A plastic beach ball has radius 20.0 cm and mass 0.10 kg, not including the air inside. (a) What is the weight of the beach ball including the air inside? Assume the air density is 1.3 kg/m3 both inside and outside. (b) What is the buoyant force on the beach ball in air? The thickness of the plastic is about 2 mm—negligible compared with the radius of the ball. (c) The ball is thrown straight up in the air. At the top of its trajectory, what is its acceleration? [Hint: When v = 0, there is no drag force.]
> A 85.0 kg canoe made of thin aluminum has the shape of half of a hollowed-out log with a radius of 0.475 m and a length of 3.23 m. (a) When this is placed in the water, what percentage of the volume of the canoe is below the waterline? (b) How much add
> A cello string has a fundamental frequency of 65.40 Hz. What beat frequency is heard when this cello string is bowed at the same time as a violin string with frequency of 196.0 Hz? [Hint: The beats occur between the third harmonic of the cello string and
> (a) If a freestyle swimmer travels 1.50 km in a time of 14 min 53 s, how fast is his average speed? (b) If the pool is rectangular and 50 m in length, how does the speed you found compare with his sustained swimming speed of 1.54 m/s during one length o
> A block of aluminum that has dimensions 2.00 cm by 3.00 cm by 5.00 cm is suspended by a thread from a spring scale. (a) What is the scale reading in grams? (b) A beaker full of oil (density 850 kg/m3) rests on a second scale, which reads 460.0 g. The b
> A musician plays a string on a guitar that has a fundamental frequency of 330.0 Hz. The string is 65.5 cm long and has a mass of 0.300 g. (a) At what speed do the waves travel on the string? (b) What is the tension in the string? (c) While the guitar
> A bridal party is at a rehearsal dinner. The best man challenges the bridegroom to pick up an olive using only a brandy snifter. How does the groom accomplish this task?
> A section of pipe with an internal diameter of 10.0 cm tapers to an inner diameter of 6.00 cm as it rises through a height of 1.70 m at an angle of 60.0° with respect to the horizontal. The pipe carries water and its higher end is open to air. (a) If th
> An auditorium has organ pipes at the front and at the rear of the hall. Two identical pipes, one at the front and one at the back, have fundamental frequencies of 264.0 Hz at 20.0°C. During a performance, the organ pipes at the back of the hall are at 25
> A beach ball is thrown straight up in the air. The graph shows its vertical velocity component as a function of time. The dashed line is tangent to the curve at the point where vy = 0. (a) What shape would the vy(t) graph have if air drag on the beach b
> Calculate the rotational inertia for each of the three arrangements.
> A piano tuner sounds two strings simultaneously. One has been previously tuned to vibrate at 293.0 Hz. The tuner hears 3.0 beats per second. The tuner increases the tension on the as-yet untuned string, and now when they are played together the beat freq
> A cube that is 4.00 cm on a side and of density 8.00 × 102 kg/m3 is attached to one end of a spring. The other end of the spring is attached to the base of a beaker. When the beaker is filled with water until the entire cube is submerged, the spring is s
> (a) What is the energy of a pendulum (L = 1.0 m, m = 0.50 kg) oscillating with an amplitude of 5.0 cm? (b) The pendulum’s energy loss (due to damping) is replaced in a clock by allowing a 2.0 kg mass to drop 1.0 m in 1 week. What average percentage of t
> The potential energy associated with surface tension is much like the elastic potential energy of a stretched spring or a balloon. Suppose we do work on a puddle of liquid, spreading it out through a distance of As along a line L perpendicular to the for
> In a playground, two slides have different angles of incline θ1 and θ2 (θ2 > θ1) A child slides down the first at constant speed; on the second, his acceleration down the slide is a. Assume the coefficient of kinetic friction is the same for both slides.
> A pendulum of length 120 cm swings with an amplitude of 2.0 cm. Its mechanical energy is 5.0 mJ. What is the mechanical energy of the same pendulum when it swings with an amplitude of 3.0 cm?
> A dinoflagellate takes 5.0 s to travel 1.0 mm. Approximate a dinoflagellate as a sphere of radius 35.0 μm (ignoring the flagellum). (a) What is the drag force on the dinoflagellate in seawater of viscosity 0.0010 Pa·s? (b) What is the power output of th
> Christy has a grandfather clock with a pendulum that is 1.000 m long. (a) If the pendulum is modeled as a simple pendulum, what would be the period? (b) Christy observes the actual period of the clock, and finds that it is 1.00% faster than that for a
> Sketch a graph of ax(t) for the car in Problem 43.
> Show that the charge of the neutron and the charge of the proton are consistent with their constituent quark content.
> An owl has good night vision because its eyes can detect a light intensity as faint as 5.0 × 10−13 W/m2. What is the minimum number of photons per second that an owl eye can detect if its pupil has a diameter of 8.5 mm and the light has a wavelength of 5
> Depressing the brake pedal in a car pushes on a piston with cross- sectional area 3.0 cm2. The piston applies pressure to the brake fluid, which is connected to two pistons, each with area 12.0 cm2. Each of these pistons presses a brake pad against one s
> The pendulum for a grandfather clock consists of a thin rigid rod (of negligible mass) with two metal disks attached to it. One disk has mass 0.600 kg and is attached to the rod 0.800 m from the pivot; the other has mass 0.750 kg and is attached 1.20 m f
> A hydraulic lift is lifting a car that weighs 12 kN. The area of the piston supporting the car is A, the area of the other piston is a, and the ratio A/a is 100.0. How far must the small piston be pushed down to raise the car a distance of 1.0 cm? [Hint:
> Max’s arm weighs 34 N and is 63 cm long. If Max lets his relaxed arm swing back and forth like a pendulum, what is the period? Model the arm as a uniform rod.
> The pressure inside a bottle of champagne is 4.5 atm higher than the air pressure outside. The neck of the bottle has an inner radius of 1.0 cm. (a) What is the frictional force on the cork due to the neck of the bottle? (b) The cork (mass 7.5 g) is lo
> Marie slides a paper plate with a slice of pizza across a horizontal table to her friend Jaden. The coefficient of friction between the table and plate is 0.32. If the pizza must travel 44 cm to get from Marie to Jaden, what initial speed should Marie gi
> A grandfather clock is constructed so that it has a simple pendulum that swings from one side to the other, a distance of 20.0 mm, in 1.00 s. What is the maximum speed of the pendulum bob? Use two different methods. First, assume SHM and use the relation
> Water enters an apartment building 0.90 m below the street level with a gauge pressure of 52.0 kPa through the main pipe, which has a 5.00 cm radius. A second-story bathroom has an open faucet with a 1.20 cm radius that is located 4.20 m above the street
> A pendulum clock has a period of 0.650 s on Earth. It is taken to another planet and found to have a period of 0.862 s. The change in the pendulum’s length is negligible. (a) Is the gravitational field strength on the other planet greater than or less t
> Atmospheric pressure is equal to the weight of a vertical column of air, extending all the way up through the atmosphere, divided by the cross-sectional area of the column. (a) Explain why that must be true. [Hint: Apply Newton’s second law to the colum
> If the skier of Example 6.6 is moving at 12 m/s at the bottom of the trail, calculate the total work done by friction and air resistance during the run. The skier’s mass is 75 kg.
> A pendulum (mass m) moves according to x = A sin ωt. (a) Write the equation for vx(t) and sketch one cycle of the vx(t) graph. (b) What is the maximum kinetic energy?
> A physics teacher draws a cutaway view of a car rounding a banked curve as a rectangle atop a right triangle. A student draws a coordinate system on the drawing. Is there another choice of axes that would make the problem easier to solve?
> A U-shaped tube is partly filled with water and partly filled with a liquid that does not mix with water. Both sides of the tube are open to the atmosphere. What is the density of the liquid (in g/cm3)?
> Each of five pendulums has a bob of mass m suspended from a string of length L. Rank them in order of their frequency for small- amplitude oscillations, greatest to smallest. (a) m = 300 g, L = 1.10 m (b) m = 330 g, L = 1.10 m (c) m = 330 g, L = 1.00 m
> To measure the airspeed of a plane, a device called a Pitot tube is used. A simplified model of the Pitot tube is a manometer with one side connected to a tube facing directly into the “wind” (stopping the air that hit
> A pendulum of length 75 cm and mass 2.5 kg swings with a mechanical energy of 0.015 J. What is the amplitude?
> A pellet is fired from a toy cannon with a velocity of 12 m/s directed 60° above the horizontal. After 0.10 s, a second pellet is fired with the same initial velocity. After an additional 0.15 s have passed, what is the velocity of the first pellet with
> Refer to Problems 11–14. Find the final speed of the sliding crate if the frictional force on the sliding crate has magnitude 19.4 N.
> On a nice day when the temperature outside is 20°C, you take the elevator to the top of the Willis Tower in Chicago, which is 440 m tall. (a) How much less is the air pressure at the top than the air pressure at the bottom? Express your answer both in P
> Are evenly spaced specific-gravity markings on the cylinder of a hydrometer equal distances apart? In other words, is the depth d to which the cylinder is submerged linearly related to the density ρ of the fluid? To answer this question, assume that the
> Rank the three arrangements in increasing order of the rotational inertia.
> What is the period of a pendulum consisting of a 6.0 kg mass hanging from a 4.0 m long string?
> Suppose the hydrometer has a cylindrical stem of cross-sectional area 0.400 cm2. The total volume of the bulb and stem is 8.80 cm3, and the mass of the hydrometer is 4.80 g. (a) How far from the top of the cylinder should a mark be placed to indicate a
> A 230.0 g object on a spring oscillates on a frictionless horizontal surface with frequency 2.00 Hz and amplitude 8.00 cm. Its position as a function of time is given by x = A sin ωt. (a) Sketch a graph of the elastic potential energy as a function of t
> A block of wood, with density 780 kg/m3, has a cubic shape with sides 0.330 m long. A cord of negligible mass is used to tie a piece of lead to the bottom of the wood. The lead pulls the wood into the water until it is just completely covered with water.
> A ball is dropped from a height h onto the floor and keeps bouncing. No energy is dissipated, so the ball regains the original height h after each bounce. Sketch the graph for y(t) and list several features of the graph that indicate that this motion is
> The figure shows a plot of vx(t) for a car traveling in a straight line. (a) What is aav,x between t = 6 s and t = 11 s? (b) What is vav,x for the same time interval? (c) What is vav,x for the interval t = 0 to t = 20 s? (d) What is the increase in the
> An object is attached to an ideal spring of spring constant 2.5 N/m. The spring is initially in its relaxed position. The object is then released and oscillates about its equilibrium position. The motion is described by What is the maximum kinetic energy
> A stone of weight W has specific gravity 2.50. (a) When the stone is suspended from a scale and submerged in water, what is the scale reading in terms of its weight in air? (b) What is the scale reading for the stone when it is submerged in oil (specif
> A gull is flying horizontally 8.00 m above the ground at 6.00 m/s. The bird is carrying a clam in its beak and plans to crack the clamshell by dropping it on some rocks below. Ignoring air resistance, (a) what is the horizontal distance to the rocks at
> Find the rotational inertia of the system of point particles shown in the figure assuming the system rotates about the (a) x-axis, (b) y-axis, c) z-axis. The z-axis is perpendicular to the xy-plane and points out of the page. Point particle A has a mass
> In 1899, Charles M. “Mile a Minute” Murphy set a record for speed on a bicycle by pedaling for a mile at an average of 62.3 mi/h (27.8 m/s) on a track of planks set over railroad ties in the draft of a Long Island Railroad train. In 1985, a record was se
> (a) Sketch a graph of x(t) = A sin ωt (the position of an object in SHM that is at the equilibrium point at t = 0). (b) By analyzing the slope of the graph of x(t), sketch a graph of vx(t). (c) Use conservation of energy along with your graphs to show
> A shallow well usually has the pump at the top of the well. (a) What is the deepest possible well for which a surface pump will work? [Hint: A pump maintains a pressure difference, keeping the outflow pressure higher than the intake pressure.] (b) Why
> The displacement of an object in SHM is given by y(t) = (8.0 cm) sin [(1.57 rad/s)t]. What is the frequency of the oscillations?
> A uniform cylinder with a radius of 15 cm has been attached to two cords and the cords are wound around it and hung from the ceiling. The cylinder is released from rest, and the cords unwind as the cylinder descends. (a) What is the acceleration of the
> An object of mass 306 g is attached to the base of a spring, with spring constant 25 N/m, that is hanging from the ceiling. A pen is attached to the back of the object, so that it can write on a paper placed behind the mass-spring system. Ignore friction
> A collection of objects is set to rolling, without slipping, down a slope inclined at 30°. The objects are a solid sphere, a hollow sphere, a solid cylinder, and a hollow cylinder. A frictionless cube is also allowed to slide down the same incline. Rank
> A baby jumper consists of a cloth seat suspended by an elastic cord from the lintel of an open doorway. The unstretched length of the cord is 1.2 m, and the cord stretches by 0.20 m when a baby of mass 6.8 kg is placed into the seat. The mother then pull
> Is there anywhere on Earth where a bathroom scale reads your true weight? If so, where? Where does your apparent weight due to Earth’s rotation differ most from your true weight?
> The 12.2 m crane weighs 18 kN and is lifting a 67 kN load. The hoisting cable (tension T1) passes over a pulley at the top of the crane and attaches to an electric winch in the cab. The pendant cable (tension T2), which supports the crane, is fixed to th
> A small rowboat has a mass of 47 kg. When a 92 kg person gets into the boat, the boat floats 8.0 cm lower in the water. If the boat is then pushed slightly deeper in the water, it will bob up and down with simple harmonic motion (neglecting any friction)
> A man is rappelling down a vertical wall. The rope attaches to a buckle strapped to his waist 15 cm to the right of his center of gravity. If the man weighs 770 N, find (a) the tension in the rope and (b) the magnitude and direction of the contact forc
> A toboggan is sliding down a snowy slope. The table shows the speed of the toboggan at various times during its trip. (a) Make a graph of the speed as a function of time. (b) Judging by the graph, is it plausible that the toboggan's acceleration is con
> The distance from the center of the breastbone to a man's hand, with the arm outstretched and horizontal to the floor, is 1.0 m. The man is holding a 10.0 kg dumbbell, oriented vertically, in his hand, with the arm horizontal. What is the torque due to t
> A 0.50 kg object, suspended from an ideal spring of spring constant 25 N/m, is oscillating vertically. How much change of kinetic energy occurs while the object moves from the equilibrium position to a point 5.0 cm lower?
> A ceiling fan has four blades, each with a mass of 0.35 kg and a length of 60 cm. Model each blade as a rod connected to the fan axle at one end. When the fan is turned on, it takes 4.35 s for the fan to reach its final angular speed of 1.8 rev/s. What t
> The diaphragm of a speaker has a mass of 50.0 g and responds to a signal of frequency 2.0 kHz by moving back and forth with an amplitude of 1.8 × 10−4 m at that frequency. (a) What is the maximum force acting on the diaphragm? (b) What is the mechanica
> The Moon's distance from Earth varies between 3.56 × 105 km at perigee and 4.07 × 105 km at apogee. What is the ratio of its orbital speed around Earth at perigee to that at apogee?
> A small bird’s wings can undergo a maximum displacement amplitude of 5.0 cm (distance from the tip of the wing to the horizontal). If the maximum acceleration of the wings is 12 m/s2, and we assume the wings are undergoing simple harmonic motion when bea
> You are mowing the lawn on a hill near your house when the lawnmower blade strikes a stone of mass 100 g and sends it flying horizontally toward a window. The lawnmower blade can be modeled as a thin rod with a mass of 2.0 kg and a length of 50 cm rotati
> In a playground, a wooden horse is attached to the ground by a stiff spring. When a 24 kg child sits on the horse, the spring compresses by 28 cm. With the child sitting on the horse, the spring oscillates up and down with a frequency of 0.88 Hz. What is
> The graph with Problem 23 shows speedometer readings as a car skids to a stop on a straight roadway. What is the magnitude of the acceleration at t = 7.0 s? Sketch a graph of ax(t). What is the coefficient of kinetic friction?
> A house painter stands 3.0 m above the ground on a 5.0 m long ladder that leans against the wall at a point 4.7 m above the ground. The painter weighs 680 N and the ladder weighs 120 N. Assuming no friction between the house and the upper end of the ladd
> A child's toy is made of a 12.0 cm radius rotating wheel that picks up 1.00 g pieces of candy in a pocket at its lowest point, brings the candy to the top, then releases it. The frequency of rotation is 1.60 Hz. (a) How far from its starting point does
> In the physics laboratory, a glider is released from rest on a frictionless air track inclined at an angle. If the glider has gained a speed of 25.0 cm/s in traveling 50.0 cm from the starting point, what was the angle of inclination of the track? Draw a
> Show that, for SHM, the maximum displacement, velocity, and acceleration are related by /
> A uniform disk is rotated about its symmetry axis. The disk goes from rest to an angular speed of 11 rad/s in a time of 0.20 s with constant angular acceleration. The rotational inertia and radius of the disk are 1.5 kg·m2 and 11.5 cm, respectively. (a)
> A 170 g object on a spring oscillates left to right on a frictionless surface with a frequency of 3.00 Hz and an amplitude of 12.0 cm. (a) What is the spring constant? (b) If the object starts at x = 12.0 cm at t = 0 and the equilibrium point is at x =
> Consider the apparatus shown in the figure (not to scale). The pulley, which can be treated as a uniform disk, has a mass of 60.0 g and a radius of 3.00 cm. The spool also has a radius of 3.00 cm. The rotational inertia of the spool, axle, and paddles ab
> An object oscillates up and down between y = +A and y = −A at the end of a stretched spring. (a) At what point(s) is the kinetic energy maximum? (Give the value(s) of y.) (b) At what point(s) is the gravitational potential energy maximum? (c) At what
> A bicycle and its rider have a total mass of 74.0 kg. Each of its wheels can be modeled as a thin hoop with mass 1.30 kg and diameter of 70.0 cm. When the brakes are applied, two brake pads squeeze the rims of each wheel. Assume that the four brake pads
> The air pressure variations in a sound wave cause the eardrum to vibrate. (a) For a given vibration amplitude, are the maximum velocity and acceleration of the eardrum greatest for high-frequency sounds or low-frequency sounds? (b) Find the maximum vel
> A hollow cylinder rolls without slipping or sliding along a horizontal surface toward an incline. (a) If the cylinder's speed is 3.00 m/s at the base of the incline and the angle of inclination is 37.0°, how far up the incline does the cylinder travel b
> A uniform diving board, of length 5.0 m and mass 55 kg, is supported at two points; one support is located 3.4 m from the end of the board and the second is at 4.6 m from the end (see Fig. 8.19). What are the forces acting on the board due to the two sup
> The human eardrum responds to sound by vibrating. If the eardrum moves in simple harmonic motion at a frequency of 4.0 kHz and an amplitude of 0.10 nm (roughly the diameter of a single hydrogen atom), what is its maximum speed of vibration? (Amazingly, t
> Is depressing the “accelerator” (gas pedal) of a car the only way that the driver can make the car accelerate (in the physics sense of the word)? If not, what else can the driver do to give the car an acceleration?
> A block of mass m1 slides to the right with coefficient of kinetic friction μk on a horizontal surface. The block is connected to a hanging block of mass m2 by a light cord that passes over a light, frictionless pulley. (a) Find the acceleration of each
> A modern sculpture has a large horizontal spring, with a spring constant of 275 N/m, that is attached to a 53.0 kg piece of uniform metal at its end and holds the metal at an angle of 50.0° above the horizontal direction. The other end of the
> The frequency of vibration of a lithotriptor, an ultrasound generator used to destroy kidney stones, is 1.0 MHz. (a) What is the period of vibration? (b) What is the angular frequency?
> A block of mass m2 hangs from a rope. The rope wraps around a pulley of rotational inertia I and then attaches to a second block of mass m1, which sits on a frictionless table. What is the acceleration of the blocks when they are released?
> A hollow hemispherical object is filled with air as in part (a) of the figure. (a) Show that the magnitude of the force due to fluid pressure on the curved surface of the hemisphere has magnitude F = πr2P, where r is the radius of the hemisph
> A person places his hand palm downward on a scale and pushes down on the scale until it reads 96 N. The triceps muscle is responsible for this arm extension force. Find the force exerted by the triceps muscle. The bottom of the triceps muscle is 2.5 cm t
> Assume a water strider has a roughly circular foot of radius 0.02 mm. (a) What is the maximum possible upward force on the foot due to surface tension of the water? (b) What is the maximum mass of this water strider so that it can keep from breaking thr
> (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
