they are at different distances from the eye.) 20-3. A retired bank president can easily read the fine print of the financial page when the newspaper is held [03] cm from the eye. What should be the focal length of an eyeglass lens that will allow her to read at the more comfortable distance of 24 cm? 21-1. An elderly sailor is shipwrecked on a desert island but manages to save his eyeglasses. The lens for one eye has a power of +1.24 diopters, and the other lens has a power of +[01] diopters. (a) what is the magnifying power of the telescope he can construct with these lenses? (b) How far apart are the lenses when the telescope is adjusted so that the eye is relaxed? 21-2. Two motorcycles, separated laterally by 2.3 m, are approaching an observer holding an infrared detector that is sensitive to radiation of wavelength 885 nm. What aperture diameter is required in the detector if the two headlights are to be resolved at a distance of [02] km? 21-3. A light source emits two major spectral lines, an orange line of wavelength [03] nm and a blue-green line of wavelength 478 nm. If the spectrum is resolved by a diffraction grating having 5000 lines/cm and viewed on a screen 2.12 m from the grating, what is the distance between the two spectral lines in the second-order spectrum? Caution: Do not use the “small-angle approximation”. 22-1. How fast must a meter stick be moving if its length is observed to shrink to [01] m? 22-2. The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 26 ns. If the meson moves with a speed of [02] c, what is (a) its mean lifetime as measured by an observer on Earth and (b) the average distance it travels before decaying as measured by an observer on Earth? (c) What distance would it travel if time dilation did not occur? 22-3. A friend in a spaceship travels past you at a high speed. He tells you that his ship is 20.23 m long and that the identical ship you are sitting in is [03] m long. According to your observations, (a) how long is your ship, (b) how long is his ship, and (c) what is the speed of your friend’s ship? 23-1. Spaceship I, which contains students taking a physics exam, approaches Earth with a speed of 0.658c, while spaceship II, which contains an instructor proctoring the exam, moves away from Earth at [01] c as in the figure. If the instructor in spaceship II stops the exam after 50.00 min have passed on his clock, how long does the exam last as measured by the students? (This is simply the time dilation of the instructor’s clock in the students’ reference frame.) 23-2. An unstable particle at rest breaks up into two fragments of unequal mass. The mass of the lighter fragment is 2.50 × 10−28 kg, and that of the heavier fragment is 1.67 × 10−27 kg. If the lighter fragment has a speed of [02] c after the breakup, what is the speed of the heavier fragment? Hint: Use conservation of relativistic momentum. Since the initial momentum is zero (before the particle breaks up), the momentum of the heavier fragment must be equal in magnitude and opposite in direction to the momentum of the lighter fragment. 23-3. An electron moves to the right with a speed of 0.902c relative to the laboratory frame. A proton moves to the left with a speed of [03] c relative to the electron. Find the speed of the proton relative to the laboratory frame. 23-4. A space vehicle is moving at a speed of 0.754c with respect to an external observer. An atomic particle is projected at [04] c in the same direction as the spaceship’s velocity with respect to an observer inside the vehicle. What is the speed of the projectile as seen by the external observer? 24-1. A proton in a high-energy accelerator is given a kinetic energy of [01] GeV. Determine (a) the momentum and (b) the speed of the proton. 24-2. A proton moves with a speed of [02] c. Calculate its (a) kinetic energy and (b) total energy. 24-3. A mass of [03] kg is converted completely into energy of other forms. (a) How much energy of other forms is produced and (b) how long would this much energy keep a 100-W light bulb burning? 24-4. In a color television tube, electrons are accelerated through a potential difference of [04] V. With what speed do the electrons strike the screen? 25-1. (a) Calculate the energy of a photon whose frequency is [01] MHz. (b) Determine the wavelength of that photon. 25-2. Red light of wavelength 670 nm produces photoelectrons from a certain photoemissive material. Green light of wavelength 520 nm produces photoelectrons from the same material with [02] times the maximum kinetic energy. What is the material’s work function? 25-3. A monochromatic x-ray beam is incident on a NaCl crystal surface where d = 0.353 nm. The second-order maximum in the reflected beam is found when the angle between the incident beam and the surface is [03] ◦ . Determine the wavelength of the x-rays. 25-4. In a Compton scattering event, the scattered photon has an energy of 120.0 keV and the recoiling electron has a kinetic energy of [04] keV. Find (a) the wavelength of the incident photon, (b) the angle θ at which the photon is scattered, and (c) the recoil angle of the electron. (Hint: Conserve both mass-energy and relativistic momentum.) 26-1. (a) If the wavelength of an electron is equal to [01] (b) If the electron has a speed of [02] m, how fast is it moving? m/s, what is its wavelength? 26-2. Calculate the de Broglie wavelength of a proton moving (a) at [03] (b) at [04] m/s and m/s. Note that in part (b) the velocity is relativistic. You must use the relativistic momentum in calculating the de Broglie wavelength. 26-3. Four possible transitions for a hydrogen atom are listed below: I. ni = 2; nf = 5 II. ni = 5; nf = 3 III. ni = 7; nf = 4 IV. ni = 4; nf = 7 (a) Which transition will emit the shortest-wavelength photon? (b) For which transition will the atom gain the most energy? (c) For which transition(s) does the atom lose energy? 26-4. (a) If an electron makes a transition from the n = [05] Bohr orbit to the n = 2 orbit, determine the wavelength of the photon created in the process. (b) Assuming that the atom was initially at rest, determine the recoil speed of the hydrogen atom when this photon was emitted. 27-1. A radioactive sample contains [01] 20.4 min. (a) How many moles of µg of pure 11 6 C 11 6 C, which has a half-life of are present initially? (The atomic mass of 11 6 C is in Appendix B of the textbook.) (b) Determine the number of nuclei present initially. What is the activity of the sample (c) initially and (d) after 8.23 h? 27-2. Suppose that you start with 1.000 mg of a pure radioactive substance and 2.09 h later determine that only [02] mg of the substance remains. What is the half-life of this substance? 27-3. Radon gas has a half-life of 3.83 days. If 3.23 g of radon gas is present at time t = 0, what mass of radon will remain after [03] 28-1. A wooden artifact is found in an ancient tomb. Its [01] days have passed? 14 6 C activity is measured to be % of that in a fresh sample of wood from the same region. Assuming the same amount of was initially present in the wood from which the artifact was made, determine the age of the artifact. 28-2. Identify X (chemical symbol and mass number) in each of the following decays: → X + e− + ν̄ (a) 12 5 B (b) 234 90 Th (c) − X → 14 7 N + e + ν̄ → 230 88 Ra + X Type the chemical symbol followed by the mass number (no spaces). For example Na23, not Na 23 or na23 or NA23. 28-3. Identify X (chemical symbol and mass number) in each of the following decays: (a) 212 83 Bi → X + 42 He (b) 95 36 Kr → X + e− + ν̄ (c) X → 42 He + 140 58 Ce Type the chemical symbol followed by the mass number (no spaces). For example Na23, not Na 23 or na23 or NA23. 29-1. Identify X (chemical symbol and mass number) in each of the following reactions: (a) 1 X + 42 He → 24 12 Mg + 0 n (b) 235 92 U 1 + 10 n → 90 38 Sr + X + 20 n Type the chemical symbol followed by the mass number (no spaces). For example Na23, not Na 23 or na23 or NA23. 29-2. A beam of [01] -MeV protons is incident on a target of 27 13 Al. Those that collide produce the reaction 27 p + 27 13 Al → 14 Si + n. (The atomic mass of 27 14 Si is 26.986721 u.) Neglect any recoil of the product nucleus and determine the kinetic energy of the emerging neutrons. Caution: Use the atomic mass of 1 1 H, not the actual mass of the proton. Can you see why? 29-3. An all-electric home uses [02] kWh of electric energy per month. How much uranium-235 would be required to provide this house with its energy needs for 1 year? (Assume 100% conversion efficiency and 208 MeV released per fission.) Answers to Homework Problems, Physics 106, Sec. 1,Fall Semester, 2007 1-1. 4.00 × 10−9 , 8.00 × 10−9 N 1-2a. −10.0, −70.0 N 1-2b. 60.0, 140.0 N 1-2c. −50.0, −80.0 N 1-3a. 3.50 × 10−7 , 5.00 × 10−7 N 1-3b. −10.0, −20.0◦ 1-4. 3.0, 15.0 nC 2-1a. −8.0 × 107 , +9.5 × 107 N/C 2-1b. −200, +200 N 2-2a. 3.50 × 1013 , 6.50 × 1013 m/s2 2-2b. 5.00 × 105 , 9.50 × 105 m/s 2-3a. 750, 950 N/C 2-3b. 105.0, 125.0◦ 3-1a. 3.50 × 10−19 , 7.50 × 10−19 J 3-1b. −3.50 × 10−19 , −7.50 × 10−19 J 3-1c. −2.00, −5.00 V 3-2a. 40.0, 90.0 V 3-2b. 3.00 × 106 , 6.00 × 106 m/s 3-3. 2.00 × 105 , 9.00 × 105 V 3-4. 600, 900 V 4-1a. 10.0, 25.0 kV/m 4-1b. 3.00, 7.00 pF 4-1c. 70, 160 pC 4-2a. 12.0, 17.0 µC 4-2b. 12.0, 17.0 µC 4-2c. 20.0, 30.0 µC 4-2d. 10.0, 60.0 µC 4-3a. 10.0, 13.0 µF 4-3b. 100, 140 µC 4-3c. 50, 70 µC 4-3d. 100, 250 µC 4-3e. 100, 250 µC 4-4a. 3.00, 6.00 µC 4-4b. 6.80, 9.20 µC 5-1. 3.00 × 1014 , 6.00 × 1014 5-2a. 10, 40 Ω 5-2b. 2.0 × 10−4 , 8.0 × 10−4 Ω·m 5-3a. 3.00, 7.00 A 5-3b. 10.0, 40.0 Ω 5-4a. 70.0, 150.0 MW 5-4b. 7.0, 14.0 % 6-1a. 20.00, 30.00 Ω 6-1b. 0.80, 1.20 A 6-1c. 0.80, 1.20 A 6-1d. 0.80, 1.20 A 6-1e. 2.00, 2.50 Ω 6-1f. 4.00, 8.00 A 6-1g. 2.00, 5.00 A 6-1h. 1.00, 3.00 A 6-2a. 15.0, 20.0 Ω 6-2b. 1.00, 1.50 A 6-3. 0.400, 0.450 A 6-4a. 0.350, 0.380 A 6-4b. 0.130, 0.290 A 6-4c. 0.490, 0.670 A 7-1a. 0.350, 0.380 A 7-1b. 0.130, 0.290 A 7-1c. 0.490, 0.670 A 7-2a. −0.100, +0.200 A 7-2b. 0.350, 0.800 A 7-2c. 0.450, 0.600 A 7-3a. 1.90, 3.20 ms 7-3b. 130, 230 µC 7-3c. 80, 150 µC 7-4a. 0.200, 0.400 mA 7-4b. 0.200, 0.400 mA 7-4c. 0, 0 mA 7-4d. 50, 150 µC 8-2a. 2.00, 7.00 N 8-3. 1.00, 2.00 N·m 9-1. 4.50 × 10−12 , 9.50 × 10−12 kg 9-2a. 2.00, 6.00 µT 9-2c. 5.00, 7.00 µT 9-2d. 70.0, 85.0◦ to the left of vertical 9-4a. 1.50 × 10−4 , 7.00 × 10−4 N/m 10-1. 0.0180, 0.0330 T 10-2. 0.0400, 0.0950 T·m2 10-3a. 40.0, 90.0 mA 11-1. 1.00, 1.60 m/s 11-2a. 6.00, 9.00 A 11-2b. 5.00, 9.00 N 12-1a. 1.00, 3.30 mH 12-1b. 23.0, 65.0 A/s 12-2a. 0, 0 12-2b. 2.00, 6.00 V 12-2c. 4.00, 8.00 V 12-2d. 1.00, 3.00 V 12-3a. 10.0, 20.0 J 12-3b. 5.00, 8.00 J 13-1a. 2.00, 4.00 A 13-1b. 50.0, 90.0 V 13-2a. 100, 300 mA 13-2b. 200, 500 mA 13-3a. 100, 300 Hz 13-3b. 30.0, 70.0 mA 13-4a. 70, 120 V 13-4b. 140, 160 V 13-4c. 60, 130 V 13-4d. 20, 90 V 14-1a. 20.0, 40.0 kW 14-1b. 0.40, 0.70% 14-2a. 1.00, 3.00 MHz 14-2b. 120, 180 m 14-3. 1.80, 3.80 µH 14-4a. 180, 560 m 14-4b. 2.70, 3.50 m 15-1a. 0.300, 0.600 cm 15-1b. 1.00 × 10−10 , 2.00 × 10−10 s 15-2. 0.20, 0.60◦ 15-3a. 44.0, 52.0◦ 15-3b. 17.0, 34.0◦ 16-1a. 15.0, 20.0 cm 16-1e. −0.300, −0.700 16-2. 10.0, 20.0 cm 16-3b. 1.00, 1.50 m 16-4. 7.20, 8.90 cm 17-1. 1.10, 1.90 m 17-2. 8.00, 9.99 cm 17-3a. −5.0, −20.0 cm 17-3b. 2.00, 4.00 17-4a. 6.00, 9.00 cm 17-4b. 1.50, 2.50 cm 18-1. 1.50, 3.50 m 18-2. 2.50, 3.50 mm 18-3. 400, 650 nm 19-1. 1.70, 2.40 mm 19-2. 5.00, 7.00◦ 20-1a. 30.0, 35.0 cm 20-1b. −0.200, −0.350 20-2a. −2.00, −5.00 diopters 20-2b. −2.00, −5.00 diopters 20-2c. 20.0, 50.0 cm 20-3. 40, 60 cm 21-1a. 5.60, 9.70 21-1b. 0.80, 1.00 m 21-2. 2.3, 7.0 mm 21-3. 24.0, 66.0 cm 22-1. 0.800, 0.920c 22-2a. 100, 160 ns 22-2b. 30.0, 45.0 m 22-2c. 7.0, 8.0 m 22-3a. 20.00, 21.00 m 22-3b. 18.00, 19.00 m 22-3c. 0.34, 0.46c 23-1. 54.00, 58.00 min 23-2. 0.230, 0.360c 23-3. 0.20, 0.60c 23-4. 0.970, 0.999c 24-1a. 35.0, 65.0 GeV/c 24-1b. 0.99970, 0.99990c 24-2a. 1600, 3000 ±10 MeV 24-2b. 2500, 4000 ±10 MeV 24-3a. 1.8 × 1016 , 6.3 × 1016 J 24-3b. 5.0, 20.0 million years 24-4. 0.230, 0.310c 25-1a. 1.50 × 10−7 , 2.50 × 10−7 eV 25-1b. 5.00, 8.00 m 25-2. 0.50, 1.50 eV 25-3. 0.100, 0.200 nm 25-4a. 7.00 × 10−12 , 9.00 × 10−12 m 25-4b. 80.0, 110.0◦ 26-1a. 1.00, 2.00 km/s 26-1b. 3.00 × 10−11 , 8.00 × 10−11 m 26-2a. 1.50 × 10−11 , 2.70 × 10−11 m 26-2b. 0.80 × 10−15 , 2.30 × 10−15 m 26-4a. 300, 700 nm 26-4b. 0.600, 1.100 m/s 27-1a. 2.20 × 10−7 , 4.10 × 10−7 mol 27-1b. 1.30 × 1017 , 2.50 × 1017 27-1c. 7.0 × 1013 , 14.0 × 1013 Bq 27-1d. 4.0 × 106 , 8.0 × 106 Bq 27-2. 0.90, 1.20 h 27-3. 1.80, 2.40 g 28-1. 2000, 6000 yr 29-2. 1.00, 4.00 MeV 29-3. 1.00, 2.00 g