An unstable particle with a mass equal to 3.34 x 10-27 kg is initially at rest. The particle decays into two fragments that fly off with velocities of 0.987c and -0.868c, respectively. Find the masses of the fragments. Hint: Conserve both mass – energy and momentum.
> What two speed measurements will two observers in relative motion always agree upon?
> Compare and contrast the eye and a camera. What parts of the camera correspond to the iris, the retina, and the cornea of the eye?
> A camera is being used with a correct exposure at f/4 and a shutter speed of 1/15 s. In addition to the f - numbers listed in Section 25.1, this camera has f - numbers f/1, f/1.4, and f/2. To photograph a rapidly moving subject, the shutter speed is chan
> A digital camera equipped with an f = 50.0 - mm lens uses a CCD sensor of width 8.70 mm and height 14.0 mm. Find the closest distance from the camera to a 1.80 - m - tall person if the person’s full image is to fit on the CCD sensor.
> An f/2.80 CCD camera has a 105 - mm focal length lens and can focus on objects from infinity to as near as 30.0 cm from the lens. (a) Determine the camera’s aperture diameter. Determine the (b) Minimum and (c) Maximum distances from the CCD sensor over w
> A certain camera has f - numbers that range from 1.2 to 22. If the focal length of the lens is 55 mm, what is the range of aperture diameters for the camera?
> A patient has a near point of 45.0 cm and far point of 85.0 cm. (a) Can a single lens correct the patient’s vision? Explain the patient’s options. (b) Calculate the power lens needed to correct the near point so that the patient can see objects 25.0 cm a
> A particular patient’s eyes are unable to focus on objects closer than 35.0 cm and corrective lenses are to be prescribed so that the patient can focus on objects 20.0 cm from their eyes. (a) Is the patient nearsighted or farsighted? (b) If contact lense
> A particular nearsighted patient can’t see objects clearly beyond 15.0 cm from their eye. Determine (a) The lens power required to correct the patient’s vision and (b) The type of lens required (converging or diverging). Neglect the distance between the
> An individual is nearsighted; his near point is 13.0 cm and his far point is 50.0 cm. (a) What lens power is needed to correct his nearsightedness? (b) When the lenses are in use, what is this person’s near point?
> Choose the option from each pair that makes the following statement correct. Because ( for an object in relative motion is always [(a) greater; (b) less] than 1, a proper time interval Δtp is always [(c) longer; (d) shorter] than the time interval Δt and
> A certain child’s near point is 10.0 cm; her far point (with eyes relaxed) is 125 cm. Each eye lens is 2.00 cm from the retina. (a) Between what limits, measured in diopters, does the power of this lens–cornea combination vary? (b) Calculate the power of
> The accommodation limits for Nearsighted Nick’s eyes are 18.0 cm and 80.0 cm. When he wears his glasses, he is able to see faraway objects clearly. At what minimum distance is he able to see objects clearly?
> A patient can’t see objects closer than 40.0 cm and wishes to clearly see objects that are 20.0 cm from his eye. (a) Is the patient nearsighted or farsighted? (b) If the eye–lens distance is 2.00 cm, what is the minimum object distance p from the lens? (
> The near point of a person’s eye is 60.0 cm. To see objects clearly at a distance of 25.0 cm, what should be the (a) Focal length and (b) Power of the appropriate corrective lens? (Neglect the distance from the lens to the eye.)
> A certain camera lens has a focal length of 175 mm. Its position can be adjusted to produce images when the lens is between 180. mm and 210. mm from the plane of the film. Over what range of object distances is the lens useful?
> A certain type of film requires an exposure time of 0.010 s with an f/11 lens setting. Another type of film requires twice the light energy to produce the same level of exposure. What f - number does the second type of film need with the 0.010 - s exposu
> (a) Use conceptual arguments to show that the intensity of light (energy per unit area per unit time) reaching the film in a camera is proportional to the square of the reciprocal of the f - number as (b) The correct exposure time for a camera set to f/
> A muon formed high in Earth’s atmosphere travels toward Earth at a speed v = 0.990c for a distance of 4.60 km as measured by an observer at rest with respect to Earth. It then decays into an electron, a neutrino, and an antineutrino. (a) How long does th
> An astronaut is traveling in a space vehicle that has a speed of 0.500c relative to Earth. The astronaut measures his pulse rate at 75.0 beats per minute. Signals generated by the astronaut’s pulse are radioed to Earth when the vehicle is moving perpendi
> The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6 x 10-8 s. If the meson moves with a speed of 0.98c, what is (a) Its mean lifetime as measured by an observer on Earth, and (b) The average distance it tra
> Suppose you are observing the interference pattern formed by a Michelson interferometer in a laboratory and a joking colleague holds a lit match in the light path of one arm of the interferometer. Will this match have an effect on the interference patter
> An astronaut at rest on Earth has a heart rate of 70. beats/min. When the astronaut is traveling in a spaceship at 0.90c, what will this rate be as measured by (a) An observer also in the ship and (b) An observer at rest on Earth?
> An alien spaceship traveling 0.600c toward Earth launches a landing craft with an advance guard of purchasing agents. The lander travels in the same direction with a velocity 0.800c relative to the spaceship. As observed on Earth, the spaceship is 0.200
> An observer moving at a speed of 0.995c relative to a rod (Fig. P26.55) measures its length to be 2.00 m and sees its length to be oriented at 30.0° with respect to its direction of motion. (a) What is the proper length of the rod? (b) What is
> An interstellar space probe is launched from Earth. After a brief period of acceleration, it moves with a constant velocity, 70.0% of the speed of light. Its nuclear - powered batteries supply the energy to keep its data transmitter active continuously.
> The identical twins Speedo and Goslo join a migration from Earth to Planet X, which is 20.0 light - years away in a reference frame in which both planets are at rest. The twins, of the same age, depart at the same time on different spacecraft. Speedo’s c
> Imagine that the entire Sun collapses to a sphere of radius Rg such that the work required to remove a small mass m from the surface would be equal to its rest energy mc2. This radius is called the gravitational radius for the Sun. Find Rg. (It is believ
> The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a reference frame in which the muons are stationary, if the number of muons at t = 0 is N0, the number at time t is given by N = N0e-t/τ, where τ is the mea
> (a) Show that a potential difference of 1.02 x 106 V would be sufficient to give an electron a speed equal to twice the speed of light if Newtonian mechanics remained valid at high speeds. (b) What speed would an electron actually acquire in falling thro
> The length of a moving spaceship is 28.0 m according to an astronaut on the spaceship. If the spaceship is contracted by 15.0 cm according to an Earth observer, what is the speed of the spaceship?
> The nonrelativistic expression for the momentum of a particle, p = mv, can be used if v
> Choose the option that makes the following statement correct. Two events at a single location define a time interval. The proper time interval Δtp is measured by an observer [(a) at rest; (b) moving] relative to the location where the two events occur.
> The cosmic rays of highest energy are protons that have kinetic energy on the order of 1013 MeV. (a) From the point of view of the proton, how many kilometers across is the galaxy? (b) How long would it take a proton of this energy to travel across the M
> A spaceship of proper length 300. m takes 0.75 µs to pass an Earth observer. Determine the speed of this spaceship as measured by the Earth observer.
> An observer in a coasting spacecraft moves toward a mirror at speed v relative to the reference frame labeled by S in Figure P26.46. The mirror is stationary with respect to S. A light pulse emitted by the spacecraft travels toward the mirror and is refl
> Owen and Dina are at rest in frame S', which is moving with a speed of 0.600c with respect to frame S. They play a game of catch while Ed, at rest in frame S, watches the action (Fig. P26.45). Owen throws the ball to Dina with a speed of 0.800c (accordin
> An alarm clock is set to sound in 10.0 h. At t = 0, the clock is placed in a spaceship moving with a speed of 0.75c (relative to Earth). What distance, as determined by an Earth observer, does the spaceship travel before the alarm clock sounds?
> An astronaut wishes to visit the Andromeda galaxy, making a one - way trip that will take 30.0 years in the spaceship’s frame of reference. Assume the galaxy is 2.00 million light - years away and his speed is constant. (a) How fast mus
> An electron has a total energy equal to five times its rest energy. (a) What is its momentum? (b) Repeat for a proton.
> A star is 5.00 ly from the Earth. At what speed must a spacecraft travel on its journey to the star such that the Earth–star distance measured in the frame of the spacecraft is 2.00 ly?
> A spring of force constant k is compressed by a distance x from its equilibrium length. (a) Does the mass of the spring change when the spring is compressed? Explain. (b) Find an expression for the change in mass of the spring in terms of k, x, and c. (c
> A meter-stick moving at 0.900c relative to the Earth’s surface approaches an observer at rest with respect to the Earth’s surface. (a) What is the meter-stick’s length as measured by the observer? (b) Qualitatively, how would the answer to part (a) chang
> A CCD camera is equipped with a lens with constant focal - length. As the f - number is decreased, determine whether the following quantities increase, decrease, or remain unchanged. Indicate your answers with I, D, or U. (a) The aperture (b) The depth o
> The rest energy of an electron is 0.511 MeV. The rest energy of a proton is 938 MeV. Assume both particles have kinetic energies of 2.00 MeV. Find the speed of (a) The electron and (b) The proton. (c) By how much does the speed of the electron exceed tha
> An electron has a speed of 0.750c. (a) Find the speed of a proton that has the same kinetic energy as the electron. (b) Find the speed of a proton that has the same momentum as the electron.
> Consider electrons accelerated to a total energy of 20.0 GeV in the 3.00 - km - long Stanford Linear Accelerator. (a) What is the ( factor for the electrons? (b) How long does the accelerator appear to the electrons? Electron mass energy: 0.511 MeV.
> Consider the reaction 92235U + 01n ( 57148La + 3587Br + 01n. (a) Write the conservation of relativistic energy equation symbolically in terms of the rest energy and the kinetic energy, setting the initial total energy equal to the final total energy. (b)
> Starting with the definitions of relativistic energy and momentum, show that E2 = p2c2 + m2c4 (Eq. 26.13).
> A chain of nuclear reactions in the Sun’s core converts four protons into a helium nucleus. (a) What is the mass difference between four protons and a helium nucleus? (b) How much energy in MeV is released during the conversion of four protons into a hel
> Determine the energy required to accelerate an electron from (a) 0.500c to 0.900c and (b) 0.900c to 0.990c.
> What speed must a particle attain before its kinetic energy is double the value predicted by the nonrelativistic expression KE = ½ mv2?
> A proton in a large accelerator has a kinetic energy of 175 GeV. (a) Compare this kinetic energy to the rest energy of the proton, and find an approximate expression for the proton’s kinetic energy. (b) Find the speed of the proton.
> A lens has a focal length of 28 cm and a diameter of 4.0 cm. What is the f - number of the lens?
> You are packing for a trip to another star, and on your journey you will be traveling at a speed of 0.99c. Can you sleep in a smaller cabin than usual, because you will be shorter when you lie down? Explain your answer.
> Refer to the following two histograms and two QQ plots of the same data. a. Match each of the histograms with the corresponding QQ plot. Histogram A goes with QQ plot ______. Histogram B goes with QQ plot ______. b. Describe the shape of the histograms.
> Refer to the following two histograms and two QQ plots of the same data. a. Match each of the histograms with the corresponding QQ plot. Histogram A goes with QQ plot ______. Histogram B goes with QQ plot ______. b. Describe the shape of the histograms.
> What summary statistics are best used to report the “typical” value of a data set when the distribution is strongly skewed?
> In addition to random samples, what other conditions are required for using the two-sample t-test?
> In what situations are nonparametric statistics useful?
> A professor tells his class that he knows their second exam score without their having to take the test. He tells them that the second exam score can be predicted from the first with this equation: Predicted second exam score = 5 + 0.75 (first exam score
> The table shows the number of floors and the height (in feet) of five of the tallest buildings in China. The regression model for predicting the height of a building from the number of floors is height = 20.888067 + 16.124191 Floors Complete the table by
> What is the fundamental condition required for inference from a sample to a population?
> Using data from Exercise 13.25, we used a randomization test to find out whether the typical number of winning runs in the American League differed from that of the National League in professional baseball. In each randomization we found the mean differe
> Looking at the data about contacting mom (exercise 13.49), for which group (ethicists or other) could you perform a log transform, and for which group could you not? Explain. Data from exercise 13.49:
> The dotplot shows the number of classes missed in a month for a random sample of 23 students from a private college in California. Explain why you cannot find the geometric mean for the numbers.
> Exercise 13.35 describes a simulation exercise. Under which of the following assumptions were the data simulated? a. Cloud seeding typically produces more rain than not seeding the cloud. b. Cloud seeding typically produces the same amount of rain as not
> Exercise 13.35 describes a simulation exercise. Which of the following is the best explanation for the process described? a. This process allows researchers to compare the actual result to what could have happened by chance (assuming the null hypothesis
> In a well-known study on the effects of cloud seeding to produce rainfall (cited on page 659 of the text by Simpson et. al), experimenters randomly assigned airplanes to release either silver nitrate (which is believed to increase the amount of rainfall
> Suppose you give a random sample of students a questionnaire about extraversion, and some (10) are classified as extraverts and some (15) as not extraverts. You want to determine whether the typical GPA is higher for extraverts than for those who are not
> Suppose a random sample of online grocery prices (15 items) is obtained at Amazon and Walmart. The same items were sampled at both sites, and a student wants to determine whether the typical price differs at the two online sites. Which test(s) can be use
> Tickets for high demand events are often resold on a secondary market, such as StubHub or VividSeats. Suppose a consumer is interested in determining if there is a significant difference in ticket prices between the two resale sites. She picks an upcomin
> Suppose you want to determine whether there is difference in wait times at two Department of Motor Vehicles offices. A random sample of customer wait times is obtained for each office. Which test(s) can be used for each situation below? a. The populaton
> Suppose you want to determine whether meditation can cause a decrease in pulse rate. You randomly select 15 students, teach them a meditation technique, and then measure their pulse rates before and after meditation. Which test(s) should you choose for e
> Suppose a college career center was interested in the starting salaries of recent graduates in Communications Studies and Sociology. The center randomly samples 15 recent graduates from each of these fields and records the starting salary for the graduat
> You know the grade point averages (GPAs) of a random sample of 10 full-time college students and 10 part-time college students. You want to test the hypothesis that the typical GPAs for full-time and part-time college students are different. Which test(s
> You have recorded the time slept on a Tuesday and the time slept on a Sunday for a random sample of 15 students. You want to investigate whether students tend to sleep more on weekends than on weekdays. Which test(s) can you use? Answer for each circumst
> A scatterplot of the waist sizes and weights of 500 people was shown in exercise 14.34. The accompanying scatterplot shows both confidence intervals and prediction intervals. Which is which? Explain how you can tell.
> A scatterplot of the heights and weights of 500 people was shown in exercise 14.33. The accompanying scatterplot shows both confidence intervals and prediction intervals. Which is which? Explain what this shows.
> The scatterplot shows shoe size and height for 83 people. From the graph, state approximate values for the prediction interval for predicting the shoe size for someone who is 68 inches tall.
> The figure shows 95% prediction intervals for predicting GPA at a certain college from math SAT score, based on data from 196 students. From the graph, give approximate prediction interval boundaries for predicting GPA from a math SAT score of 750. State
> A scatterplot of the waist sizes and weights of the same 500 people mentioned in exercise 14.33 is shown. The accompanying scatterplot uses the same people and displays 95% prediction intervals. From the graph, estimate the upper and lower values for the
> A scatterplot of the heights and weights of 500 people was shown in Chapter 4. The accompanying scatterplot uses the same data but displays 95% prediction intervals. From the graph, estimate the upper and lower values for the prediction interval used for
> A mother is interested in predicting the adult height of her 6-year-old daughter. She has information on the heights of mothers and daughters in her community. Should she use a prediction interval or a confidence interval for her prediction? Explain.
> A logging company has the diameter of each of a large number of trees and wants to estimate the mean number of usable cubic feet of wood the company will get if it cuts the trees down. Working with a sample of trees, company planners find the regression
> A dean of students at a college wishes to estimate the typical future cumulative GPA for all first-year students who earned a 2.0 GPA during their first year. Should she use a prediction interval or a confidence interval? Why?
> A mother wants to predict the height of her full-grown son on the basis of his height at the age of 8 years. Should she use a prediction interval or a confidence interval? Why?
> A used-car dealer is purchasing 50 used BMWs from one dealer in order to sell them for a profit. Working with collected data, the dealer has found a regression model to predict the selling price on the basis of the car’s age. He wants to predict the tota
> A student who has been accepted by two colleges wants to estimate what GPA he might get at the two colleges. His data consist of SAT scores and GPAs from random samples of recent graduates at each college. He wishes to predict his GPA at each school, usi
> In exercise 14.16 you examined the association between movie budgets and box office gross income. Would a 95% confidence interval for the slope, based on the same data, include 0? Explain.
> The output provided for exercise 14.20 provides a regression line to predict the amount of trash produced by a household on the basis of the number of people living in the household. Suppose you found a 95% confidence interval for the intercept of the re
> A regression analysis was conducted using data on success rates and retention rates in transfer courses at a sample of California community colleges. Assume the conditions for the linear model regression model are satisfied. a. Interpret the slope in con
> Figure A shows a scatterplot of the percent passing the bar exam within two years of graduation and the percent employed at graduation for U.S. law school graduates in 2015. Figure B shows the residual plot of the data. Evaluate the residual plot to dete
> Figure A shows a scatterplot of the price and age of a random sample of used Acura MDX cars and includes the regression line. Figure B shows a residual plot based on the regression line. (Source: cars.com) a. Is the regression model appropriate for these
> The table shows the number of floors and the height (in feet) of the five tallest buildings in Dubai. The regression model for predicting the height of a building from the number of floors is height = -558.45931 + 19.934126 Floors Complete the table by f
> The registrar at a small college says she can predict the number of units that a full-time student has accumulated on the basis of the number of semesters the student has attended the college by using the equation Predicted Units = 0 + 14 Semesters This
> A doctor says he can predict the height (in inches) of a child between 2 and 9 years old from the child’s age (in years) by using the equation Predicted Height = 31.78 + 2.45 Age This tells us the deterministic part of the regression model. What factors
> Figure A shows a scatterplot of some simulated data, and Figure B shows a residual plot of the same data. Is the linear regression model appropriate for these data? Why or why not? Assume the observations are independently measured.
> Figure A shows a scatterplot of wages of twins for a group of 183 pairs of twins. Figure B shows a residual plot of the same data. Figure C shows a QQ plot of these residuals. Is the linear regression model appropriate for these data? Why or why not? Ass
> Figure A shows a scatterplot of the number of print and electronic holdings for a sample of large U.S. libraries. Figure B shows a QQ plot of the residuals. Is the Normality condition of the linear regression model satisfied? Explain.
