Question: Assume Earth is a uniform solid sphere

> Nine-banded armadillos (Dasypus novemcinctus) have a typical mass density of 1200 kg/m3 and a mass of 7.0 kg (including their armor). When faced with a body of water to cross, the armadillo has two choices: to hold its breath and walk across the bottom o

> A plate of uniform thickness is shaped as shown. Where is the center of gravity? Assume the origin (0, 0) is located at the lower left corner of the plate; the upper left corner is at (0, s); and the upper right corner is at (s, s).

> A square loop of wire of side 3.0 cm carries 3.0 A of current. A uniform magnetic field of magnitude 0.67 T makes an angle of 37° with the plane of the loop. (a) What is the magnitude of the torque on the loop? (b) What is the net magnetic force on the l

> Why does a 1 kg sandbag fall with the same acceleration as a 5 kg sandbag? Explain in terms of Newton's second law and his law of gravitation.

> For a system of three particles moving along a line, an observer in a laboratory measures the following masses and velocities. What is the velocity of the CM of the system?

> A car traveling at 29 m/s runs into a bridge abutment after the driver falls asleep at the wheel. (a) If the driver is wearing a seat belt and comes to rest within a 1.0 m distance, what is his acceleration (assumed constant)? (b) A passenger who isn't

> A solid piece of plastic, with a density of 890 kg/m3, is placed in oil with a density of 830 kg/m3 and the plastic sinks (1). Then the plastic is placed in water and it floats (2). (a) What percentage of the plastic is submerged in the water? (b) Fina

> A 0.122 kg dart is fired from a gun with a speed of 132 m/s horizontally into a 5.00 kg wooden block. The block is attached to a spring with a spring constant of 8.56 N/m. The coefficient of kinetic friction between the block and the horizontal surface i

> A fish uses a swim bladder to change its density so it is equal to that of water, enabling it to remain suspended under water. If a fish has an average density of 1080 kg/m3 and mass 10.0 g with the bladder completely deflated, to what volume must the fi

> Two pendulum bobs have equal masses and lengths (5.1 m). Bob A is initially held horizontally while bob B hangs vertically at rest. Bob A is released and collides elastically with bob B. How fast is bob B moving immediately after the collision?

> A streetcar named Desire travels between two stations 0.60 km apart. Leaving the first station, it accelerates for 10.0 s at 1.0 m/s2 and then travels at a constant speed until it is near the second station, when it brakes at 2.0 m/s2 in order to stop at

> An aluminum cylinder weighs 1.03 N. When this same cylinder is completely submerged in alcohol, the volume of the displaced alcohol is 3.90 × 10−5 m3. If the cylinder is suspended from a scale while submerged in the alcohol, the scale reading is 0.730 N.

> A boy of mass 60 kg is sledding down a 70 m slope starting from rest. The slope is angled at 15° below the horizontal. After going 20 m along the slope, he passes his friend, who hops onto the sled. The friend has a mass of 50 kg, and the coefficient of

> How should the disk be oriented to prevent rocking from side to side and from bow to stern? Does this orientation make it difficult to steer the ship? Explain.

> At the surface of a freshwater lake the air pressure is 1.0 atm. At what depth under water in the lake is the water pressure 4.0 atm?

> A door weighing 300.0 N measures 2.00 m × 3.00 m and is of uniform density; that is, the mass is uniformly distributed throughout the volume. A doorknob is attached to the door as shown. Where is the center of gravity if the doorknob weighs 5.0 N and is

> A Vulcan spaceship has a mass of 65 000 kg and a Romulan spaceship is twice as massive. Both have engines that generate the same total force of 9.5 × 106 N. (a) If each spaceship fires its engine for the same amount of time, starting from rest, which wi

> If the cylinder rotates at 300.0 rev/min, what is the magnitude of the average torque required to tilt its axis by 60.0° in a time of 3.00 s? [Hint: Draw a vector diagram of the initial and final angular momenta.]

> If a feather and a lead brick are dropped simultaneously from the top of a ladder, the lead brick hits the ground first. What would happen if the experiment is repeated on the surface of the Moon?

> A baseball batter hits a long fly ball, giving it an initial velocity 45° above the horizontal. The ball rises to a maximum height of 44 m. An outfielder on the opposing team starts running at 7.6 m/s the instant the ball is hit. What is the farthest the

> At the beginning of a scene in an action movie, the 78.0 kg star, Indianapolis Jones, stands on a ledge 3.70 m above the ground and the 55.0 kg heroine, Georgia Smith, stands on the ground. Jones swings down on a rope, grabs Smith around the waist, and c

> The snow leopard (Uncia uncia) is an endangered species that lives in the mountains of central Asia. It is thought to be the longest jumper in the animal kingdom. If a snow leopard jumps at 35° above the horizontal and lands 15.0 m away on flat ground, w

> Consider the merry-go-round of Practice Problem 8.1. The child is initially standing on the ground when the merry-go-round is rotating at 0.75 rev/s. The child then hops onto the merry-go-round. How fast is the merry-go-round rotating now? By how much di

> Pendulum bob A has half the mass of pendulum bob B. Each bob is tied to a string that is 5.1 m long. When bob A is held with its string horizontal and then released, it swings down and, once bob A's string is vertical, it collides elastically with bob B.

> The rotational inertia for a diver in a pike position is about 15.5 kg·m2; it is only 8.0 kg·m2 in a tuck position. (a) If the diver gives himself an initial angular momentum of 106 kg·m2/s as he jumps off the b

> It is the bottom of the ninth inning at a baseball game. The score is tied and there is a runner on second base when the batter gets a hit. The 85 kg base runner rounds third base and is heading for home with a speed of 8.0 m/s. Just before he reaches ho

> A potentiometer is a resistor with a sliding contact. It can be used to measure emfs accurately (Problem 131) or to supply a variable voltage to a circuit (Problem 132). In the diagram with switch S1 closed and S2 open, there is no current through the ga

> A diver can change his rotational inertia by drawing his arms and legs close to his body in the tuck position. After he leaves the diving board (with some unknown angular velocity), he pulls himself into a ball as closely as possible and makes 2.00 compl

> A weightless rod, 10.0 m long, supports three weights as shown. Where is its center of gravity?

> Gerald wants to know how fast he can throw a ball, so he hangs a 2.30 kg target on a rope from a tree. He picks up a 0.50 kg ball of putty and throws it horizontally against the target. The putty sticks to the target and the putty and target swing up a v

> A spoked wheel with a radius of 40.0 cm and a mass of 2.00 kg is mounted horizontally on frictionless bearings. JiaJun puts his 0.500 kg guinea pig on the outer edge of the wheel. The guinea pig begins to run along the edge of the wheel with a speed of 2

> A radium nucleus (mass 226 u) at rest decays into a radon nucleus (symbol Rn, mass 222 u) and an alpha particle (symbol α, mass 4 u). (a) Find the ratio of the speeds vα/vRn after the decay. (b) Find the ratio of the magnitudes of the momenta pα/pRn. (

> Two otherwise identical conducting spheres carry charges of +5.0 µC and −1.0 µC. They are initially a distance L apart. The distance L is much larger than the radii of the spheres. The spheres are brought together, touched together, and then returned to

> A uniform disk with a mass of 800 g and radius 17.0 cm is rotating on frictionless bearings with an angular speed of 18.0 Hz when Jill drops a 120 g clod of clay on a point 8.00 cm from the center of the disk, where it sticks. What is the new angular spe

> A particle has a constant acceleration of 5.0 m/s2 to the east. At time t = 0, it is 2.0 m east of the origin and its velocity is 20 m/s north. What are the components of its position vector at t = 2.0 s?

> Can a body in free fall be in equilibrium? Explain.

> In Example 7.8, suppose instead that the fragment of mass 2M/3 has zero velocity immediately after the explosion. Where does the other fragment land?

> A figure skater is spinning at 10.0 rad/s with her arms extended. Her rotational inertia is 2.50 kg·m2. After pulling her arms in, her rotational inertia is 1.60 kg·m2. How much work does she do to pull her arms in while spinning?

> In each of six electric motors, a cylindrical coil with N turns and radius r is immersed in a magnetic field of magnitude B. The current in the coil is I. Rank the motors in order of the maximum torque on the coil, greatest to smallest. (a) N = 100, r =

> Two identical gliders, each with elastic bumpers and mass 0.10 kg, are on a horizontal air track. Friction is negligible. Glider 2 is stationary. Glider 1 moves toward glider 2 from the left with a speed of 0.20 m/s. They collide. After the collision, wh

> A skater is initially spinning at a rate of 10.0 rad/s with a rotational inertia of 2.50 kg·m2 when her arms are extended. What is her angular velocity after she pulls her arms in and reduces her rotational inertia to 1.60 kg·m2?

> A trap door, of length and width 1.65 m, is held open at an angle of 65.0° with respect to the floor. A rope is attached to the raised edge of the door and fastened to the wall behind the door in such a position that the rope pulls perpendicul

> A flat, circular metal disk of uniform thickness has a radius of 3.0 cm. A hole is drilled in the disk that is 1.5 cm in radius. The hole is tangent to one side of the disk. Where is the CM of the disk now that the hole has been drilled? [Hint: The origi

> Find the mass (in kg) of one molecule of CO2.

> A figure skater is spinning at a rate of 1.0 rev/s with her arms outstretched. She then draws her arms in to her chest, reducing her rotational inertia to 67% of its original value. What is her new rate of rotation?

> Plot a graph of this data for a spring resting horizontally on a table. Use your graph to find (a) the spring constant and (b) the relaxed length of the spring.

> Six flywheels have masses, thicknesses, radii, and angular speeds as given in the table. Each flywheel is a solid disk. Rank the flywheels in order of their angular momentum, smallest to largest.

> The last step in the carbon cycle CNO-I that takes place inside stars is p + 15N → 12C + (?). (a) Show that the reaction product “(?)” must be an alpha particle. (b) How much energy is released by this step of the cycle? (c) In order for this reaction

> The graph for this problem shows the vertical velocity component vy of a bouncing ball as a function of time. The y-axis points up. Answer these questions based on the data in the graph. (a) At what time does the ball reach its maximum height? (b) For h

> A gold wire and an aluminum wire have the same dimensions and carry the same current. The electron density (in electrons/cm3) in aluminum is three times larger than the density in gold. How do the drift speeds of the electrons in the two wires, vAu and v

> Can the velocity of an object be nonzero and the acceleration be zero at the same time? Explain.

> Suppose that a radioactive sample contains equal numbers of two radioactive nuclides A and B at t = 0. A has a half-life of 3.0 h, whereas B has a half-life of 12.0 h. Find the ratio of the decay rates or activities RA/RB at (a) t = 0, (b) t = 12.0 h,

> A uniform disk of mass 5.00 kg has a radius of 0.100 m and spins with a frequency of 0.550 rev/s. What is its angular momentum?

> Hilda holds a gardening book of weight 10 N at a height of 1.0 m above her patio for 50 s. How much work does she do on the book during that 50 s?

> As shown in the top-view diagram, a 46.4 N force is applied to the outer edge of a door of width 1.26 m in such a way that it acts (a) perpendicular to the door, (b) at an angle of 43.0° with respect to the door surface, (c) so that the line

> The natural abundance of deuterium in water is 0.0156% (i.e., 0.0156% of the hydrogen nuclei in water are 2H). If the fusion reaction (2H + 2H) yields 3.65 MeV of energy on average, how much energy could you get from 1.00 L of water? (There are two react

> The string in a yo-yo is wound around an axle of radius 0.500 cm. The yo-yo has both rotational and translational motion, like a rolling object, and has mass 0.200 kg and outer radius 2.00 cm. Starting from rest, it rotates and falls a distance of 1.00 m

> Radon gas (Rn) is produced by the alpha decay of radium / . (a) How many neutrons and how many protons are present in the nucleus of the isotope of Rn produced by this decay? (b) The air in a student’s basement apartment contains 1.0 × 107 Rn nuclei. T

> A solid sphere of mass 0.600 kg rolls without slipping along a horizontal surface with a translational speed of 5.00 m/s. It comes to an incline that makes an angle of 30° with the horizontal surface. Ignoring energy losses due to friction, to what verti

> A neutron star is a star that has collapsed into a collection of tightly packed neutrons. Thus, it is something like a giant nucleus; but since it is electrically neutral, there is no Coulomb repulsion to break it up. The force holding it together is gra

> A solid sphere is released from rest and allowed to roll down a board that has one end resting on the floor and is tilted at 30° with respect to the horizontal. If the sphere is released from a height of 60 cm above the floor, what is the sphere's speed

> Repeat Problem 50 if the magnetic field is 2.5 T in the plane of the loop, 60.0° below the +x-axis.

> Suppose a charge q is placed at point x = 0, y = 0. A second charge q is placed at point x = 8.0 m, y = 0. What charge must be placed at the point x = 4.0 m, y = 0 in order that the field at the point x = 4.0 m, y = 3.0 m be zero?

> Explain why an ideal spring must exert forces of equal magnitude on the objects attached to each end, even if the spring itself has a nonzero acceleration. [Hint: Use one of Newton’s laws of motion and remember that an ideal spring has zero mass.] Is the

> You drop a stone into a deep well and hear it hit the bottom 3.20 s later. This is the time it takes for the stone to fall to the bottom of the well, plus the time it takes for the sound of the stone hitting the bottom to reach you. Sound travels about 3

> The invention of the cannon in the fourteenth century made the catapult unnecessary and ended the safety of castle walls. Stone walls were no match for balls shot from cannons. Suppose a cannonball of mass 5.00 kg is launched from a height of 1.10 m, at

> A hydrogen atom in its ground state is immersed in a continuous spectrum of ultraviolet light with wavelengths ranging from 96 nm to 110 nm. After absorbing a photon, the atom emits one or more photons to return to the ground state. (a) What wavelength(

> A hollow cylinder, a uniform solid sphere, and a uniform solid cylinder all have the same mass m. The three objects are rolling on a horizontal surface with identical translational speeds v. Find their total kinetic energies in terms of m and v and order

> Can the velocity of an object be zero and the acceleration be nonzero at the same time? Explain.

> Any pair of equal and opposite forces acting on the same object is called a couple. Consider the couple in part (a) of the figure. The rotation axis is perpendicular to the page through point P. (a) Show that the magnitude of the net torque is equal to

> Suppose that you have a glass tube filled with atomic hydrogen gas (H, not H2).Assume that the atoms start out in their ground states. You illuminate the gas with monochromatic light of various wavelengths, ranging through the entire IR, visible, and UV

> A solid cylinder (mass 160 g, radius 2.0 cm) rolls without slipping at a speed of 5.0 cm/s. What is its total kinetic energy?

> Follow the steps outlined in this problem to estimate the time lag (predicted classically but not observed experimentally) in the photoelectric effect. Let the intensity of the incident radiation be 0.01 W/m2. (a) If the area of the atom is (0.1 nm)2, f

> A solid sphere is rolling without slipping down a board that is tilted at an angle of 35° with respect to the horizontal. What is its acceleration?

> A spaceship passes over an observation station on Earth. Just as the nose of the ship passes the station, a light in the nose of the ship flashes. As the tail of the ship passes the station, a light flashes in the ship's tail. According to an Earth obser

> When is the first time for t > 0 that the string looks exactly as it does at t = 0?

> A town is planning on using the water flowing through a river at a rate of 5.0 × 106 kg/s to carry away the heat from a new power plant. Environmental studies indicate that the temperature of the river should only increase by 0.50°C. The maximum design e

> Why would we expect atmospheric testing of nuclear weapons to increase the relative abundance of carbon-14 in the atmosphere? Why would we expect the widespread burning of fossil fuels to decrease the relative abundance of carbon-14 in the atmosphere?

> Why can we ignore the binding energies of the atomic electrons in calculations such as Example 29.4? Isn’t there a mass defect due to the binding energy of the electrons?

> In a CRT television, electrons of kinetic energy 2.0 keV strike the screen. No EM radiation is emitted below a certain wavelength. Calculate this wavelength.

> Explain why neutron-activated nuclides tend to decay by β− rather than β+.

> Jorge is going to bungee jump from a bridge that is 55.0 m over the river below. The bungee cord has an unstretched length of 27.0 m. To be safe, the bungee cord should stop Jorge’s fall when he is at least 2.00 m above the river. If Jorge has a mass of

> Why is a slow neutron more likely to induce a nuclear reaction (as in neutron activation and induced fission) than a proton with the same kinetic energy?

> What technique could Becquerel and others have used to determine that alpha rays are positively charged, beta rays negatively charged, and gamma rays uncharged? Explain how they could find that alpha rays have a charge-to-mass ratio half that of the H+ i

> Why does a fission reaction tend to release one or more neutrons? Why is the release of neutrons necessary in order to sustain a chain reaction?

> A square brass plate, 8.00 cm on a side, has a hole cut into its center of area 4.908 74 cm2 (at 20.0°C). The hole in the plate is to slide over a cylindrical steel shaft of cross-sectional area 4.910 00 cm2 (also at 20.0°C). To wha

> Why would a fusion reactor produce less radioactive waste than a fission reactor? [Hint: Compare the products of a fission reaction with those from a fusion reaction.]

> Fission reactors and cyclotrons tend to produce different kinds of isotopes. A reactor produces isotopes primarily through neutron activation; thus, the isotopes tend to be neutron-rich (high neutron-to- proton ratio). A cyclotron can only accelerate cha

> Hydrogen bonding is responsible for many of the unusual properties of water (see Sec. 16.1). A simplified model represents a hydrogen bond as the electrostatic interaction of four point charges arranged along a straight line, as shown in the figure. (a)

> Radioactive alpha emitters are relatively harmless outside the body, but can be dangerous if ingested or inhaled. Explain.

> Radon-222 is created in a series of radioactive decays starting with / and ending with / . The half-life of 222Rn is 3.8 days. (a) If the half-life is so short, why hasn’t all the 222Rn gas decayed by now? (b) If the half-life of 222Rn were much sho

> How could Henri Becquerel and other scientists determine that there were three different kinds of radiation before having determined the electric charges or masses of the alpha, beta, and gamma rays?

> The Lyman series in the hydrogen emission spectrum is formed by electron transitions from an excited state to the ground state. Calculate the longest three wavelengths in the Lyman series.

> In an optically pumped laser, the light that causes optical pumping is always shorter in wavelength than the laser beam. Explain.

> Describe some differences between the beam of light from a flashlight and from a laser.

> A 0.500 kg block of iron at 60.0°C is placed in contact with a 0.500 kg block of iron at 20.0°C. (a) The blocks soon come to a common temperature of 40.0°C. Estimate the entropy change of the universe when this occurs. [Hint: Assume that all the heat flo

> How should we interpret electron cloud representations of electron states in atoms?

> A steel sphere with radius 1.0010 cm at 22.0°C must slip through a brass ring that has an internal radius of 1.0000 cm at the same temperature. To what temperature must the brass ring be heated so that the sphere, still at 22.0°C, can just slip through?

> What is the length of a simple pendulum whose horizontal position is described by What assumption do you make when answering this question?

> Light of wavelength 0.500 µm (in air) enters the water in a swimming pool. The speed of light in water is 0.750 times the speed in air. What is the wavelength of the light in water?