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physics
mechanics

Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

Two identical beakers are filled to the brim and placed on balance scales. The base area of the beakers is large enough that any water that spills out of the beakers will fall onto the table the scales are resting on. A block of pine (density = 420 kg/m3) is placed in one of the beakers. The block
A very large vat of water has a hole 1.00 cm in diameter located a distance 1.80 m below the water level. (a) How fast does water exit the hole? (b) How would your answer differ if the vat were filled with gasoline? (c) How would your answer differ if the vat contained water, but was on the Moon,
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 stretched by 1.00 cm. What is the spring
You are hiking through a lush forest with some of your friends when you come to a large river that seems impossible to cross. However, one of your friends notices an old metal barrel sitting on the shore. The barrel is shaped like a cylinder and is 1.20 m high and 0.76 m in diameter. One of the
A nurse applies a force of 4.40 N to the piston of a syringe. The piston has an area of 5.00 × 10−5 m2. What is the pressure increase in the fluid within the syringe?
The deepest place in the ocean is the Marianas Trench in the western Pacific Ocean, which is over 11.0 km deep. On January 23, 1960, the research sub Trieste went to a depth of 10.915 km, nearly to the bottom of the trench. This still is the deepest dive on record. The density of seawater is 1025
The pressure in a water pipe in the basement of an apartment house is 4.10 × 105 Pa, but on the seventh floor it is only 1.85 × 105 Pa. What is the height between the basement and the seventh floor? Assume the water is not flowing; no faucets are opened?
The body of a 90.0-kg person contains 0.020 m3 of body fat. If the density of fat is 890 kg/m3, what percentage of the person's body weight is composed of fat?
Near sea level, how high a hill must you ascend for the reading of a barometer you are carrying to drop by 1.0 cm Hg? Assume the temperature remains at 20 °C as you climb. The reading of a barometer on an average day at sea level is 76.0 cm Hg.
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 (specific gravity = 0.90)?
If you watch water falling from a faucet, you will notice that the flow decreases in radius as the water falls. This can be explained by the equation of continuity, since the cross-sectional area of the water decreases as the speed increases. If the water flows with an initial velocity of 0.62 m/s
The average speed of blood in the aorta is 0.3 m/s and the radius of the aorta is 1 cm. There are about 2 × 109 capillaries with an average radius of 6 μm. What is the approximate average speed of the blood flow in the capillaries?
If the cardiac output of a small dog is 4.1 × 10−3 m3 /s, the radius of its aorta is 0.50 cm, and the aorta length is 40.0 cm, determine the pressure drop across the aorta of the dog. Assume the viscosity of blood is 4.0 × 10−3 Pa·s?
In an aortic aneurysm, a bulge forms where the walls of the aorta are weakened. If blood flowing through the aorta (radius 1.0 cm) enters an aneurysm with a radius of 3.0 cm, how much on average is the blood pressure higher inside the aneurysm than the pressure in the unenlarged part of the aorta?
Scuba divers are admonished not to rise faster than their air bubbles when rising to the surface. This rule helps them avoid the rapid pressure changes that cause the bends. Air bubbles of 1.0 mm radius are rising from a scuba diver to the surface of the sea. Assume a water temperature of 20
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? [Consider the work to be done.]
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? [A pump maintains a pressure difference, keeping the outflow pressure higher than the intake pressure.] (b) Why is there not the same depth restriction on wells with
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/m 3 both inside and outside. (b) What is the buoyant force on the beach ball in air? The thickness of the
A block of wood, with density 780 kg/m3, has a cubic shape with sides 0.330 m long. A rope 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. What is the mass of the lead? [Don't forget
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 r of the fluid? To answer this question, assume that the cylinder has radius r and mass m. Find an
A hydrometer is an instrument for measuring the specific gravity of a liquid. For example, vintners use a hydrometer to determine the density changes as wine is fermented, and producers of maple sugar and maple syrup use the hydrometer to find how much sugar is in the collected sap. Markings along
A house with its own well has a pump in the basement with an output pipe of inner radius 6.3 mm. Assume that the pump can maintain a gauge pressure of 410 kPa in the output pipe. A showerhead on the second floor (6.7 m above the pump's output pipe) has 36 holes, each of radius 0.33 mm. The shower
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 hits it head-on) and the other side connected to a tube so that the "wind" blows
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)?
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. [Apply Newton's second law to the column of air.] (b) If the air all the way up had a
On a nice day when the temperature outside is 20 °C, you take the elevator to the top of the Sears 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 pascals and atm. (b) How many pascals does the
Young's modulus for diamond is about 20 times as large as that of glass. Does that tell you which is stronger? If not, what does it tell you?
Does it take more force to break a longer rope or a shorter rope? Assume the ropes are identical except for their lengths and are ideal-there are no weak points. Does it take more energy to break the long rope or the short rope? Explain.
A pilot is performing vertical loop-the-loops over the ocean at noon. The plane speeds up as it approaches the bottom of the circular loop and slows as it approaches the top of the loop. An observer in a helicopter is watching the shadow of the plane on the surface of the water. Does the shadow
Are you more likely to find steel rods in a horizontal concrete beam or in a vertical concrete column? Is concrete more in need of reinforcement under tensile or compressive stress?
Suppose that it takes tensile forces of magnitude F to produce a given strain Δ L / L in a steel wire of cross sectional area A. If you had two such wires side by side and stretched them simultaneously, what magnitude tensile forces would be required to produce the same strain? By thinking of a
Think of a crystalline solid as a set of atoms connected by ideal springs. When a wire is stretched, how is the elongation of the wire related to the elongation of each of the interatomic springs? Use your answer to explain why a given tensile stress produces an elongation of the wire proportional
What are the advantages of using the concepts of stress and strain to describe deformations?
An old highway is built out of concrete blocks of equal length. A car traveling on this highway feels a little bump at the joint between blocks. The passengers in the car feel that the ride is uncomfortable at a speed of 45 mi/h, but much smoother at speeds either lower or higher than that? Explain.
The period of oscillation of a simple pendulum does not depend on the mass of the bob. By contrast, the period of a mass-spring system does depend on mass. Explain the apparent contradiction. [What provides the restoring force in each case? How does the restoring force depend on mass?]
A mass connected to an ideal spring is oscillating without friction on a horizontal surface. Sketch graphs of the kinetic energy, potential energy, and total energy as functions of time for one complete cycle?
A karate student hits downward on a stack of concrete blocks supported at both ends. A block breaks. Explain where it starts to break first, at the bottom or at the top. (The block experiences shear, compressive, and tensile stresses. Recall that concrete has much less tensile strength than
A cylindrical steel bar is compressed by the application of forces of magnitude F at each end. What magnitude forces would be required to compress by the same amount (a) A steel bar of the same cross-sectional area but one half the length? (b) A steel bar of the same length but one half the radius?
The columns built by the ancient Greeks and Romans to support temples and other structures are tapered; they are thicker at the bottom than at the top. This certainly has an aesthetic purpose, but is there an engineering purpose as well? What might it be?
Explain how the period of a mass-spring system can be independent of amplitude, even though the distance traveled during each cycle is proportional to the amplitude?
In a reciprocating saw, a Scotch yoke converts the rotation of the motor into the back-and-forth motion of the blade.The Scotch yoke is a mechanical device used to convert oscillatory motion to circular motion or vice versa. A wheel with a fixed knob rotates at constant angular velocity; the knob
A mass hanging vertically from a spring and a simple pendulum both have a period of oscillation of 1 s on Earth. An astronaut takes the two devices to another planet where the gravitational field is stronger than that of Earth. For each of the two systems, state whether the period is now longer
A bungee jumper leaps from a bridge and comes to a stop a few centimeters above the surface of the water below. At that lowest point, is the tension in the bungee cord equal to the jumper's weight? Explain why or why not?
A steel beam is placed vertically in the basement of a building to keep the floor above from sagging. The load on the beam is 5.8 × 104 N, the length of the beam is 2.5 m, and the cross-sectional area of the beam is 7.5 × 10−3 m2. Find the vertical compression of the beam?
An acrobat of mass 55 kg is going to hang by her teeth from a steel wire and she does not want the wire to stretch beyond its elastic limit. The elastic limit for the wire is 2.5 × 108 Pa. What is the minimum diameter the wire should have to support her?
A hair breaks under a tension of 1.2 N. What is the diameter of the hair? The tensile strength is 2.0 × 108 Pa?
The ratio of the tensile (or compressive) strength to the density of a material is a measure of how strong the material is "pound for pound." (a) Compare tendon (tensile strength 80.0 MPa, density 1100 kg / m3) with steel (tensile strength 0.50 GPa, density 7700 kg/m 3): which is stronger "pound
What is the maximum load that could be suspended from a copper wire of length 1.0 m and radius 1.0 mm without permanently deforming the wire? Copper has an elastic limit of 2.0 × 108 Pa and a tensile strength of 4.0 × 108 Pa?
What is the maximum load that could be suspended from a copper wire of length 1.0 m and radius 1.0 mm without breaking the wire? Copper has an elastic limit of 2.0 × 108 Pa and a tensile strength of 4.0 × 108 Pa?
The leg bone (femur) breaks under a compressive force of about 5 × 104 N for a human and 10 × 104 N for a horse. The human femur has a compressive strength of 1.6 × 108 Pa, while the horse femur has a compressive strength of 1.4 × 108 Pa. What is the effective cross-sectional area of the femur
The maximum strain of a steel wire with Young's modulus 2.0 × 1011 N/m2, just before breaking, is 0.20%. What is the stress at its breaking point, assuming that strain is proportional to stress up to the breaking point?
A marble column with a cross-sectional area of 25 cm2 supports a load of 7.0 × 104 N. The marble has a Young's modulus of 6.0 × 1010 Pa and a compressive strength of 2.0 × 108 Pa? (a) What is the stress in the column? (b) What is the strain in the column? (c) If the column is 2.0 m high, how
A copper wire of length 3.0 m is observed to stretch by 2.1 mm when a weight of 120 N is hung from one end? (a) What is the diameter of the wire and what is the tensile stress in the wire? (b) If the tensile strength of copper is 4.0 × 108 N/m2, what is the maximum weight that may be hung from
A sphere of copper is subjected to 100 MPa of pressure. The copper has a bulk modulus of 130 GPa. By what fraction does the volume of the sphere change? By what fraction does the radius of the sphere change?
A 91-kg man's thighbone has a relaxed length of 0.50 m, a cross-sectional area of 7.0 × 10−4 m2, and a Young's modulus of 1.1 × 1010 N/m2 . By how much does the thighbone compress when the man is standing on both feet?
By what percentage does the density of water increase at a depth of 1.0 km below the surface?
Atmospheric pressure on Venus is about 90 times that on Earth. A steel sphere with a bulk modulus of 160 GPa has a volume of 1.00 cm3 on Earth. If it were put in a pressure chamber and the pressure were increased to that of Venus (9.12 MPa), how would its volume change?
How would the volume of 1.00 cm3 of aluminum on Earth change if it were placed in a vacuum chamber and the pressure changed to that of the Moon (less than 10−9 Pa)?
Two steel plates are fastened together using four bolts. The bolts each have a shear modulus of 8.0 Ã— 1010 Pa and a shear strength of 6.0 Ã— 108 Pa. The radius of each bolt is 1.0 cm. Normally, the bolts clamp the two plates together and the frictional forces between the
An anchor, made of cast iron of bulk modulus 60.0 × 109 Pa and of volume 0.230 m3, is lowered over the side of the ship to the bottom of the harbor where the pressure is greater than sea level pressure by 1.75 × 106 Pa. Find the change in the volume of the anchor?
The upper surface of a cube of gelatin, 5.0 cm on a side, is displaced 0.64 cm by a tangential force. If the shear modulus of the gelatin is 940 Pa, what is the magnitude of the tangential force?
A large sponge has forces of magnitude 12 N applied in opposite directions to two opposite faces of area 42 cm2 (see Fig. 10.7 for a similar situation). The thickness of the sponge (L) is 2.0 cm. The deformation angle (() is 8.0°. (a) What is Δx? (b) What is the shear modulus of the sponge?
The period of oscillation of a spring-and-mass system is 0.50 s and the amplitude is 5.0 cm. What is the magnitude of the acceleration at the point of maximum extension of the spring?
A sewing machine needle moves with a rapid vibratory motion, rather like SHM, as it sews a seam. Suppose the needle moves 8.4 mm from its highest to its lowest position and it makes 24 stitches in 9.0 s. What is the maximum needle speed?
The prong of a tuning fork moves back and forth when it is set into vibration. The distance the prong moves between its extreme positions is 2.24 mm. If the frequency of the tuning fork is 440.0 Hz, what are the maximum velocity and the maximum acceleration of the prong? Assume SHM?
A brass wire with Young's modulus of 9.2 × 1010 Pa is 2.0 m long and has a cross-sectional area of 5.0 mm2. If a weight of 5.0 kN is hung from the wire, by how much does it stretch?
The period of oscillation of an object in an ideal spring and- mass system is 0.50 s and the amplitude is 5.0 cm. What is the speed at the equilibrium point?
Show that the equation a = − (2x is consistent for units, and that √k/m has the same units as (?
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 = 0, what equation describes its position as a
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 velocity and acceleration of the eardrum for
Show that, for SHM, the maximum displacement, velocity, and acceleration are related by v2m = amA?
An empty cart, tied between two ideal springs, oscillates with ( = 10.0 rad/s. A load is placed in the cart, making the total mass 4.0 times what it was before. What is the new value of (?
A cart with mass m is attached between two ideal springs, each with the same spring constant k. Assume that the cart can oscillate without friction?(a) When the cart is displaced by a small distance x from its equilibrium position, what force magnitude acts on the cart?(b) What is the angular
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 oscillation frequency of the spring when
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 beating, what is the oscillation frequency of
Equipment to be used in airplanes or spacecraft is often subjected to a shake test to be sure it can withstand the vibrations that may be encountered during flight. A radio receiver of mass 5.24 kg is set on a platform that vibrates in SHM at 120 Hz and with a maximum acceleration of 98 m/s 2
A wire of length 5.00 m with a cross-sectional area of 0.100 cm2 stretches by 6.50 mm when a load of 1.00 kN is hung from it. What is the Young's modulus for this wire?
In an aviation test lab, pilots are subjected to vertical oscillations on a shaking rig to see how well they can recognize objects in times of severe airplane vibration. The frequency can be varied from 0.02 to 40.0 Hz and the amplitude can be set as high as 2 m for low frequencies. What are the
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 mechanical energy of the diaphragm?
An ideal spring has a spring constant k = 25 N/m. The spring is suspended vertically. A 1.0-kg body is attached to the unstretched spring and released. It then performs oscillations. (a) What is the magnitude of the acceleration of the body when the extension of the spring is a maximum? (b) What is
An ideal spring with a spring constant of 15 N/m is suspended vertically. A body of mass 0.60 kg is attached to the unstretched spring and released. (a) What is the extension of the spring when the speed is a maximum? (b) What is the maximum speed?
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 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). What will be the period of oscillation for
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 pulls the seat down by 8.0 cm and releases it? (a)
A body is suspended vertically from an ideal spring of spring constant 2.5 N/m. The spring is initially in its relaxed position. The body is then released and oscillates about its equilibrium position. The motion is described by y = (4.0 cm) sin [(0.70 rad/s)t] What is the maximum kinetic energy of
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) Describe the pattern traced on the
Two steel wires (of the same length and different radii) are connected together, end to end, and tied to a wall. An applied force stretches the combination by 1.0 mm. How far does the midpoint move?
(a) Sketch a graph of x (t) = A sin (t (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). Is vx(t) a sine or cosine function?(c) By analyzing the slope of the graph of vx(t), sketch a x(t).(d)
A mass-and-spring system oscillates with amplitude A and angular frequency (? (a) What is the average speed during one complete cycle of oscillation? (b) What is the maximum speed? (c) Find the ratio of the average speed to the maximum speed? (d) Sketch a graph of vx(t), and refer to it to explain
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 not SHM?
A 230.0-g object on a spring oscillates left to right on a frictionless surface with a frequency of 2.00 Hz. Its position as a function of time is given by x = (8.00 cm) sin ( t.? (a) Sketch a graph of the elastic potential energy as a function of time. (b) The object's velocity is given by vx =
(a) Given that the position of an object is x(t) = A cos (t, show that vx(t) = − (A sin (t. [Draw the velocity vector for point P in Fig. 10.17b and then find its x - component.] (b) Verify that the expressions for x(t) and vx(t) are consistent with energy conservation. [Use the trigonometric
What is the period of a pendulum consisting of a 6.0-kg mass oscillating on a 4.0-m-long string?
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 bob of mass m is suspended from a string of length L, forming a pendulum. The period of this pendulum is 2.0 s. If the pendulum bob is replaced with one of mass 1/3 m and the length of the pendulum is increased to 2 L, what is the period of oscillation?
A pendulum (mass m, unknown length) moves according to x = A sin (t? (a) Write the equation for vx(t) and sketch one cycle of the vx(t) graph? (b) What is the maximum kinetic energy?
Abductin is an elastic protein found in scallops, with a Young's modulus of 4.0 × 106 N/m2. It is used as an inner hinge ligament, with a cross-sectional area of 0.78 mm 2 and a relaxed length of 1.0 mm. When the muscles in the shell relax, the shell opens. This increases efficiency as the muscles
A clock has a pendulum that performs one full swing every 1.0 s (back and forth). The object at the end of the pendulum weighs 10.0 N. What is the length of the pendulum?
A pendulum of length L1 has a period T1 = 0.950 s. The length of the pendulum is adjusted to a new value L2 such that T2 = 1.00 s. What is the ratio L2 / L1?
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 than that on Earth? (b) Find the gravitational

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