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 bike at the bottom. (b) Would the speed at the bottom be the same for a less massive rider? Explain.
> (a) Redo Example 8.7 to find an algebraic solution for d in terms of M, m, μs, L, and θ. (b) Use this expression to show that placing the ladder at a larger angle θ (that is, more nearly vertical) enables the person to climb farther up the ladder withou
> Four identical uniform metersticks are stacked on a table as shown. Where is the x-coordinate of the CM of the metersticks if the origin is chosen at the left end of the lowest stick? Why does the system balance?
> An underwater air bubble has an excess inside pressure of 10 Pa. What is the excess pressure inside an air bubble with twice the radius?
> A student stands on a platform that is free to rotate and holds two dumbbells, each at a distance of 65 cm from his central axis. Another student gives him a push and starts the system of student, dumbbells, and platform rotating at 0.50 rev/s. The stude
> An aluminum sphere (specific gravity = 2.7) falling through water reaches a terminal speed of 5.0 cm/s. What is the terminal speed of an air bubble of the same radius rising through water? Assume viscous drag in both cases and ignore the possibility of c
> When salmon head upstream to spawn, they may encounter a waterfall. If the water is not moving too fast, the salmon can swim right up through the falling water. Otherwise, the salmon jump out of the water to get to a place in the waterfall where the wate
> The graph shows vx versus t for an object moving along the x-axis. (a) What is ax at t = 11 s? (b) What is ax at t = 3 s? (c) Sketch a graph of ax(t). (d) How far does the object travel from t = 12 s to t = 14 s?
> A circus roustabout is attaching the circus tent to the top of the main support post of length L when the post suddenly breaks at the base. The worker's weight is negligible relative to that of the uniform post. What is the speed with which the roustabou
> A flea is on the back of a squirrel climbing a tall tree. When the squirrel is near the top, the flea jumps off. (a) Assuming the drag force is viscous, estimate the terminal speed of the flea. Treat the flea as a drop of water of radius 1.0 mm falling
> A bicycle travels up an incline at constant velocity. The magnitude of the frictional force due to the road on the rear wheel is f = 3.8 N. The upper section of chain pulls on the sprocket wheel, which is attached to the rear wheel, with a force / . Th
> What keeps a cloud from falling? A cumulus (fair-weather) cloud consists of tiny water droplets of average radius 5.0 μm. Find the terminal velocity for these droplets at 20°C, assuming viscous drag. (Besides the viscous drag force, there are also upward
> A spool of thread of mass m rests on a plane inclined at angle θ. The end of the thread is tied as shown. The outer radius of the spool is R, and the inner radius (where the thread is wound) is r. The rotational inertia of the spool is I. Gi
> A house painter is standing on a uniform, horizontal platform that is held in equilibrium by two cables attached to supports on the roof. The painter has a mass of 75 kg, and the mass of the platform is 20.0 kg. The distance from the left end of the plat
> An air bubble of 1.0 mm radius is rising in a container of vegetable oil with specific gravity 0.85 and viscosity 0.12 Pa·s. The container of oil and the air bubble are at 20°C. What is its terminal velocity?
> A 68 kg woman stands straight with both feet flat on the floor. Her center of gravity is a horizontal distance of 3.0 cm in front of a line that connects her two ankle joints. The Achilles tendon attaches the calf muscle to the foot a distance of 4.4 cm
> A sphere of radius 1.0 cm is dropped into a glass cylinder filled with a viscous liquid. The mass of the sphere is 12.0 g, and the density of the liquid is 1200 kg/m3. The sphere reaches a terminal speed of 0.15 m/s. What is the viscosity of the liquid?
> A merry-go-round (radius R, rotational inertia Ii) spins with negligible friction. Its initial angular velocity is ωi. A child (mass m) on the merry-go-round moves from the center out to the rim. (a) Calculate the angular velocity after the child moves
> You want to make a plot of the trajectory of a projectile. That is, you want to make a plot of the height y of the projectile as a function of horizontal distance x. The projectile is launched from the origin with initial velocity components vix and viy.
> Two identical spheres are dropped into two different columns: one column contains a liquid of viscosity 0.5 Pa·s; the other contains a liquid of the same density but unknown viscosity. The sedimentation velocity in the second tube is 20% higher than the
> What force(s) act on a parachutist descending to Earth with a constant velocity? What is the acceleration of the parachutist?
> A planet moves around the Sun in an elliptical orbit (see Fig. 8.40). (a) Show that the external torque acting on the planet about an axis through the Sun is zero. (b) Since the torque is zero, the planet's angular momentum about this axis is constant.
> Five spheres are falling through the same viscous fluid, not necessarily at their terminal speeds. The radii r and speeds v of the spheres are given. Rank the spheres in order of decreasing viscous drag force on them. (a) r = 1.0 mm, v = 15 mm/s (b) r =
> A large clock has a second hand with a mass of 0.10 kg concentrated at the tip of the pointer. (a) If the length of the second hand is 30.0 cm, what is its angular momentum? (b) The same clock has an hour hand with a mass of 0.20 kg concentrated at the
> A sculpture is 4.00 m tall and has its center of gravity located 1.80 m above the center of its base. The base is a square with a side of 1.10 m. To what angle θ can the sculpture be tipped before it falls over?
> Blood plasma (at 37°C) is to be supplied to a patient at the rate of 2.8 × 10−6 m3/s. If the tube connecting the plasma to the patient’s vein has a radius of 2.0 mm and a length of 50 cm, what is the pressure difference between the plasma and the patient
> A hoop of 2.00 m circumference is rolling down an inclined plane of length 10.0 m in a time of 10.0 s. It started out from rest. (a) What is its angular velocity when it arrives at the bottom? (b) If the mass of the hoop, concentrated at the rim, is 1.
> (a) Since the flow rate is proportional to the pressure difference, show that Poiseuille’s law can be written in the form ΔP = IR, where I is the volume flow rate and R is a constant of proportionality called the fluid flow resistance. (Written this way,
> A 2.0 kg uniform flat disk is thrown into the air with a linear speed of 10.0 m/s. As it travels, the disk spins at 3.0 rev/s. If the radius of the disk is 10.0 cm, what is the magnitude of its angular momentum?
> (a) What is the pressure difference required to make blood flow through an artery of inner radius 2.0 mm and length 0.20 m at an average speed of 6.0 cm/s? (b) What is the pressure difference required to make blood flow at an average speed of 0.60 mm/s
> Locusts can jump to heights of 0.30 m. (a) Assuming the locust jumps straight up, and ignoring air resistance, what is the takeoff speed of the locust? (b) The locust actually jumps at an angle of about 55° to the horizontal, and air resistance is not
> A crustacean (Hemisquilla ensigera) rotates its anterior limb to strike a mollusk, intending to break it open. The limb reaches an angular velocity of 175 rad/s in 1.50 ms. We can approximate the limb as a thin rod rotating about an axis perpendicular to
> A capillary carries blood in the direction shown. Viscosity is not negligible. Points C and D are on the central axis of the capillary. Rank the points in order of decreasing fluid speed.
> Sketch the acceleration of the elevator in Problem 28 as a function of time. If the elevator is supported by a single cable, what are the maximum and minimum tensions in the cable, expressed in terms of the elevator’s weight W?
> 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
> 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
> 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. Ma
> 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
