If diffraction were the only limitation, what would be the maximum distance at which the headlights of a car could be resolved (seen as two separate sources) by the naked human eye? The diameter of the pupil of the eye is about 7 mm when dark-adapted. Make reasonable estimates for the distance between the headlights and for the wavelength.
> Nina wants to lean a ladder of mass 15 kg and length 8.0 m against a wall. She lifts one end over her head. Then she “walks” her hands from rung to rung toward the other end, which rests on the ground. (a) When she is holding the ladder 2.0 m from the e
> A charge Q = −50.0 nC is located 0.30 m from point A and 0.50 m from point B. (a) What is the potential at A? (b) What is the potential at B? (c) If a point charge q is moved from A to B while Q is fixed in place, through what potent
> If the total volume flow rates in systems A and B are the same, at what pressure does the pump supply water in system A?
> A box of mass 42 kg sits on top of a ladder. Ignoring the weight of the ladder, find the tension in the rope. Assume that the rope exerts horizontal forces on the ladder at each end. [Hint: Use a symmetry argument; then analyze the forces and torques on
> If the total volume flow rate in system B is 0.020 m3/s, what is the total volume flow rate in system C?
> The operation of the Princeton Tokomak Fusion Test Reactor requires large bursts of energy. The power needed exceeds the amount that can be supplied by the utility company. Prior to pulsing the reactor, energy is stored in a giant flywheel of mass 7.27 &
> If the total volume flow rates in systems A and C are the same and the average flow speed in each of the pipes in C is 3.0 m/s, what is the average flow speed in system A?
> A flat object in the xy-plane is free to rotate about the z-axis. The gravitational field is uniform in the −y-direction. Think of the object as a large number of particles with masses mn located at coordinates (xn, yn), as in the figur
> The minimum stopping distance of a car moving at 30.0 mi/h is 12 m. Under the same conditions (so that the maximum braking force is the same), what is the minimum stopping distance for 60.0 mi/h? Work by proportions to avoid converting units.
> A bug from South America known as Rhodnius prolixus extracts the blood of animals. Suppose Rhodnius prolixus extracts 0.30 cm3 of blood in 25 min from a human arm through its feeding tube of length 0.20 mm and radius 5.0 μm. What is the absolute pressure
> An experimental flywheel, used to store energy and replace an automobile engine, is a solid disk of mass 200.0 kg and radius 0.40 m. (a) What is its rotational inertia? (b) When driving at 22.4 m/s (50 mi/h), the fully energized flywheel is rotating at
> A hypodermic syringe is attached to a needle that has an internal radius of 0.300 mm and a length of 3.00 cm. The needle is filled with a solution of viscosity 2.00 × 10−3 Pa·s; it is injected into a vein at a gauge pressure of 16.0 mmHg. Ignore the extr
> A Ferris wheel rotates because a motor exerts a torque on the wheel. The radius of the London Eye, a huge observation wheel on the banks of the Thames, is 67.5 m and its mass is 1.90 × 106 kg. The cruising angular speed of the wheel is 3.50 × 10−3 rad/s.
> What does it mean when we refer to a cord as an “ideal cord” and a pulley as an “ideal pulley”?
> A painter (mass 61 kg) is walking along a trestle, consisting of a uniform plank (mass 20.0 kg, length 6.00 m) balanced on two sawhorses. Each sawhorse is placed 1.40 m from an end of the plank. A paint bucket (mass 4.0 kg, diameter 0.28 m) is placed as
> A viscous liquid is flowing steadily through a pipe of diameter D. Suppose you replace it by two parallel pipes, each of diameter D/2, but the same length as the original pipe. If the pressure difference between the ends of these two pipes is the same as
> A person on a bicycle (combined total mass 80.0 kg) starts from rest and coasts down a hill to the bottom 20.0 m below. Each wheel can be treated as a hoop with mass 1.5 kg and radius 40 cm. Ignore friction and air resistance. (a) Find the speed of the
> Using Poiseuille’s law [Eq. (9-41)], show that viscosity has SI units of pascal-seconds.
> A uniform solid cylinder rolls without slipping or sliding down an incline. The angle of inclination is 60.0°. Use energy considerations to find the cylinder's speed after it has traveled a distance of 30.0 cm along the incline.
> The volume flow rate of the water supplied by a well is 2.0 × 10−4 m3/s. The well is 40.0 m deep. (a) What is the power output of the pump—in other words, at what rate does the well do work on the water? (b) Find the pressure difference the pump must m
> Spider silk has a Young’s modulus of 4.0 GPa and can withstand stresses up to 1.4 GPa. A single web strand has a cross- sectional area of 1.0 × 10−11 m2, and a web is made up of 50 radial strands. A bug la
> In a motor, a flywheel (solid disk of radius R and mass M) is rotating with angular velocity ωi. When the clutch is released, a second disk (radius r and mass m) initially not rotating is brought into frictional contact with the flywheel. The two disks s
> A water tower supplies water through the plumbing in a house. A 2.54 cm diameter faucet in the house can fill a cylindrical container with a diameter of 44 cm and a height of 52 cm in 12 s. How high above the faucet is the top of the water in the tower?
> In gamma-ray astronomy, the existence of positrons (e+) can be inferred by characteristic gamma-ray photons that are emitted when a positron and an electron (e−) annihilate. For simplicity, assume that the electron and positron are at rest with respect t
> A 5.60 kg uniform door is 0.760 m wide by 2.030 m high, and is hung by two hinges, one at 0.280 m from the top and one at 0.280 m from the bottom of the door. If the vertical components of the forces on each of the two hinges are identical, find the vert
> Suppose air, with a density of 1.29 kg/m3, is flowing into a Venturi meter. The narrow section of the pipe at point A has a diameter that is / of the diameter of the larger section of the pipe at point B. The U-shaped tube is filled with water and the d
> The graph with Problem 24 shows vx(t) for a skateboard moving along the x-axis. Rank the times t = 0.5 s, 1.5 s, 2.5 s, 3.5 s, 4.5 s, and 5.5 s, in order of the magnitude of the acceleration, from largest to smallest.
> What is the quark content of an antiproton? [Hint: Replace each of the three quarks that compose a proton with its corresponding antiquark.]
> A rotating star collapses under the influence of gravitational forces to form a pulsar. The radius of the pulsar is 1.0 × 10−4 times the radius of the star before collapse. There is no change in mass. In both cases, the mass of the star is uniformly dist
> A nozzle is connected to a horizontal hose. The nozzle shoots out water moving at 25 m/s. What is the gauge pressure of the water in the hose? Ignore viscosity and assume that the diameter of the nozzle is much smaller than the inner diameter of the hose
> A 0.185 kg spherical steel ball is used in a pinball machine. The ramp is 1.35 m long and tilted at an angle of 5.00°. Just after a flipper hits the ball at the bottom of the ramp, the ball has an initial speed of 2.20 m/s. What is the speed of the ball
> An airplane flies on a level path. There is a pressure difference of 500 Pa between the lower and upper surfaces of the wings. The area of each wing surface is about 100 m2. The air moves below the wings at a speed of 80.5 m/s. Estimate (a) the weight o
> A beanbag is thrown horizontally from a dorm room window a height h above the ground. It hits the ground a horizontal distance h (the same distance h) from the dorm wall directly below the window from which it was thrown. Ignoring air resistance, find th
> A grating in a spectrometer is illuminated with red light (λ = 690 nm) and blue light (λ = 460 nm) simultaneously. The grating has 10 000.0 slits/cm. Sketch the pattern that would be seen on a screen 2.0 m from the grating. Label distances from the centr
> A flywheel of mass 182 kg has an effective radius of 0.62 m (assume the mass is concentrated along a circumference located at the effective radius of the flywheel). (a) How much work is done to bring this wheel from rest to an angular speed of 120 rev/m
> A lawyer is on his way to court carrying his briefcase. The mass of the briefcase is 5.00 kg. The lawyer realizes that he is going to be late. Starting from rest, he starts to run, reaching a speed of 2.50 m/s. What is the work done by the lawyer on the
> Instead of an antireflective coating, suppose you wanted to coat a glass surface to enhance the reflection of visible light. Assuming that 1 < ncoating < nglass, what should the minimum thickness of the coating be to maximize the reflected intensity for
> A “blink of an eye” is a time interval of about 150 ms for an average adult. The “closure” portion of the blink takes only about 55 ms. Let us model the closure of the upper eyelid as uniform angular acceleration through an angular displacement of 15°.
> (a) What would be the maximum intensity of the light falling on the screen if only one slit were open? (b) Find the wavelength of the light.
> A disk rotates with constant angular acceleration. The initial angular speed of the disk is 2.0π rad/s. After the disk rotates through 10.0π radians, the angular speed is 7.0π rad/s. (a) What is the magnitude of the angular acceleration? (b) How much t
> The Very Large Array (VLA) is a set of 30 dish radio antennas located near Socorro, New Mexico. The dishes are spaced 1.0 km apart and form a Y-shaped pattern, as in the diagram. Radio pulses from a distant pulsar (a rapidly rotating neutron star) are de
> A car that is initially at rest moves along a circular path with a constant tangential acceleration component of 2.00 m/s2. The circular path has a radius of 50.0 m. The initial position of the car is at the far west location on the circle and the initia
> A thin layer of an oil (n = 1.60) floats on top of water (n = 1.33). One portion of this film appears green (λ = 510 nm) in reflected light. How thick is this portion of the film? Give the three smallest possibilities.
> A wheel’s angular acceleration is constant. Initially its angular velocity is zero. During the first 1.0 s time interval, it rotates through an angle of 90.0°. (a) Through what angle does it rotate during the next 1.0 s time interval? (b) Through what
> Light with a wavelength of 660 nm is incident on two slits and the pattern shown in the figure is viewed on a screen. Point A is directly opposite a point midway between the two slits. What is the path length difference of the light that passes through t
> A clothes washer reaches an angular speed of 1400 rev/min in 2.0 s, starting from rest, during the spin cycle. (a) Assuming the angular acceleration is constant, what is its magnitude? (b) How many revolutions does the washer make during this time inte
> The maximum height of a cylindrical column is limited by the compressive strength of the material; if the compressive stress at the bottom were to exceed the compressive strength of the material, the column would be crushed under its own weight. (a) For
> In bright light, the pupils of the eyes of a cat narrow to a vertical slit 0.30 mm across. Suppose that a cat is looking at two mice 18 m away. What is the smallest distance between the mice for which the cat can tell that there are two mice rather than
> A hamster of mass 0.100 kg gets into its exercise wheel and starts to run at t = 0. After t = 0.800 s, the wheel turns with a constant rotational frequency of 1.00 Hz. What is the tangential acceleration of the inner surface of the wheel between t = 0 an
> A child pushes a merry-go-round from rest to a final angular speed of 0.50 rev/s with constant angular acceleration. In doing so, the child pushes the merry-go-round 2.0 revolutions. What is the angular acceleration of the merry-go-round?
> A beam of coherent light of wavelength 623 nm in air is incident on a rectangular block of glass with index of refraction 1.40. If, after emerging from the block, the wave that travels through the glass is 180° out of phase with the wave that
> A car approaches the top of a hill that is shaped like a vertical circle with a radius of 55.0 m. What is the fastest speed that the car can go over the hill without losing contact with the ground?
> (a) What is the angular size of the Moon as viewed from Earth's surface? See Appendix B for necessary information. (b) Elysha is gazing at a full Moon at night. The diameter of her pupil is 7.0 mm and the diameter of her eye is 2.0 cm. What is the diame
> 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
