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physics
mechanics
Fundamentals of Physics 8th Extended edition Jearl Walker, Halliday Resnick - Solutions
If a force F acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.
Why is it more difficult to do a sit-up with your hands behind your head than when you arms are stretched out in front of you? A diagram may help you to answer this.
A 21-speed bicycle has seven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?
Mammals that depend on being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8-34) On the basis of rotational dynamics, explain why this distribution of mass is advantageous.
Why do tightrope walkers (Fig 8-35) carry a long, narrow beam?
If the net force on a system is zero, is the net torque also zero? If the net torque on a system is zero, is the net force zero?
Two inclines have the same height but make different angles with the horizontal. The same steel ball is rolled down each incline will the speed of the ball at the bottom be greater? Explain
Two solid spheres simultaneously start rolling (from rest) down and incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?
A sphere and a cylinder have the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?
We claim that momentum and angular momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Explain
If there were a great migration of people toward the Earth’s equator, how would this affect the length of the day?
Can the diver of Fig 8-29 do a somersault without having any initial rotation when she leaves the board?
The moment of inertia of a rotating solid disk about an axis through its center of mass is ½ MR2 (Fig 8-21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?
Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.
Two spheres look identical and have the same mass. However, one is hollow and the other is solid. Describe and experiment to determine which is which.
In what direction is the Earth’ angular velocity vector as it rotates daily about its axis?
The angular velocity of a wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed
Suppose you are standing on the edge of a large freely rotating turntable. What happens if you walk toward the center?
A shortstop may leap into the air to catch a ball and throw it quickly. AS he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8-36). Explain
On the basis of the low of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.
The following functions give the position as a function of time:i) x = Aii) x = Btiii) x = Ct2iv) x = D cos !tv) x = E sin !t where A;B;C;D;E; ! are constants.A) What are the units for A;B;C;D;E; !?B) Write down the velocity and acceleration equations as a function of time. Indicate for what
The figures below show position-time graphs. Sketch the corresponding velocity-time and acceleration-time graphs.
If you drop an object from a height H above the ground, work out a formula for the speed with which the object hits the ground.
A car is traveling at constant speed v1 and passes a second car moving at speed v2. The instant it passes, the driver of the second car decides to try to catch up to the first car, by stepping on the gas pedal and moving at acceleration a. Derive a formula for how long it takes to catch up. (The
If you start your car from rest and accelerate to 30mph in 10 seconds, what is your acceleration in mph per sec and in miles per hour2?
If you throw a ball up vertically at speed V, with what speed does it return to the ground? Prove your answer using the constant acceleration equations, and neglect air resistance.
Calculate the angle between the vectors r = i + 2j and t = j - k.
Evaluate (r + 2t): f where r = i + 2j and t = j - k and f = i - j.
Two vectors are defined as u = j + k and v = i + j. Evaluate: A) u + v B) u - v C) u . v D) u x v
A) A projectile is fired with an initial speed vo at an angle θ with respect to the horizontal. Neglect air resistance and derive a formula for the horizontal range R, of the projectile. (Your formula should make no explicit reference to time, t) at what angle is the range a maximum? B) If v0
A projectile is fired with an initial speed vo at an angle µ with respect to the horizontal. Neglect air resistance and derive a formula for the maximum height H, which the projectile reaches. (Your formula should make no explicit reference to time, t).
A) If a bulls-eye target is at a horizontal distance R away, derive an expression for the height L, which is the vertical distance above the bulls-eye that one needs to aim a rifle in order to hit the bulls-eye.Assume the bullet leaves the rifle with speed v0.B) How much bigger is L compared to the
Normally if you wish to hit a bulls-eye some distance away you need to aim a certain distance above it, in order to account for the downward motion of the projectile. If a bulls-eye target is at a horizontal distance D away and if you instead aim an arrow directly at the bulls-eye (i.e. directly
Prove that the trajectory of a projectile is a parabola (neglect air resistance).
Even though the Earth is spinning and we all experience a centrifugal acceleration, we are not flung off the Earth due to the gravitational force. In order for us to be flung off, the Earth would have to be spinning a lot faster.A) Derive a formula for the new rotational time of the Earth, such
A satellite is in a circular orbit around a planet of mass M and radius R at an altitude of H. Derive a formula for the additional speed that the satellite must acquire to completely escape from the planet. Check that your answer has the correct units.
A mass m is attached to the end of a spring with spring constant k on a frictionless horizontal surface. The mass moves in circular motion of radius R and period T. Due to the centrifugal force, the spring stretches by a certain amount x from its equilibrium position. Derive a formula for x in
A cannon ball is fired horizontally at a speed v0 from the edge of the top of a cliff of height H. Derive a formula for the horizontal distance (i.e. the range) that the cannon ball travels. Check that your answer has the correct units.
A skier starts from rest at the top of a frictionless ski slope of height H and inclined at an angle θ to the horizontal. At the bottom of the slope the surface changes to horizontal and has a coefficient of kinetic friction ¹k between the horizontal surface and the skis. Derive a formula for
A stone is thrown from the top of a building upward at an angle µ to the horizontal and with an initial speed of v0 as shown in the figure. If the height of the building is H, derive a formula for the time it takes the stone to hit the ground below.
A mass m1 hangs vertically from a string connected to a ceiling. A second mass m2 hangs below m1 with m1 and m2 also connected by another string. Calculate the tension in each string.
What is the acceleration of a snow skier sliding down a frictionless ski slope of angle θ? Check that your answer makes sense for θ = 0o and for µ = 90o.
A ferries wheel rotates at constant speed in a vertical circle of radius R and it takes time T to complete each circle. Derive a formula, in terms of m, g, R, T, for the weight that a passenger of mass m feels at the top and bottom of the circle. Comment on whether your answers make sense.
A block of mass m1 on a rough, horizontal surface is connected to a second mass m2 by a light cord over a light frictionless pulley as shown in the figure. (`Light' means that we can neglect the mass of the cord and the mass of the pulley.) A force of magnitude F is applied to the mass m1 as shown,
If you whirl an object of mass m at the end of a string in a vertical circle of radius R at constant speed v, derive a formula for the tension in the string at the top and bottom of the circle.
Two masses m1 and m2 are connected by a string passing through a hollow pipe with m1 being swung around in a circle of radius R and m2 hanging vertically as shown in the figure.Obviously if m1 moves quickly in the circle then m2 will start to move upwards, but if m1 moves slowly m2 will start to
A) What friction force is required to stop a block of mass m moving at speed v0, assuming that we want the block to stop over a distance d?B) Work out a formula for the coefficient of kinetic friction that will achieve this.C) Evaluate numerical answers to the above two questions assuming the mass
A block of mass m slides down a rough incline of height H and angle µ to the horizontal. Calculate the speed of the block when it reaches the bottom of the incline, assuming the coefficient of kinetic friction is µk.
A particle of mass m is located on the x axis at the position x = 1 and a particle of mass 2m is located on the y axis at position y = 1 and a third particle of mass m is located off-axis at the position (x; y) = (1; 1). What is the location of the center of mass?
Consider a square flat table-top. Prove that the center of mass lies at the center of the table-top, assuming a constant mass density.
A child of mass mc is riding a sled of mass ms moving freely along an icy frictionless surface at speed v0. If the child falls o® the sled, derive a formula for the change in speed of the sled. (Note: energy is not conserved!) WRONG WRONG WRONG ?????????????? Speed of sled remains same - person
In a game of billiards, the player wishes to hit a stationary target ball with the moving projectile ball. After the collision, show that the sum of the scattering angles is 90o, Ignore friction and rolling motion and assume the collision is elastic. Also both balls have the same mass.
Show that the ratio of the angular speeds of a pair of coupled gear wheels is in the inverse ratio of their respective radii.
Show that the magnitude of the total linear acceleration of a point moving in a circle of radius r with angular velocity w and angular acceleration a is given by a = w4 + a2
The turntable of a record player rotates initially at a rate of 33 revolutions per minute and takes 20 seconds to come to rest. How many rotations does the turntable make before coming to rest, assuming constant angular deceleration?
A cylindrical shell of mass M and radius R rolls down an incline of height H. With what speed does the cylinder reach the bottom of the incline? How does this answer compare to just dropping an object from a height H?
Four point masses are fastened to the corners of a frame of negligible mass lying in the xy plane. Two of the masses lie along the x axis at positions x = + a and x = - a and are both of the same mass M. The other two masses lie along the y axis at positions y = +b and y = ¡b and are both of the
A uniform object with rotational inertia I = amR2 rolls without slipping down an incline of height H and inclination angle θ. With what speed does the object reach the bottom of the incline? What is the speed for a hollow cylinder (I = mR2) and a solid cylinder (I = 1/2MR2)? Compare to the
A pencil of length L, with the pencil point at one end and an eraser at the other end, is initially standing vertically on a table with the pencil point on the table. The pencil is let go and falls over. Derive a formula for the speed with which the eraser strikes the table, assuming that the
A bullet of mass m traveling with a speed v is shot into the rim of a solid circular cylinder of radius R and mass M as shown in the figure. The cylinder has a fixed horizontal axis of rotation, and is originally at rest. Derive a formula for the angular speed of the cylinder after the bullet has
Figure P6.61 shows a Ferris wheel that rotates four times each minute. It carries each car around a circle of diameter 18.0 m.(a) What is the centripetal acceleration of a rider? What force does the seat exert on a 40.0-kg rider?(b) At the lowest point of the ride and(c) At the highest point of the
The micrometer (1μm) is often called the micron. (a) How many microns make up 1.0 km? (b) What fraction of a centimeter equals 1.0μm? (c) How many microns are in 1.0 yd?
Spacing in this book was generally done in units of points and picas: 12 points = 1 pica and 6 picas = 1 inch. If a figure was misplaced in the page proofs by 0.80 cm, what was the misplacement in(a) Picas and(b) Points?
Horses are to race over a certain English meadow for a distance of 4.0 furlongs. What is the race distance in?(a) Rods and(b) Chains? (1 furlong = 201.168 m, 1, rod = 5.0292m, and 1 chain = 20.1.17m.)
A gry is an old English measure for length, defined as 1/10 of a line, where line is another old English measure for length, defined as l/12 inch. A common measure for length in the publishing business is a point, defined as l/72 inch. What is an area of 0.50 gry2 in points squared (points2)?
Earth is approximately a sphere of radius 6.37 x 106 m. What are? (a) Its circumference in kilometers, (b) Its surface area in square kilometers, and (c) Its volume in cubic kilometers?
Harvard Bridge, which connects MIT with its fraternities across the Charles River, has a length of 364.4 Smoots plus one ear. The unit of one Smoot is based on the length of Oliver Reed Smoot, Jr., class of 1962, who was carried or dragged length by length across the bridge so that other pledge
Antarctica is roughly semicircular with a radius of 2000 km (Fig. 1-5).The average thickness of its ice cover is 3000 m. How many cubic centimeters of ice does Antarctica contain? (Ignore the curvature ofEarth.)
You can easily convert common units and measures electronically, but you still should be able to use a conversion table, such as those in Appendix D. Table 1-6 is part of a conversion table for a system of volume measures once common in Spain; a volume of 1 fanega is equivalent to 55.501 dm3?(cubic
Hydraulic engineers in the United States often use, as a unit of volume of water, the acre-foot, defined as the volume of water that will cover 1 acre of land to a depth of 1 ft. A severe thunderstorm dumped 2.0 tn. of rain in 30 min on a town of area 26 km2. What volume of water, in acre-feet,
The fastest growing plant on record is a Hesperoyucca whipplei that grew 3.7m in 1.4 days. What was its growth rate in micrometers per second?
A fortnight is a charming English measure of time equal to 2.0 weeks (the word is a contraction of "fourteen nights"). That is a nice amount of time in pleasant company but perhaps a painful string of microseconds in unpleasant company. How many microseconds are in a fortnight?
A lecture period (50 min) is close to 1 micro century.(a) How long is a micro century in minutes?(b) Using percentage difference = (actual-approximation/actual) 100, find the percentage difference from the approximation.
For about 10 years after the French Revolution, the French government attempted to base measures of time on multiples of ten: One week consisted of 10 days, one day consisted of 10 hours, one hour consisted of 100 minutes, and one minute consisted of 100 seconds. What are the ratios of?(a) The
Time standards are now based on atomic clocks. A promising second standard is based on pulsars, which are rotating neutron, stars (highly compact stars consisting only of neutrons). Some rotate at a rate that is highly stable, sending out a radio beacon that sweeps briefly across Earth once with
Three digital clocks A, B, and C run at different rates and do not have simultaneous readings of zero. Figure 1-6 shows simultaneous readings on pairs of the clocks for four occasions. (At the earliest occasion, for example, B reads 25.0s and C reads 92.0s.) If two events are 600s apart on clock A,
Until 1883, every city and town in the United States kept its own local time. Today, travelers reset their watches only when the time change equals 1.0h. How far, on the average, must you travel in degrees of longitude between the time-zone boundaries at which your watch must be reset by 1.0h?
Five clocks are being tested in a laboratory. Exactly at noon, as determined by the WWV time signal, on successive days of a week the clocks read as in the following table. Rank the five clocks according to their relative value as good timekeepers, best to worst. Justify yourchoice.
Because Earth's rotation is gradually slowing, the length of each day increases: The day at the end of 1.0 century is 1.0 ms longer than the day at the start of the century. In 20 centuries, what is the total of the daily increases in time?
Suppose that, while lying on a beach near the equator watching the Sun set over a calm ocean you start a stopwatch just as the top of the Sun disappears. You then stand elevating your eyes by a height H = 1.70m, and stop the watch when the top of the Sun again disappears. If the elapsed time is t =
Suppose that, while lying on a beach near the equator watching the Sun set over a calm ocean, you start a stopwatch just as the top of the Sun disappears. You then stand, elevating your eyes by a height H = 1.70m, and stop the watch when the top of the Sun again disappears. If the elapsed time is t
(a) Assuming that water has a density of exactly 1g/cm3, find the mass of one cubic meter of water in kilograms.(b) Suppose that it takes 10.0 h to drain a container of 5700 m3 of water. What is the "mass flow rate," in kilograms per second, of water from the container?
The record for the largest glass bottle was set in 1992 by u team in Millville, New Jersey-they blew a bottle with a volume of 193 U.S. fluid gallons. (a) How much short of 1.0 million cubic centimeters is that? (b) If the bottle were filled with water at the leisurely rate of 1.8 g/min,
Earth has a mass of 5.98 x 1.024 kg. The average mass of the atoms that make up Earth is 40 u. How many atoms are there in Earth?
One cubic centimeter of a typical cumulus cloud contains 50 to 500 water drops, which have a typical radius of 10μm. For that range, give the lower value and the higher value, respectively, for the following.(a) How many cubic meters of water are in a cylindrical cumulus cloud of height 3.0 km and
Iron has a density of 7 .87 g/cm3, and the mass of an iron atom is 9.27 x 10-26 kg. If the atoms are spherical and tightly packed, (a) What is the volume of an iron atom and (b) What is the distance between the centers of adjacent atoms?
Grains of fine California beach sand are approximately spheres with an average radius of 50μm and are made of silicon dioxide, which has a density of 2600 kg/m3. What mass of sand grains would have a total surface area (the total area of all the individual spheres) equal to the surface area of a
During heavy rain, a section of a mountainside measuring 2.5 km horizontally, 0.80 km up along the slope, and 2.0m deep slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a surface area of the valley measuring 0.40 km x 0.40 km and that mud has a density of
Table 1-7 shows some old measures of liquid volume. To complete the table, what numbers (to three significant figures) should be entered in (a) The way column, (b) The chaldron column, (c) The bag column, (d) The pottle column, and (e) The gill column, starting with the top blank? (f) The volume of
An old English child’s rhyme states, "Little Miss Muffed sat on a tuffet, eating her curds and whey, when along came a spider who sat down beside her. . . ." The spider sat down not because of the curds and whey but because Miss Muffed had a stash of l1 tuffets of dried flies. The volume measure
An old manuscript reveals that a landowner in the time of King Arthur held 3.00 acres of plowed land plus a livestock area of 25.0 perches by 4.00 perches. What was the total area in? (a) The old unit of roods and(b) The more modern unit of square meters? Here, 1 acre is an area of 40perches by
A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car's fuel consumption was at the rate of 40 miles per gallon on the open road. The tourist does not realize that the U.K. gallon differs from the U.S. gallon:1 U.K. gallon = 4.545 9631
Two types of barrel units were in use in the I920s in the United States. The apple barrel had a legally set volume of 7056 cubic inches; the cranberry barrel, 5826 cubic inches. If a merchant sells 20 cranberry barrels of goods to a customer who thinks he is receiving apple barrels, what is the
The description for a certain brand of house paint claims a coverage of 460ft2/gal.(a) Express this quantity in square meters per liter.(b) Express this quantity in an SI unit (see Appendices A and n).(c) What is the inverse of the original quantity, and(d) What is its physical significance?
In the United States, a doll house has the scale of 1:12 of a real house (that is, each length of the doll house is 1/12 that of the real house) and a miniature house (a doll house to fit within a doll house) has the scale of l: 144 of a real house. Suppose a real house (Fig. l-7) has a front
A cord is a volume of cut wood equal to a stack 8 ft long, 4 ft wide, and 4 ft high. How many cords are in 1.0 m3?
One molecule of water (H2O) contains two atoms of hydrogen and one atom of oxygen. A hydrogen atom has a mass of 1.0 u and an atom of oxygen has a mass of 16 u, approximately.(a) What is the mass in kilograms of one molecule of water?(b) How many molecules of water are in the world's oceans, which
A ton is a measure of volume frequently used in shipping, but that use requires some care because there are at least three types of tons: A displacement ton is equal to 7 barrels bulk, a freight ton is equal to B barrels bulk, and a register ton is equal to 20 barrels bulk. A barrel bulk is another
Strangely, the wine for a large wedding reception is to be served in a stunning cut-glass receptacle with the interior dimensions of 40 cm x 40 cm x 30 cm (height). The receptacle is to be initially filled to the top. The wine can be purchased in bottles of the sizes given in the following table.
A typical sugar cube has an edge length of 1 cm. If you had a cubical box that contained a mole of sugar cubes, what would its edge length be? (One mole = 6.02 x 1023 units.)
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