Question: Consider the apparatus shown in the figure (

> 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

> 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

> 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 =

> 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

> 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