Animals that can run fast always have thin legs. Their leg muscles are concentrated close to the hip joint; only tendons extend into the lower leg. Using the concept of rotational inertia, explain how this helps them run fast.
> A 6.0 kg object is at rest on a frictionless surface when it is struck head-on by a 2.0 kg object moving at 10 m/s. If the collision is elastic, what is the speed of the 6.0 kg object after the collision? [Hint: You will need two equations.]
> In an experiment to measure the index of refraction of human skin, it was found that if a beam of unpolarized light was shone on a skin sample from air at an incident angle of 54.7°, the reflected light was completely polarized. What is the index of refr
> What is the index of refraction of the core of an optical fiber if the cladding has n = 1.20 and the critical angle at the core-cladding boundary is 45.0°?
> (a) Find the potential at points a and b in the following diagram for charges Q1 = +2.50 nC and Q2 = −2.50 nC. (b) How much work must be done by an external agent to bring a point charge q from infinity to point b?
> Sketch the shape of the string at t = 1.6 s.
> Light rays from the Sun, which is at an angle of 35° above the western horizon, strike the still surface of a pond. (a) What is the angle of incidence of the Sun's rays on the pond? (b) What is the angle of reflection of the rays that leave the pond su
> Sketch the shape of the string at t = 2.2 s.
> The intensity of sunlight that reaches Earth's atmosphere is 1400 W/m2. What is the intensity of the sunlight that reaches Jupiter? Jupiter is 5.2 times as far from the Sun as Earth. [Hint: Treat the Sun as an isotropic source of light waves.]
> A motor scooter travels east at a speed of 12 m/s. The driver then reverses direction and heads west at 15 m/s. What is the change in velocity of the scooter? Give magnitude and direction.
> Compare the orbital radii of the He+ and H atoms for levels of equal energy (not the same value of n). Can you draw a general conclusion from your results?
> The radioactive decay of 238U produces alpha particles with a kinetic energy of 4.17 MeV. (a) At what speed do these alpha particles move? (b) Put yourself in the place of Rutherford and Geiger. You know that alpha particles are positively charged (fro
> (a) Using the result of Problem 26, calculate the numerical aperture of a fiber-optic cable whose cladding and core have indices of refraction 1.40 and 1.62, respectively. (b) Light enters the fiber from a balloon of saline solution (n = 1.35), which is
> A useful measure of the quality of a fiber-optic cable such as those used in endoscopes and other medical equipment is the numerical aperture. The larger the numerical aperture, the more light will be carried by the fiber. If light is incident on the fib
> The figure shows some light rays reflected from a small defect in the glass toward the surface of the glass. (a) If θc = 40.00°, what is the index of refraction of the glass? (b) Is there any point above the glass at which a vie
> Is there a critical angle for a light ray coming from a medium with an index of refraction 1.2 and incident on a medium that has an index of refraction 1.4? If so, what is the critical angle that allows total internal reflection in the first medium?
> (a) Find the electric potential at points a and b for charges of +4.2 nC and −6.4 nC located as shown in the following figure. (b) What is the potential difference ΔV for a trip from b to a? (c) How much work must be done
> The prism in the figure is made of crown glass. Its index of refraction ranges from 1.517 for the longest visible wavelengths to 1.538 for the shortest. Find the range of refraction angles for the light transmitted into air through the right side of the
> In Figure 23.11, a coin is right up against the far edge of the mug. In picture (a) the coin is just hidden from view and in picture (b) we can almost see the whole coin. If the mug is 6.5 cm in diameter and 8.9 cm tall, what is the diameter of the coi
> Why is it that your own voice sounds strange to you when you hear it played back on a tape recorder, but your friends all agree that it is just what your voice sounds like? [Hint: Consider the medium through which the sound wave travels when you usually
> A glass lens has a scratch-resistant plastic coating on it. The speed of light in the glass is 0.67c, and the speed of light in the coating is 0.80c. A ray of light in the coating is incident on the plastic-glass boundary at an angle of 12.0° with respec
> In a certain region of space, there is a uniform electric field V/m directed due east and a uniform magnetic field / also directed due east. What is the electromagnetic force on an electron moving due south at 5.0 × 106 m/s?
> The Wheatstone bridge is a circuit used to measure unknown resistances. The bridge in the figure is balanced—no current flows through the galvanometer G (a sensitive detector of current whose operation is based on magnetic forces). (a) What is the unkno
> A bicycle travels 3.2 km due east in 0.10 h, then 4.8 km at 15.0° east of north in 0.15 h, and finally another 3.2 km due east in 0.10 h to reach its destination. The time lost in turning is negligible. What is the average velocity for the entire trip?
> In a synchrotron, charged particles are accelerated as they travel around in circles; in a linear accelerator they move in a straight line. What are some of the advantages and disadvantages of each design?
> In Fig. 20.6, side 3 of the rectangular coil in the electric generator rotates about the axis at constant angular speed m. The figure with this problem shows side 3 by itself. (a) First consider the right half of side 3. Although the speed of the wire d
> A beam of light in air is incident on a stack of four flat transparent materials with indices of refraction 1.20, 1.40, 1.32, and 1.28. If the angle of incidence for the beam on the first of the four materials is 60.0°, what angle does the beam make with
> A 58 kg astronaut is in space, far from any objects that would exert a significant gravitational force on him. He would like to move toward his spaceship, but his jet pack is not functioning. He throws a 720 g socket wrench with a velocity of 5.0 m/s in
> A uniform solid cylinder rolls without slipping down an incline. A hole is drilled through the cylinder along its axis. The radius of the hole is 0.50 times the (outer) radius of the cylinder. (a) Does the cylinder take more or less time to roll down th
> At a point due east of the transmitter, how should a magnetic dipole antenna be oriented to serve as a receiver?
> A sign along the road in Tompkins County reads, “State Law: Noise Limit, 90 decibels.” If you were subjected to such a noise level for an extended period of time, would you need to worry about your hearing being affected?
> The nucleus in a / atom captures one of the atom’s electrons, changing the nucleus to / and emitting a neutrino. What is the total energy of the emitted neutrino? [Hint: You can use the classical expression for the kinetic energy of the / atom
> Rachel is on the roof of a building, h meters above ground. She throws a heavy ball into the air with a speed v, at an angle θ with respect to the horizontal. Ignore air resistance. (a) Find the speed of the ball when it hits the ground in terms of h, v
> At a point due east of the transmitter, what is the direction of the wave’s electric field?
> A point charge q1 = +5.0 µC is fixed in place at x = 0, and a point charge q2 = −3.0 µC is fixed at x = −20.0 cm. Where can we place a point charge q3 = −8.0 µC so that the net electric force on q1 due to q2 and q3 is zero?
> The radio telescope in Arecibo, Puerto Rico, has a diameter of 305 m. It can detect radio waves from space with intensities as small as 10−26 W/m2. (a) What is the average power incident on the telescope due to a wave at normal incidence with intensity
> Fernando detects the electric field from an isotropic source that is 22 km away by tuning in an electric field with an rms amplitude of 55 mV/m. What is the average power of the source?
> A 1.0 m2 solar panel on a satellite that keeps the panel oriented perpendicular to radiation arriving from the Sun absorbs 1.4 kJ of energy every second. The satellite is located at 1.00 AU from the Sun. (The Earth-Sun distance is approximately 1 AU.) Ho
> A car is speeding up and has an instantaneous velocity of 1.0 m/s in the +x-direction when a stopwatch reads 10.0 s. It has a constant acceleration of 2.0 m/s2 in the +x-direction. (a) What is the speed when the stopwatch reads 12.0 s? (b) How far does t
> Julia is delivering newspapers. Suppose she is driving at 15 m/s along a straight road and wants to drop a paper out the window from a height of 1.00 m so it slides along the shoulder and comes to rest in the customer's driveway. At what horizontal dista
> Jennifer lifts a 2.5 kg carton of cat litter from the floor to a height of 0.75 m, starting and ending with the carton held at rest. (a) How much total work is done on the carton during this operation? Jennifer then pours 1.2 kg of the litter into the c
> For low-frequency sounds, the ear uses the phase difference between the sound waves arriving at the two ears to determine direction. Why can't the ear reliably use phase difference for high- frequency sounds? Explain.
> In any hydraulic system, it is important to “bleed” air out of the line. Why?
> It is easier to get a good draft in a chimney on a windy day than when the outside air is still, all other things being equal. Why?
> Your ears “pop” when you change altitude quickly—such as during takeoff or landing in an airplane, or during a drive in the mountains. Curiously, if you are a passenger in a high-speed train, your ears sometimes pop as the speed of the train increases ra
> Before getting an oil change, it is a good idea to drive a few miles to warm up the engine. Why?
> Bernoulli’s equation applies only to steady flow. Yet Bernoulli’s equation allows the fluid velocity at one point to be different than the velocity at another point. For the fluid velocity to change, the fluid must be accelerated as it moves from one poi
> Does a manometer (with one side open) measure absolute pressure or gauge pressure? How about a barometer? A tire pressure gauge? A sphygmomanometer?
> An ideal solenoid has length I. If the windings are compressed so that the length of the solenoid is reduced to 0.50ℓ, what happens to the inductance of the solenoid?
> The bungee jumper of Example 6.4 made a jump into the Gorge du Verdon in southern France from a platform 182 m above the bottom of the gorge. The jumper weighed 780 N and came within 68 m of the bottom of the gorge. The cord’s unstretched length is 30.0
> A parallel plate capacitor has a charge of 0.020 µC on each plate with a potential difference of 240 V. The parallel plates are separated by 0.40 mm of air. What energy is stored in this capacitor?
> A cell membrane has a surface area of 1.1×10−7 m2, a dielectric constant of 5.2, and a thickness of 7.2 nm. The potential difference across the membrane is 70 mV. (a) What is the magnitude of the charge on each surface of the membrane? (b) How many ion
> A large barrel lies on its side. In order to roll it across the floor, you apply a horizontal force, as shown in the figure. If the applied force points toward the axis of rotation, which runs down the center of the barrel through the center of mass, it
> Four brass wires are subjected to the same tensile stress. The wires have unstretched lengths and diameters as follows. Rank the four wires in decreasing order of the amount of stretch. (a) length L, diameter d (b) length 2L, diameter d (c) length 4L,
> 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.
