A 1200 kg airplane starts from rest and, with a constant acceleration of magnitude 5.0 m/s2, reaches its takeoff speed in 9.00 s. (a) What is the magnitude of the net force on the airplane during this time interval? (b) Assume that when the plane is just reaching its takeoff speed the drag force is equal to one-half of the thrust. Sketch an FBD and label the magnitudes of the forces. (c) What is its takeoff speed?
> A 35.0 kg child swings on a rope with a length of 6.50 m that is hanging from a tree. At the bottom of the swing, the child is moving at a speed of 4.20 m/s. What is the tension in the rope?
> A concave mirror has radius of curvature R. A ray of light parallel to and a distance / away from the optical axis is incident on the mirror. (a) Use the law of reflection to find the distance from the vertex to the point where the reflected ray cros
> A pendulum is 0.80 m long, and the bob has a mass of 1.0 kg. At the bottom of its swing, the bob’s speed is 1.6 m/s. (a) What is the tension in the string at the bottom of the swing? (b) Explain why the tension is greater than the weight of the bob.
> Jane is sitting on a chair with her lower leg at a 30.0° angle with respect to the vertical, as shown. You need to develop a computer model of her leg to assist in some medical research. If you assume that her leg can be modeled as two uniform
> Use the thin-lens equation to show that the transverse magnification due to the objective of a microscope is mo = −L/fo. [Hints: The object is near the focal point of the objective; do not assume it is at the focal point. Eliminate po to find the magnifi
> Use the expression in Problem 54 to find (a) the maximum range of a projectile with launch speed vi and (b) the launch angle θ at which the maximum range occurs.
> An object is located at x = 0. At x = 2.50 cm is a converging lens with a focal length of 2.00 cm, at x = 16.5 cm is an unknown lens, and at x = 19.8 cm is another converging lens with focal length 4.00 cm. An upright image is formed at x = 39.8 cm. For
> The range R of a projectile is defined as the magnitude of the horizontal displacement of the projectile when it returns to its original altitude. In other words, the range is the distance between the launch point and the impact point on flat ground. A p
> An object is placed between a concave mirror with a radius of curvature of 18.0 cm and a diverging lens with a focal length of magnitude 12.5 cm. The object is 15.0 cm from the mirror and 20.0 cm from the lens. Looking through the lens, you see two image
> The citizens of Paris were terrified during World War I when they were suddenly bombarded with shells fired from a long-range gun known as Big Bertha. The barrel of the gun was 36.6 m long, and it had a muzzle speed of 1.46 km/s. When the gun's angle of
> A microscope has an eyepiece of focal length 2.00 cm and an objective of focal length 3.00 cm. The eyepiece produces a virtual image at the viewer's near point (25.0 cm from the eye). (a) How far from the eyepiece is the image formed by the objective?
> After being assaulted by flying cannonballs, the knights on the castle walls (12 m above the ground) respond by propelling flaming pitch balls at their assailants. One ball lands on the ground at a distance of 50 m from the castle walls. If it was launch
> A converging lens with a focal length of 5.500 cm is placed 8.00 cm to the left of a diverging lens with a focal length of −4.20 cm. An object that is 1.0 cm tall is placed 9.000 cm to the left of the converging lens. (a) Where is the final image formed
> You have been employed by the local circus to plan their human cannonball performance. For this act, a spring-loaded cannon will shoot a human projectile, the Great Flyinski, across the big top to a net below. The net is located 5.0 m lower than the muzz
> Martin caught a fish and wanted to know how much it weighed, but he didn’t have a scale. He did, however, have a stopwatch, a spring, and a 4.90 N weight. He attached the weight to the spring and found that the spring would oscillate 20 times in 65 s. Ne
> Two lenses, separated by a distance of 21.0 cm, are used in combination. The first lens has a focal length of +30.0 cm; the second has a focal length of −15.0 cm. An object, 2.0 mm long, is placed 1.8 cm before the first lens. (a) What are the intermedi
> Jason is practicing his tennis stroke by hitting balls against a wall. The ball leaves his racquet at a height of 60 cm above the ground at an angle of 80° with respect to the vertical. (a) The speed of the ball as it leaves the racquet is 20 m/s, and i
> An object is placed 20.0 cm from a converging lens with focal length 15.0 cm (see the figure, not drawn to scale). A concave mirror with focal length 10.0 cm is located 75.0 cm to the right of the lens. Light goes through the lens, reflects from the mirr
> You are planning a stunt to be used in an ice skating show. For this stunt a skater will skate down a frictionless ice ramp that is inclined at an angle of 15.0° to the horizontal. At the bottom of the ramp, there is a short horizontal section that ends
> Two converging lenses, separated by a distance of 50.0 cm, are used in combination. The first lens, located to the left, has a focal length of 15.0 cm. The second lens, located to the right, has a focal length of 12.0 cm. An object, 3.00 cm high, is plac
> A ballplayer standing at home plate hits a baseball that is caught by another player at the same height above the ground from which it was hit. The ball is hit with an initial velocity of 22.0 m/s at an angle of 60.0° above the horizontal. (a) How high
> A refracting telescope has an objective lens with a focal length of 2.20 m and an eyepiece with a focal length of 1.5 cm. If you look through this telescope the wrong way, that is, with your eye placed at the objective lens, by what factor is the angular
> An arrow is shot into the air at an angle of 60.0° above the horizontal with a speed of 20.0 m/s. (a) What are the x- and y- components of the velocity of the arrow 3.0 s after it leaves the bowstring? (b) What are the x- and y-components of the displa
> A convex lens of refractive power +12 D is used as a magnifier to examine a wildflower. What is the angular magnification if the final image is at (a) infinity or (b) the near point of 25 cm?
> An archer fish spies a meal of a grasshopper sitting on a long stalk of grass at the edge of the pond in which he is swimming. If the fish is to successfully spit at and strike the grasshopper, which is 0.200 m away horizontally and 0.525 m above his mou
> In a lab experiment, two identical gliders on an air track are held together by a piece of string, compressing a spring between the gliders. While they are moving to the right at a common speed of 0.50 m/s, one student holds a match under the string and
> A cub scout makes a microscope by placing two converging lenses of +18 D at opposite ends of a 28 cm long tube. (a) What is the tube length of the microscope? (b) What is the angular magnification? (c) How far should an object be placed from the objec
> A ball is thrown from a point 1.0 m above the ground. The initial velocity is 19.6 m/s at an angle of 30.0° above the horizontal. (a) Find the maximum height of the ball above the ground. (b) Calculate the speed of the ball at the highest point in the
> A dissecting microscope is designed to have a large distance between the object and the objective lens. Suppose the focal length of the objective of a dissecting microscope is 5.0 cm, the focal length of the eyepiece is 4.0 cm, and the distance between t
> In Fig. 3.30 an astronaut is playing shuffleboard on Earth. The puck has a mass of 2.0 kg. Between the board and puck the coefficient of static friction is 0.35 and that of kinetic friction is 0.25. (a) If she pushes the puck with a force of 5.0 N in the
> The image sensor of a camera measures 24 mm by 36 mm. The focal length of the camera lens is 50.0 mm. A picture is taken of a person 182 cm tall. What is the minimum distance from the camera for the person to stand so that the image fits on the sensor? G
> In Example 3.10, find T3, the tension in the coupling between cars 2 and 3.
> An astronomical telescope provides an angular magnification of 12. The two converging lenses are 66 cm apart. Find the focal length of each of the lenses.
> Five objects all start from rest at t = 0. Each is pushed to the right by a constant net force. Rank the objects according to their speeds at the instants of time indicated, from largest to smallest. (a) mass m, net force F; speed at time t1; (b) mass 2
> Two lenses, of focal lengths 3.0 cm and 30.0 cm, are used to build a small telescope. (a) Which lens should be the objective? (b) What is the angular magnification? (c) What is the distance between the intermediate image (formed by the eyepiece) and th
> In each motion diagram, the dots are labeled with the “frame” number (frame 1 is the first position of the object). Choose the x-axis pointing to the right. For each diagram, sketch graphs of x(t), vx(t), and ax(t) and
> When a steel cable supports a heavy load of weight W, its length increases by an amount ΔL compared with its length without a load. Suppose the cable is cut into three equal pieces, and the three resulting cables are used side by side to support the same
> A slide projector, using slides of width 5.08 cm, produces an image that is 2.00 m wide on a screen 3.50 m away. What is the focal length of the projector lens?
> In a binary star system, two stars orbit their common center of mass. In one such system, star A has 4.0 times the mass of star B. (a) Draw and label vector arrows for the gravitational forces that each star exerts on the other, showing how their direct
> A slide projector has a projection lens of 10.0 cm focal length, and the screen is located 2.5 m from the projector. (a) What is the distance between the slide and the projection lens? (b) What is the magnification of the image? (c) How wide is the im
> Draw a motion diagram and sketch graphs of x(t), vx(t), and ax(t) for a sprinter running a short race on a straight track, from just before the start of the race until the sprinter has stopped after finishing the race. Sketch FBDs for the runner while sp
> You have two lenses of focal lengths 25.0 cm and 5.0 cm. (a) To build an astronomical telescope that gives an angular magnification of 5.0, how should you use the lenses (which for objective and which for eyepiece)? Explain. (b) How far apart should th
> A tennis ball (mass 57.0 g) moves toward the player’s racquet at 47.5 m/s. It is in contact with the racquet for 3.60 ms, after which it moves in the opposite direction at 50.2 m/s. What is the average force on the ball due to the racquet?
> A camera has a telephoto lens of 240 mm focal length. The lens can be moved in and out a distance of 16 mm from the image sensor by rotating the lens barrel. If the lens can focus objects at infinity, what is the closest object distance for which the cam
> (a) Using Fig. 3.26, estimate Damon’s acceleration at t = 2.0 s. (b) Estimate his average velocity between t = 0 and t = 10.0 s.
> Good lenses used in cameras and other optical devices are actually compound lenses made of several lenses put together to minimize aberrations. Suppose a converging lens with a focal length of 4.00 cm is placed right next to a diverging lens with focal l
> An automobile is traveling along a straight road to the southeast at 24 m/s when the driver sees a deer begin to cross the road ahead of her. She steps on the brake and brings the car to a complete stop in an elapsed time of 8.0 s. A data recording devic
> A police officer is investigating the scene of an accident where two cars collided at an intersection. One car with a mass of 1100 kg moving west had collided with a 1300 kg car moving north. The two cars, stuck together, skid at an angle of 30° north of
> (a) Sunlight reflected from the smooth ice surface of a frozen lake is totally polarized when the incident light is at what angle with respect to the horizontal? (b) In what direction is the reflected light polarized? (c) What is the direction of the m
> A diamond in air is illuminated with white light. On one particular facet, the angle of incidence is 26.00°. Inside the diamond, red light (λ = 660.0 nm in vacuum) is refracted at 10.48° with respect to the normal; blue light (λ = 470.0 nm in vacuum) is
> A cannonball is catapulted toward a castle. The cannonball's velocity when it leaves the catapult is 40 m/s at an angle of 37° with respect to the horizontal, and the cannonball is 7.0 m above the ground at this time. (a) What is the maximum height abov
> Show that the deviation angle δ for a ray striking a thin converging lens at a distance d from the principal axis is given by δ = d/f. Therefore, a ray is bent through an angle δ that is proportional to d and does n
> A circus performer is shot out of a cannon and flies over a vertical net that is placed at a horizontal distance of 6.0 m from the cannon. When the cannon is aimed at an angle of 40° above the horizontal, the performer is moving in the horizontal directi
> A ray of light passes from air through dense flint glass and then back into air. The angle of incidence on the first glass surface is 60.0°. The thickness of the glass is 5.00 mm; its front and back surfaces are parallel. How far is the ray displaced as
> How much energy is released in the fusion reaction 2H + 3H - 4He + n?
> A ray of light in air is incident on benzene contained in a shallow tank made of crown glass, making an angle of 60.0° with the surface. What is the angle of refraction of the light ray (measured from the normal) when it enters the glass at th
> What is the total energy released by the proton-proton cycle [Eq. (29- 54)]?
> A roller coaster has a vertical loop with radius 29.5 m. With what minimum speed should the roller coaster car be moving at the top of the loop so that the passengers do not lose contact with the seats?
> (a) A particle is made up of the quarks sū. Is this a meson or a baryon? What is the charge of this particle? (b) A particle is made up of the quarks udc. Is this a meson or a baryon? What is the charge of this particle? (c) The particle in (b) can decay
> Draw a ray diagram and locate the image for the object shown in the figure.
> One possible fission reaction for 235U is 235U + n → 141Cs + 93Rb + ?n, where “?n” represents one or more neutrons. (a) How many neutrons? (b) From the graph in Fig. 29.2, you can read the approximate binding energies per nucleon for the three nuclides
> A glass block (n = 1.7) is submerged in an unknown liquid. A ray of light inside the block undergoes total internal reflection. What can you conclude concerning the index of refraction of the liquid?
> Calculate the energy released in the fission reaction of Eq. (29-47).
> A beam of light consisting of a mixture of red, yellow, and blue light originates from a source submerged in some carbon disulfide. The light beam strikes an interface between the carbon disulfide and air at an angle of incidence of 37.5° as s
> Estimate the energy released in the fission reaction of Eq. (29-48) from the values of the binding energy per nucleon in Fig. 29.2.
> A ray of light is reflected from two mirrored surfaces as shown in the figure. If the initial angle of incidence is 34°, what are the values of angles α and β? (The figure is not to scale.)
> A 235U nucleus captures a low-energy neutron to form the compound nucleus 236U*. Find the excitation energy of the compound nucleus. Ignore the small initial kinetic energy of the captured neutron.
> The focal length of a thin lens is −20.0 cm. A screen is placed 160 cm from the lens. What is the y-coordinate of the point where the light ray shown hits the screen? The incident ray is parallel to the central axis and is 1.0 cm from t
> An effective treatment for cancer takes advantage of the fact that boron readily captures slow neutrons. In the body, boron is much more likely to capture a neutron than are carbon, oxygen, or hydrogen. Because of the chemical similarity of boron and car
> A man with a mass of 65 kg skis down a frictionless hill that is 5.0 m high. At the bottom of the hill the terrain levels out. As the man reaches the horizontal section, he grabs a 20 kg backpack and skis off a 2.0 m high ledge. At what horizontal distan
> A letter on a page of the compact edition of the Oxford English Dictionary is 0.60 mm tall. A magnifying glass (a single thin lens) held 4.5 cm above the page forms an image of the letter that is 2.4 cm tall. (a) Is the image real or virtual? (b) Where
> The reactions listed in Problem 53 did not stop there. To the surprise of the Curies, the phosphorus decay continued after the alpha bombardment ended with the phosphorus/ emitting a β+ to form yet another product. Write out this reaction, identifying
> An object of height 5.00 cm is placed 20.0 cm from a converging lens of focal length 15.0 cm. Draw a ray diagram to find the height and position of the image.
> Irène and Jean Frédéric Joliot-Curie, in an experiment that led to the 1935 Nobel Prize in chemistry, bombarded aluminum / with alpha particles to form a highly unstable isotope of phosphorus, / . The phosphoru
> A 3.00 cm high pin, when placed at a certain distance in front of a concave mirror, produces an upright image 9.00 cm high, 30.0 cm from the mirror. Find the position of the pin relative to the mirror and the image. Draw a ray diagram to illustrate.
> A certain nuclide absorbs a neutron. It then emits an electron, and then breaks up into two alpha particles. (a) Identify the original nuclide and the two intermediate nuclides (after absorbing the neutron and after emitting the electron). (b) Would an
> A scuba diver in a lake aims her underwater spotlight at the lake surface. (a) If the beam makes a 75° angle of incidence with respect to a normal to the water surface, is it reflected, transmitted, or both? Find the angles of the reflected and transmitt
> A neutron-activated sample emits gamma rays at energies that are consistent with the decay of mercury-198 nuclei from an excited state to the ground state. If the reaction that takes place is , what is the nuclide “(?)”
> A laser beam is traveling through an unknown substance. When it encounters a boundary with air, the angle of reflection is 25.0° and the angle of refraction is 37.0°. (a) What is the index of refraction of the substance? (b) What is the speed of light
> Make an order-of-magnitude estimate of the amount of radon- 222 gas, measured in curies, found in the lungs of an average person. Assume an average exposure of 1 mSv/yr due to the alpha particles emitted by radon-222. The half-life is 3.8 days. You will
> While on an elevator, Jaden's apparent weight is 550 N. When he was on the ground, the scale reading was 600 N. What is Jaden's acceleration?
> In many cars the passenger's side mirror says: “Objects in the mirror are closer than they appear.” (a) Does this mirror form real or virtual images? (b) Since the image is diminished in size, is the mirror concave or convex? Why? (c) Show that the im
> The greatest concentration of iodine in the body is in the thyroid gland, so radioactive iodine-131 is often used as a tracer to help diagnose thyroid problems. Suppose the activity of 131I in a patient’s thyroid is initially 1.85 × 106 Bq. 131I decays v
> Samantha puts her face 32.0 cm from a makeup mirror and notices that her image is magnified by 1.80 times. (a) What kind of mirror is this? (b) Where is her face relative to the radius of curvature or focal length? (c) What is the radius of curvature
> Some types of cancer can be effectively treated by bombarding the cancer cells with high energy protons. Suppose 1.16 × 1017 protons, each with an energy of 950 keV, are incident on a tumor of mass 3.82 mg. If the RBE for these protons is 3.0, what is th
> A 5.0 cm tall object is placed 50.0 cm from a lens with focal length −20.0 cm. (a) How tall is the image? (b) Is the image upright or inverted?
> If meat is irradiated with 2000.0 Gy of x-rays, most of the bacteria are killed and the shelf life of the meat is greatly increased. (a) How many 100.0 keV photons must be absorbed by a 0.30 kg steak so that the absorbed dose is 2000.0 Gy? (b) Assuming
> A concave mirror has a radius of curvature of 14 cm. If a pointlike object is placed 9.0 cm away from the mirror on its principal axis, where is the image?
> A 65 kg patient undergoes a diagnostic chest x-ray and receives a biologically equivalent dose of 0.2 mSv distributed over 33% of the patient’s body mass. If the x-rays have a relative biological effectiveness of 0.90, how much energy is absorbed by the
> An object is placed 10.0 cm in front of a lens. An upright, virtual image is formed 30.0 cm away from the lens. What is the focal length of the lens? Is the lens converging or diverging?
> An alpha particle produced in radioactive decay has a kinetic energy of typically about 6 MeV. When an alpha particle passes through matter (e.g., biological tissue), it makes ionizing collisions with molecules, giving up some of its kinetic energy to su
> A 115 g ball is traveling to the left with a speed of 30 m/s when it is struck by a racket. The force on the ball, directed to the right and applied over 21 ms of contact time, is shown in the graph. What is the speed of the ball immediately after it lea
> An object 8.0 cm high forms a virtual image 3.5 cm high located 4.0 cm behind a mirror. (a) Find the object distance. (b) Describe the mirror: is it plane, convex, or concave? (c) What are its focal length and radius of curvature?
> A sample of potassium-40 has an activity of 9.0 mCi. What is its mass?
> A point source of light is placed 10 cm in front of a concave mirror; the reflected rays are parallel. What is the radius of curvature of the mirror?
> A radioactive sample has equal numbers of 15O and 19O nuclei. Use the half-lives found in Appendix B.8 to determine how long it will take before there are twice as many 15O nuclei as 19O. What percent of the 19O nuclei have decayed during this time?
> You are standing 1.2 m from a heat lamp that draws an rms current of 12.5 A when connected to 120 V rms. (a) Assuming that the energy of the heat lamp is radiated uniformly in a hemispherical pattern, what is the intensity of the light on your face? (b
> To perform a bone scan, 3.8 × 106 Bq of 85Sr is injected into a patient. The half-life of 85Sr is 30.1 yr, and its mass is 84.9 u. What mass of 85Sr is injected into the patient?
> Using Faraday’s law, show that if a magnetic dipole antenna’s axis makes an angle θ with the magnetic field of an EM wave, the induced emf in the antenna is reduced from its maximum possible value by a factor of cos θ. [Hint: Assume that, at any instant,
> In this problem, you will verify the statement (in Section 29.4) that the 14C activity in a living sample is 0.25 Bq per gram of carbon. (a) What is the decay constant λ for 14C? (b) How many 14C atoms are in 1.00 g of carbon? One mole of carbon atoms h
