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college physics reasoning
College Physics Reasoning and Relationships 2nd edition Nicholas Giordano - Solutions
An electron is accelerated through an electric potential difference ∆V such that its kinetic energy is equal to its rest energy. Find ∆V.
The kinetic energy of a particle is equal to the rest energy of the particle. What is the speed of the particle?
The relativistic momentum of a particle of rest mass m0 and speed v is equal to 5m0v. What is the speed of the particle?
At what value of v is the relativistic momentum of a particle twice its classical (Newton’s law) momentum?
A proton has a relativistic momentum 10 times larger than its classical (Newton’s law) momentum. What is the speed of the proton? Express your answer with three significant figures.
A baseball has a mass of about 0.14 kg; if thrown by a major league pitcher, it has a speed of about 50 m/s. Now suppose an electron is given a very large speed v so that it has the same momentum as the baseball. Find v. Express your answer as c - v.
An electron moves with speed 0.95c. (a) What is the momentum of the electron according to Newton’s mechanics? (b) What is the correct value of the electron’s momentum according to special relativity?(c) Explain in words why the answer to part (b) is larger than the answer to part (a).
A distant galaxy is moving at a speed of 0.93c away from the Earth. The galaxy ejects some material toward the Earth with speed 0.85c relative to the Earth. What is the speed of the material relative to the galaxy?
An ice skater travels on a frozen lake at a speed of 30 m/s relative to the shore. The skater then throws a baseball in the direction parallel to her velocity with a speed of 20 m/s relative to the skater. Using the relativistic addition of velocities relation, what is the speed v of the baseball
Two asteroids are traveling along a common line and are on course for a head-on collision. Astronomers on the Earth observe that one asteroid has a speed of 0.75c and the other has a speed of 0.95c. What is the relative speed of the two asteroids as measured by an observer on one of the asteroids?
Spacecraft 1 is moving at speed 0.85c and is catching up with spacecraft 2, which is moving at speed 0.75c (both measured by an observer on the Earth). What is the speed of spacecraft 2 as measured by the pilot of spacecraft 1?
Two electrons are moving on course for a head-on collision, each with speed 0.99c relative to a stationary observer. What is the speed of one electron as measured by an observer traveling on the other? Express your answer to five significant figures.
An electron (electron 1) moves to the left with speed 0.95c while a second electron (electron 2) moves to the left with speed 0.70c. What is the speed of electron 2 as measured by an observer sitting on electron 1?
Traveling on a light beam. When he was first thinking about relativity (and before he developed his theory), Einstein considered how the universe would look to a person who traveled on a light beam. uppose you are traveling on a light beam when you encounter a friend who is traveling on a second
In studies of elementary particles such as electrons, physicists use machines called “accelerators” in which the particles move at very high speeds. Suppose an electron in one of these machines has a speed of 0.9999c and it travels along a straight line for a distance of 500 m as measured by
A military jet that is L0 = 35 m long (as measured on its runway prior to taking off) travels at a speed of 600 m/s. What is the length L of the jet as measured by an observer on the ground? Keep extra significant figures so that you can obtain the difference in length ∆L = L0 - L to two
Parking in a hurry. Your car is 5.0 m long, but you need to fit into a parking space that is only 4.5 m long. How fast must your car be moving so that you will not get a parking ticket from the police officer observing your predicament?
An astronaut travels from a distant star to the Earth at speed 0.999c. The astronaut ages 4.0 years during his journey. What is the distance from the star to the Earth as measured by an observer on the Earth?
A car of proper length 2.5 m moves past you at speed v, and you measure its length to be 2.2 m. What is the car’s speed?
A meter-stick moves toward you at speed 0.93c. What length do you measure for the meter-stick?
A muon is created at the top of Mount Everest (height 8900 m) and travels at constant speed to sea level, where it decays. According to a person traveling on the muon, what is the height of Mount Everest? Assume the muon travels vertically downward.
A spaceship moves past you at speed v. You measure the ship to be 300 m long, whereas an astronaut on the ship measures a length of 400 m. Find v.
An astronaut travels away from the Earth at a speed of 0.95c and sends a light signal back to the Earth every 1.0 s as measured by his clock. An observer on the Earth finds that the arrival time between consecutive signals is Δt. Find Δt.
An astronaut is traveling to the Moon at a speed of 0.85c. When his spacecraft is 2.0x108 m from the Moon, there is an explosion on the Moon. How long does it take for light from the explosion to reach the astronaut as measured on the astronaut’s clock?
A subatomic particle has an unknown lifetime t. The particle is created at t = 0 and travels around the Earth’s equator at speed 0.999c. If the particle decays at the moment it completes one trip around the Earth, what is τ?
An astronaut travels at a speed of 0.98c from the Earth to a distant star that is 4.5 x 1017 m away. If the astronaut is 25 years old when she begins her trip, how old is she when she arrives at the star?
Consider the motion of a muon as it moves through the Earth’s atmosphere (Example 27.4). A particular muon is created 15,000 m above the Earth’s surface and just reaches the ground before it decays. What is the speed of the muon?
Ted is traveling in his railroad car at speed v relative to Alice. He is also carrying a light clock in his luggage. Alice compares notes with Ted and finds that each tick of the light clock takes 1.0 s in Ted’s reference frame, whereas Alice measures 3.0 s per tick. Find v.
Identify inertial and non-inertial reference frames in the following list. (a) A spinning ice skater.(b) A car turning a corner.(c) A spacecraft moving at constant speed in a straight line.(d) A spacecraft moving with constant velocity.(e) A spacecraft landing on the Moon.(f) A spacecraft
The spotlight in Problem 2 emits light at a wavelength λ = 450 nm as viewed by the police officer. The wavelength seen by the driver is l. What is the percentage difference between these two wavelengths? Use the results for the Doppler effect in Chapter 23.
A person travels in a car with a speed of 75 m/s. To get the driver’s attention, a stationary police officer behind the car shines his spotlight at the car. If the officer is 300 m behind the car when he turns on his spotlight, how long does it take for the light to reach the car according to the
If the Earth were compressed to the density of a black hole, would it be about the size of (a) an atom, (b) a grape, (c) an orange, (d) a basketball
If you are traveling very close to the speed of light and hold a mirror in front of your face, what will you see?
Two identical clocks are synchronized. One stays on the Earth while the other goes in orbit around the Earth for 1 year as measured by the clock on the Earth. Which of the following statements are true after both clocks are again on the Earth? Explain. For answers (d) and (e), you should explain
You are standing on the Earth and observe a spherical spacecraft fly past at very high speed. Sketch the shape of the ship as observed by you.
Suppose an object moves away from a plane mirror at a speed of 0.9c. Does the image recede from the source at a speed of 1.8c? Explain.
Two spaceships, each traveling at 0.5c relative to an observer on the Earth, approach each other head on. One ship fires its laser beam weapon at the other ship. What does the other ship measure for the speed of the laser light?
Travelers onboard a spaceship are moving at 0.9c from one star to another. The stars are at rest relative to each other, and this is the speed of the spaceship relative to the stars. Which of the following statements are true? Assume observers on the spaceship or on the stars are in inertial
A wind-up toy has a coil spring that stores spring potential energy. As the toy is wound, does its mass increase, decrease, or stay the same? Explain.
At a typical everyday speed such as 65 mi/h, does length contract, time dilate, and mass increase by amounts that could be easily measured? Explain.
Two astronauts travel on spaceships that are both moving with constant velocities, but at different speeds. On which of the following quantities will the astronauts agree? In each case, give a reason for your answer. (a) The length of an object (e.g., a third spaceship) (b) The time interval
A particle is “extremely” relativistic if its speed is very close to c. What is the ratio of the total energy to the momentum for such a particle?
Length contraction applies to the length of an object measured in the direction of motion. Consider the length of an object measured in a direction perpendicular to its velocity. Give an argument that explains why there is no contraction along the perpendicular direction.
The speed of light inside a substance depends on the index of refraction n. For water, n = 1.33. (a) What is the speed of light in water? (b) Is it possible for a particle to travel faster than your result in part (a)? Explain why or why not.
Give four examples of noninertial reference frames.
Give an example of an inertial reference frame.
A constant force F is applied to a spacecraft of mass m. The spacecraft is initially at rest. Sketch the speed of the spacecraft as a function of time according to Newton’s laws (a) without allowing for relativity (b) allowing for relativity. Compare the two results and explain why they are
You are traveling in a windowless spacecraft, far from any planets or stars. Describe an experiment you could do to tell whether you are in an inertial or a noninertial frame.
It is impossible for a particle of rest mass m0 to travel at a speed greater than c. Is there an upper limit to the momentum or kinetic energy of the particle? Explain why or why not.
Suppose a compound microscope is used underwater so that the lenses are surrounded by water rather than air. Assuming the resolution is limited by diffraction and described by the Rayleigh criterion, will operating the microscope in water improve or degrade the ultimate resolution of the
Consider a digital camera with a lens of focal length f = 1.0 cm and diameter d = 0.5 cm. If the CCD sensor is rectangular with edge lengths 6.4 mm and 4.8 mm, what is the approximate upper limit on the number of usable pixels that such a camera could have?
The star closest to our Sun is Proxima Centauri, at a distance of about 3.8 x 1016 m (about 4 light-years). If Proxima Centauri had a planet similar to the Earth (i.e., with the same orbital radius), approximately how large would an optical telescope need to be to resolve that planet as an object
The constellation Orion is approximately 800 lightyears from the Earth. (One light-year is the distance traveled by light in a vacuum in one year.) Assume one of the stars in this constellation has a planet orbiting at the same distance as Saturn orbits the Sun. How large should the aperture of a
Consider the water fountain in Figure Q26.16, where the stream of water acts like an optical fiber. What is the minimum angle of total internal reflection in the stream of water for blue light with λ = 450 nm?
As the name implies, the Blu-ray disc has the same diameter and refractive index as a DVD or CD, but the laser light used is in the blue–violet region with a wavelength in air of 405 nm. The index of refraction of the plastic coating on the disc is n = 1.55. (a) What is the wavelength of this
A digital camera has an 8.3-megapixel CCD array with the pixels evenly spaced over a rectangular region, 7.2 mm 5.3 mm. The camera has a lens 2.0 cm in diameter with a focal length of 3.5 cm. (a) What is the resolution limit due to pixel size? (b) What is the approximate resolution limit due to
Two lenses are mounted in a tube such that the distance between them can be varied. This device can be used as either a telescope or a compound microscope. One lens has a focal length of 27 cm. (a) Find the focal length of the second lens such that a telescope made from the two lenses would have
You have lenses with focal lengths f1 = 4.0 cm and f2 = 12 cm. Assume your near-point distance is 25 cm and consider the following configurations of these lenses. (a) For magnifying glasses, what magnification could you achieve with each lens? (b) What is the maximum magnification you could
An objective lens has a focal length of 0.50 cm. Use it to design a compound microscope with a total magnification with m = 500. First identify the quantities whose values you must choose for the design and then find a set of appropriate values.
In Example 26.10, we discussed how light pulses in a multimode optical fiber are “smeared out” in time due to the different angles of travel that are possible within the fiber. This problem does not occur in single-mode fibers because all light travels along the axis of the fiber, but there is
The light used in a CD has a wavelength of 503 nm (inside the plastic coating), whereas a Blu-ray disc uses a wavelength of 260 nm (again, inside the plastic coating). Based solely on the effects of diffraction, a Blu-ray disc can contain more pits and thus hold more information than a CD. Estimate
A real CD can hold approximately 600 Mbytes of information. Each byte is an 8-bit binary number, so it takes eight digits of zeros and ones to make 1 byte. So that each pit edge can be optically resolved by the laser beam that reflects from the CD (Fig. 26.30), the length of a pit must be no
A hypothetical CD player uses a laser with λ = 780 nm in air. Inside the plastic coating of a hypothetical CD the wavelength is 490 nm. What is the index of refraction of the plastic?
The author has an inexpensive digital camera that has the following specifications: “5X optical zoom, 7X digital zoom.” (a) The “lens” is actually a combination of several lenses, and the value of the optical zoom is adjusted by changing the focal length f of the lens system. If the
A 35-mm camera uses film that is 24 mm tall and 35 mm wide. If it is used to take a photograph of a car that is 2.5 m long and 11 m away from the camera and the car just fills the photo, what is the focal length of the lens?
A camera has an aperture of 2.0 cm and a lens with f = 4.2 cm. (a) What is the f-number? (b) If the f-number is reduced by a factor of three, by what factor should the exposure time be changed to have the same total light energy strike the detector?
A photograph of a particular scene is nicely exposed with an f-number of 5.6 and an exposure time of 0.010 s. If the exposure time is changed to 0.020 s, what f-number should be used?
For a camera with a shutter speed set to “250” as read on the camera, how long is the detector exposed to light?
The shutter speed on a camera is increased from 1/60 s to 1/500 s. If the f-number is originally 2.8, what new setting would you recommend?
The f-number on a camera is changed from 4 to 8. If the photographer wants to have the same amount of light energy strike the detector, should she increase or decrease the shutter speed, and by what factor?
The distance between a camera lens and the detector in a particular camera is 5.0 cm. If this lens is focused on an object that is very far away, what is the focal length of the lens?
A film camera uses a single lens with a focal length f = 60 mm. (a) Calculate the image distance for an object at infinity. (b) Calculate the image distance for an object that is 2.5 m away. (c) How far must the lens be moved with respect to the film when an object moves from infinity to a point
One of the largest refracting telescopes made to date has an objective lens with a focal length of approximately 20 m. When this telescope is used to look at the full Moon, what is the angle subtended by the edges of the Moon in the image formed by the objective? If the eyepiece has a focal length
The Hubble Space Telescope is a Cassegrain reflecting telescope (Fig. 26.15B) with a primary mirror diameter of 2.4 m. What is the size of the smallest object that this telescope can resolve (a) on Mars, (b) on the Moon, (c) on the surface of one of the moons of Saturn?
Galileo was famous for his use of a telescope to study the solar system. Among his many discoveries, he showed that there are mountains on the surface of the Moon. Estimate the size of the smallest object that Galileo’s telescope could resolve on the Moon. Galileo used a refracting telescope with
You wish to design a telescope using an objective lens with fobj = 0.75 m. If you use an eyepiece with a magnification of 20, what are (a) the total magnification of the telescope (b) the length of the telescope?
Consider a refracting telescope like that described in Figure 26.12. If it has an objective lens with fobj = 1.5 m and an eyepiece with feyepiece = 2.0 cm, what is the angular magnification of this telescope?
A compound microscope has a total magnification |m| = 500, using an eyepiece whose magnification is 20. What is the focal length of the objective lens?
A compound microscope has an objective lens that by itself produces a magnification of 15. The total magnification of the microscope is designed to be 150. (a) What is the focal length of the eyepiece? (b) Why is the value of the magnification negative?
The distance between the objective lens and the eyepiece of a microscope is 30 cm. If the eyepiece has a magnification of 20 and the total magnification of the microscope is |m| = 250, what is the focal length of the objective lens?
A compound microscope in which the objective and eyepiece are 20 cm apart uses an objective lens with fobj = 1.0 cm and an eyepiece with feyepiece = 5.0 cm. What is the magnification of the microscope?
Consider again Problem 20. With a near-point distance of 25 cm, what is the smallest object a person can resolve using a magnifying glass with a magnifi cation of 10?
Suppose you have a near-point distance of 25 cm. The angular resolution of the eye is determined by diffraction and the Rayleigh criterion (Chapter 25) and is approximately 1 arcmin = 1'. What is the smallest object your eye can resolve without a magnifying glass?
Will you achieve a larger magnifi cation with a particular magnifying glass if you have a near-point distance of 25 cm or of 15 cm? If the focal length of the magnifying glass is 7.5 cm, what is the ratio of the magnifi cations in the two cases?
A person with a near-point distance of 25 cm is able to get a usable magnification of 20 with a particular magnifying glass. Her friend is only able to get a usable magnification of 15. What is the friend’s near-point distance?
An entomologist with a near-point distance of 30 cm has two lenses that she uses to examine small beetles. One lens has a focal length f1 = 2.3 cm, and the second has a focal length f2 = 7.5 cm.(a) Which of the two lenses would allow her to see the smallest detail?(b) Calculate the maximum
A magnifying glass gives an actual magnification of 10 for a person with a near-point distance of sN = 35 cm. What is the focal length of the lens?
A relaxed human eye has a focal length of about 2.5 cm. When looking at something very close, however, the refractive power of the eye can change by up to 16 diopters for a young adult. The shaping of the lens of the eye through muscles that stretch and compress is known as the process of
A pair of glasses is designed for a person with a far-point distance of 3.0 m so that she can read street signs 20 m away. (The far-point distance is the distance from the eye at which you are just able to properly focus a distant object.) (a) If the glasses are to be worn 1.0 cm from her eyes,
Design a set of eyeglasses for a nearsighted person. Assume the person is able to focus only on objects closer than about arm’s length. What type of lens (converging or diverging) with approximately what focal length is required so that the person can view an object at infinity?
The cornea of an average human eye has a refractive power of about 40 diopters. To what focal length does this value correspond? How does this focal length compare to the size of the eye?
What is the refractive power of a lens whose focal length is f = 37 cm? Give your answer in diopters. Does the refractive power increase or decrease if the focal length is decreased?
The author’s near-point distance is about 40 cm. What is the focal length of his reading glasses if using them allows him to bring his newspaper to within 10 cm of his eyes? Assume the glasses are placed 2.0 cm in front of his eyes.
The author is nearsighted and (at present) is unable to focus clearly on objects that are farther than about 2.0 m from his eyes. (a) What type of lens (converging or diverging) should his eyeglasses contain so that he can focus on more distant objects? (b) What should be the focal length of his
A person uses eyeglasses that have a focal length f = -25 cm and are mounted 1.5 cm in front of his eyes to look at objects that are very far away.(a) If he switches to contact lenses that are mounted in contact with the eye, what focal length should the contact lenses have?(b) Make a qualitative
The distance from the front of the eye to the retina is about 2.5 cm. If this eye is focused on a newspaper that is 40 cm in front of the eye, what is the focal length of the eye?
Consider again the nearsighted person in Problem 3, but now assume the borrowed glasses make things worse; that is, the person can now focus only on things that are within 1.5 m away. Do these glasses contain converging lenses or diverging lenses? What is the focal length of the glasses?
A person is nearsighted and can clearly focus on objects that are no farther than 3.0 m away from her eyes. She borrows a friend’s glasses and fi nds that she can now focus on objects as far away as 4.5 m. What is the focal length of the glasses? Do they use converging lenses or diverging lenses?
Your friend is farsighted with a near-point distance of 500 cm. What should the focal length be for the lenses in his reading glasses? Assume the glasses are placed 2.0 cm in front of his eyes.
You are nearsighted and can only focus clearly on things that are closer than 2.5 m. What should the focal length be for contact lenses that correct this problem?
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