The particle in a box model is often used to make rough estimates of energy level spacings. Suppose that you have a proton confined to a one-dimensional box of length equal to a nuclear diameter (about 10−14 m). (a) What is the energy difference between the first excited state and the ground state of this proton in the box? (b) If this energy is emitted as a photon as the excited proton falls back to the ground state, what is the wavelength and frequency of the electromagnetic wave emitted? In what part of the spectrum does it lie?
> In the “Pinewood Derby,” Cub Scouts construct cars and then race them down an incline. Some say that, everything else being equal (friction, drag coefficient, same wheels, etc.), a heavier car will win; others maintain that the weight of the car does not
> If a man has an average useful power output of 40.0 W, what minimum time would it take him to lift fifty 10.0 kg boxes to a height of 2.00 m?
> Why do many helicopters have a small propeller attached to the tail that rotates in a vertical plane? Why is this attached at the tail rather than somewhere else? [Hint: Most of the helicopter's mass is forward, in the cab.]
> A pinhole camera doesn't have a lens; a small circular hole lets light into the camera, which then exposes the film. For the sharpest image, light from a distant point source makes as small a spot on the film as possible. What is the optimum size of the
> An object in equilibrium has only two forces acting on it. The forces must be equal in magnitude and opposite in direction in order to give a translational net force of zero. What else must be true of the two forces for the object to be in equilibrium? [
> Paula swims across a river that is 10.2 m wide. She can swim at 0.833 m/s in still water, but the river flows with a speed of 1.43 m/s. If Paula swims in such a way that she crosses the river in as short a time as possible, how far downstream is she when
> A book measures 3 cm by 16 cm by 24 cm. About which of the axes shown in the figure is its rotational inertia smallest?
> Capacitors are used in many applications where you need to supply a short burst of energy. A 100.0 µF capacitor in an electronic flash lamp supplies an average power of 10.0 kW to the lamp for 2.0 ms. (a) To what potential difference must the capacitor i
> Why is it easier to push open a swinging door from near the edge away from the hinges rather than in the middle of the door?
> One of the effects of significant global warming is the melting of part or all of the polar ice caps. This, in turn, would change the length of the day (the period of Earth's rotation). Explain why. Would the day get longer or shorter?
> One way to find the center of gravity of an irregular flat object is to suspend it from various points so that it is free to rotate. When the object hangs in equilibrium, a vertical line is drawn downward from the support point. After drawing lines from
> In a region where there is an electric field, the electric forces do +8.0 × 10−19 J of work on an electron as it moves from point X to point Y. (a) Which point, X or Y, is at a higher potential? (b) What is the potential difference, VY − VX, between poi
> Explain why it is easier to drive a wood screw using a screwdriver with a large-diameter handle rather than one with a thin handle.
> A tightrope walker who weighs 640 N walks along a steel cable. When he is halfway across, the cable makes an angle of 0.040 rad below the horizontal. (a) What is the strain in the cable? Assume the cable is horizontal with a tension of 80 N before he st
> The rotor is an amusement park ride where people stand against the inside of a cylinder. Once the cylinder is spinning fast enough, the floor drops out. (a) What force keeps the people from falling out the bottom of the cylinder? (b) If the coefficient
> Five ideal mass-spring systems are described in Problem 36. Rank them in decreasing order of their total energy.
> You are riding your bicycle and approaching a rather steep hill. Which gear should you use to go uphill, a low gear or a high gear? With a low gear the wheel rotates less than with a high gear for one rotation of the pedals.
> Poiseuille's law [Eq. (9-41)] gives the volume flow rate of a viscous fluid through a pipe. (a) Show that Poiseuille's law can be written in the form ΔP = IR, where I = ΔV/Δt represents the volume flow rate and R is a constant of proportionality called
> (a) What is the equivalent resistance between points A and B? (b) A 276 V emf is connected to the terminals A and B. What is the current in the 12 Ω resistor?
> In this problem, you can show from Coulomb’s law that the constant of proportionality in Gauss’s law must be 1/ϵ0. Imagine a sphere with its center at a point charge q. (a) Write an expression for the electric flux in terms of the field strength E and t
> Your door is hinged to close automatically after being opened. Where is the best place to put a wedge-shaped door stopper on a slippery floor in order to hold the door open? Should it be placed close to the hinge or far from it?
> An astronaut wants to remove a bolt from a satellite in orbit. He positions himself so that he is at rest with respect to the satellite, then pulls out a wrench and attempts to remove the bolt. What is wrong with his method? How can he remove the bolt?
> The forces required to extend a spring to various lengths are measured. The results are shown in the following table. Using the data in the table, plot a graph that helps you to answer the following two questions: (a) What is the spring constant? (b) W
> The center of gravity of the upper body of a bird is located below the hips; in a human, the center of gravity of the upper body is located well above the hips. Since the upper body is supported by the hips, are birds or humans more stable? Consider what
> Explain why the posture taken by defensive football linemen makes them more difficult to push out of the way. Consider both the height of the center of gravity and the size of the support base (the area on the ground bounded by the hands and feet touchin
> The figure shows a balancing toy with weights extending on either side. The toy is extremely stable. It can be pushed quite far off center one way or the other but it does not fall over. Explain why it is so stable.
> The potential difference across a cell membrane is −90 mV. If the membrane's thickness is 10 nm, what is the magnitude of the electric field in the membrane? Assume the field is uniform.
> A playground merry-go-round (see Fig. 8.5) spins with negligible friction. A child moves from the center out to the rim of the merry- go-round platform. Let the system be the merry-go-round plus the child. Which of these quantities change: angular veloci
> A boat that can travel at 4.0 km/h in still water crosses a river with a current of 1.8 km/h. At what angle must the boat be pointed upstream to travel straight across the river? In other words, in what direction is the velocity of the boat relative to t
> In Section 8.6, it was asserted that the sum of all the internal torques (i.e., the torques due to internal forces) acting on a rigid object is zero. The figure shows two particles in a rigid object. The particles exert forces / and / on each other
> A parallel plate capacitor is composed of two square plates, 10.0 cm on a side, separated by an air gap of 0.75 mm. (a) What is the charge on this capacitor when there is a potential difference of 150 V between the plates? (b) What energy is stored in
> A solenoid is made of 300.0 turns of wire, wrapped around a hollow cylinder of radius 1.2 cm and length 6.0 cm. What is the self- inductance of the solenoid?
> Part (a) of the figure shows a simplified model of how the biceps muscle enables the forearm to support a load. What are the advantages of this arrangement as opposed to the alternative shown in part (b), where the flexor muscle is in the forearm instead
> Five ideal mass-spring systems are described by their masses, spring constants, and amplitudes of oscillation as follows. Rank them in decreasing order of the frequency of oscillations. (a) mass m, spring constant k, amplitude A (b) mass 2m, spring con
> Part (a) of the figure shows a simplified model of how the triceps muscle connects to the forearm. As the angle θ is changed, the tendon wraps around a nearly circular arc. Explain how this is much more effective than if the tendon is connec
> A 4.0 kg block is released from rest at the top of a frictionless plane of length 8.0 m that is inclined at an angle of 15° to the horizontal. A cord is attached to the block and trails along behind it. When the block reaches a point 5.0 m alo
> In Fig. 8.2b, where should the doorknob be located to make the door easier to open?
> In your own words, phrase each of Newton's three laws of motion as a statement about momentum.
> A refracting telescope is 36.4 cm long and has a 6.0 cm diameter aperture. The magnifying power is 90.0. (a) What are the focal lengths of the lenses? (b) What is the diffraction limit on the minimum angular separation of objects that the telescope can
> Sonya is designing a diffraction experiment for her students. She has a laser that emits light of wavelength 627 nm and a grating with a distance of 2.40 × 10−3 mm between slits. She hopes to shine the light through the grating and display a total of nin
> In a uniform electric field of magnitude E, the field lines cross through a rectangle of area A at an angle of 60.0° with respect to the plane of the rectangle. What is the flux through the rectangle?
> Two cars, each of mass 1300 kg, are approaching each other on a head-on collision course. Each speedometer reads 19 m/s. What is the magnitude of the total momentum of the system?
> What is the tension in the string when the ball hangs straight down at rest?
> Many home heating systems operate by pumping hot water through radiator pipes. The flow of the water to different “zones” in the house is controlled by zone valves that open in response to thermostats. The opening and
> A radioactive nucleus is at rest when it spontaneously decays by emitting an electron and neutrino. The momentum of the electron is 8.20 × 10−19 kg·m/s, and it is directed at right angles to that of the neutri
> Mary and Daryl are new to the sport of rock climbing. Mary says she wants a stiff rope because a stiff rope is a strong rope. Daryl insists that a good climbing rope must have some stretch. Who is correct, and why?
> Which would be more effective: a hammer that collides elastically with a nail, or one that collides perfectly inelastically? Assume that the mass of the hammer is much larger than that of the nail.
> An astronaut hits a golf ball on the surface of the Moon. Is the momentum of the ball conserved while it is in flight? Is there a component of its momentum that is conserved?
> An astronaut in deep space is taking a space walk when the tether connecting him to his spaceship breaks. How can he get back to the ship? He doesn't have a rocket propulsion backpack, unfortunately, but he is carrying a big wrench.
> A plane weighing 220 kN (25 tons) lands on an aircraft carrier. The plane is moving horizontally at 67 m/s (150 mi/h) when its tailhook grabs hold of the arresting cables. The cables bring the plane to a stop in a distance of 84 m. (a) How much work is
> A firecracker at rest explodes, sending fragments off in all directions. Initially the firecracker has zero momentum, but after the explosion the fragments flying off each have quite a lot of momentum. Hasn't momentum been created? If not, explain why no
> Figure 17.31b shows a thundercloud before a lightning strike has occurred. The bottom of the thundercloud and Earth's surface might be modeled as a charged parallel plate capacitor. The base of the cloud, which is roughly parallel to Earth's surface, ser
> If you take a rifle and saw off part of the barrel, the muzzle speed (the speed at which bullets emerge from the barrel) will be smaller. Why?
> A force of 30 N is applied for 5 s to each of two objects of different masses. (a) Which one has the greater momentum change? (b) The greater velocity change? (c) The greater acceleration?
> Micah is standing on his frictionless skateboard facing a concrete wall. He wants to project himself backward by throwing small balls at the wall. His friend Jeremy says that Micah need not throw the balls against the wall, he just needs to throw the bal
> A lambda particle (Λ) decays at rest to a proton and pion through the reaction Λ → p + π−. The rest energies of the particles are: Λ, 1115.7 MeV; p, 938.3 MeV; and π−, 139.6 MeV. Use conservation of energy and momentum to determine the kinetic energies o
> At an antique car rally, a Stanley Steamer automobile travels north at 40 km/h and a Pierce Arrow automobile travels east at 50 km/h. Relative to an observer riding in the Stanley Steamer, what are the x- and y-components of the velocity of the Pierce Ar
> Two parallel plates are 4.0 cm apart. The bottom plate is charged positively and the top plate is charged negatively, producing a uniform electric field of 5.0 × 104 N/C in the region between the plates. What is the time required for an electron, which s
> A planet with a radius of 6.00 × 107 m has a gravitational field of magnitude 30.0 m/s2 at the surface. What is the escape speed from the planet?
> A baseball batting coach emphasizes the importance of “follow- through” when a batter is trying for a home run. The coach explains that the follow-through keeps the bat in contact with the ball for a longer time so the ball will travel a greater distance
> An ideal spring has a spring constant k = 20.0 N/m. What is the amount of work that must be done to stretch the spring 0.40 m from its relaxed length?
> In the “executive toy,” two balls are pulled back and then released. After the collision, two balls move away on the opposite side. Why do we never see three balls move away following this action, although with a lower
> Two coherent sound waves have intensities of 0.040 W/m2 and 0.090 W/m2 where you are listening. (a) If the waves interfere constructively, what is the intensity that you hear? (b) What if they interfere destructively? (c) If they were incoherent, what
> In an egg toss, two people try to toss a raw egg back and forth without breaking it as they move farther and farther apart. Discuss a strategy in terms of impulse and momentum for catching the egg without breaking it.
> The momentum of a system can only be changed by an external force. What is the external force that changes the momentum of a bicycle (with its rider) as it speeds up, slows down, or changes direction? Is it true that changes in the bicycle's kinetic ener
> A top fuel drag racer with a mass of 500.0 kg completes a quarter- mile (402 m) drag race in a time of 4.2 s starting from rest. The car’s final speed is 125 m/s. What is the engine’s average power output? Ignore friction and air resistance.
> A woman is 1.60 m tall. When standing straight, is her CM necessarily 0.80 m above the floor? Explain.
> Two solenoids, of N1 and N2 turns respectively, are wound on the same form. They have the same length â„“ and radius r. (a) If an ac current flows in solenoid 1 (N1 turns), write an expression for the total flux through solenoid 2 as a f
> Two objects with different masses have the same kinetic energy. Which has the larger magnitude of momentum?
> An airplane has a velocity relative to the ground of 210 m/s toward the east. The pilot measures his airspeed (the speed of the plane relative to the air) to be 160 m/s. What is the minimum wind velocity possible?
> You are trapped on the second floor of a burning building. The stairway is impassable, but there is a balcony outside your window. Describe what might happen in the following situations. (a) You jump from the second-story balcony to the pavement below,
> (a) Find the electric flux through each side of a cube of edge length a in a uniform electric field of magnitude E. The field direction is perpendicular to two of the faces. (b) What is the total flux through the cube?
> (a) Calculate the net electric force acting on the dipole. (b) Show that the magnitude of the torque on the dipole is τ = qEd sin θ. (c) Calculate the torque acting on the dipole for θ = 0, 36.9°, and 90.0°.
> A cheetah can accelerate from rest to 24 m/s in 2.0 s. Assuming the acceleration is constant over the time interval, (a) what is the magnitude of the acceleration of the cheetah? (b) What is the distance traveled by the cheetah in these 2.0 s? (c) A r
> A bicycle rider notices that he is approaching a steep hill. Explain, in terms of energy, why the bicyclist pedals hard to gain as much speed as possible on level road before reaching the hill.
> A gymnast is swinging in a vertical circle about a crossbar. In terms of energy conservation, explain why the speed of the gymnast’s body is slowest at the top of the circle and fastest at the bottom.
> When a ball is dropped to the floor from a height h, it strikes the ground and briefly undergoes a change of shape before rebounding to a maximum height less than h. Explain why it does not return to the same height h.
> A roller coaster car (mass = 988 kg including passengers) is about to roll down a track. The diameter of the circular loop is 20.0 m and the car starts out from rest 40.0 m above the lowest point of the track. Ignore friction and air resistance. (a) At
> A green laser has a wavelength of 532 nm. A grating and a lens are used to split the beam into three parallel beams spaced 1.85 cm apart. (a) What range of slit spacings can the grating have to produce three and only three beams? (b) If the slit spacing
> The field between the plates of a parallel plate capacitor, E = Q/(ϵ0A), is due to the superposition of equal contributions from the charges on the two plates. Therefore, each plate exerts an electric force on the other. (a) Find the magnitude of this f
> In the design of a roller coaster, is it possible for any hill of the ride to be higher than the first one? If so, how?
> Can static friction do work? If so, give an example. [Hint: Static friction acts to prevent relative motion along the contact surface.]
> A car is driving directly north on the freeway at a speed of 110 km/h, and a truck is leaving the freeway driving 85 km/h in a direction that is 35° west of north. What is the velocity of the truck relative to the car?
> 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?
> A copper washer is to be fit in place over a steel bolt. Both pieces of metal are at 20.0°C. If the diameter of the bolt is 1.0000 cm and the inner diameter of the washer is 0.9980 cm, to what temperature must the washer be raised so it will fit over the
> A mango falls to the ground. During the fall, does Earth’s gravitational field do positive or negative work Wm on the mango? Does the mango’s gravitational field do positive or negative work WE on Earth? Compare the signs and the magnitudes of Wm and WE.
> Why do roads leading to the top of a mountain have switchbacks that wind back and forth? [Hint: Think of the road as an inclined plane.]
> An infinitely long conducting cylinder sits near an infinite conducting sheet (side view in the diagram). The cylinder and sheet have equal and opposite charges; the cylinder is positive. (a) Sketch some electric field lines. (b) Sketch some equipotent
> You are standing on a balcony overlooking the beach. You throw a ball straight up into the air with speed vi and throw an identical ball straight down with speed vi. Ignoring air resistance, how do the speeds of the balls compare just before they hit the
> Why might an elevator cable break during acceleration when lifting a lighter load than it normally supports at rest or at constant velocity?
> If air resistance is ignored, what force(s) act on an object in free fall?
> An ideal transformer takes an ac voltage of amplitude 170 V as its input and supplies a 7.8 V amplitude to a circuit that converts it to dc. The primary has 300 turns. (a) How many turns does the secondary have? (b) When the circuit uses a power of 5.0
> If the trajectory is parabolic in one reference frame, is it always, never, or sometimes parabolic in another reference frame that moves at constant velocity with respect to the first reference frame? If the trajectory can be other than parabolic, what e
> What is the acceleration of an object thrown straight up into the air at the highest point of its motion? Does the answer depend on whether air resistance is negligible or not? Explain.
> Is it possible for two identical projectiles with identical initial speeds, but with two different angles of elevation, to land in the same spot? Explain. Ignore air resistance and sketch the trajectories.
> A large parallel plate capacitor with air between the plates has plate separation 1.00 cm and plate area 314 cm2. The capacitor is connected to a 20.0 V battery and then disconnected. How much work is done on the capacitor as the plate separation is incr
> A Nile cruise ship takes 20.8 h to go upstream from Luxor to Aswan, a distance of 208 km, and 19.2 h to make the return trip downstream. Assuming the ship’s speed relative to the water is the same in both cases, calculate the speed of the current in the
> How much work is done on the bowstring of Example 6.9 to draw it back by 20.0 cm? [Hint: Rather than recalculate from scratch, use proportional reasoning.]
> You are on the Moon and would like to send a probe into space so that it does not fall back to the surface of the Moon. What launch speed do you need?
> Each prong of a vibrating tuning fork moves back and forth quite precisely in simple harmonic motion. 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 an
