Bouncing Ball A 650-gram rubber ball is dropped from an initial height of 250 m, and on each bounce it returns to 75% of its previous height (a) What is the initial mechanical energy of the ball,...

A demonstration gyroscope wheel is constructed by removing the tire from a bicycle wheel 0.650 m in diameter, wrapping lead wire around the rim, and taping it in place. The shaft projects 0.200 m at...

(a) What is the power of a 20.5-cm-focal-length lens? (b) What is the focal length of a 6.25-diopter lens? (c) Are these lenses converging or diverging?

A small block with a mass of 0.120 kg is attached to a cord passing through a hole in a frictionless, horizontal surface (Fig. 6.34). The block is originally revolving at a distance of 0.40 m from...

A current of 17.0 mA is maintained in a single circular loop of 2.00 m circumference. A magnetic field of 0.800 T is directed parallel to the plane of the loop. (a) Calculate the magnetic moment of...

Knocking Over a Post One end of a post weighing 400 N and with height h rests on a rough horizontal surface with p" = 0.30. The upper end is held by a rope fastened to the surface and making an angle...

A uniform rod of length L oscillates through small angles about a point a distance x from its center. (a) Prove that its angular frequency is Vgx/[(L2/12) + x']. (b) Show that its maximum angular...

A boat with initial speed v0 is launched on a lake. The boat is slowed by the water by a force F = ae. (a) Find an expression for the speed v (t). (b) Find the time and (c) Distance for the boat to...

A sled starts from rest at the top of a hill and slides down with a constant acceleration. At some later time it is 14.4 m from the top; 2.00 s after that it is 25.6 m from the top, 2.00s later 40.0...

A copper wire has a square cross section 2.3 mm on a side. The wire is 4.0 m long and carries a current of 3.6 A. The density of free electrons is 8.5 X 1028/m3. Find the magnitudes of (a) The...

A bicyclist coasts down a 7.0o hill at a steady speed of 5.0m/s. Assuming a total mass of 75kg (bicycle plus rider), what must be the cyclists power output to climb the same hill at the same speed?

An athlete whose mass is 90.0 kg is performing weight-lifting exercises. Starting from the rest position, he lifts, with constant acceleration, a barbell that weighs 490 N. He lifts the barbell a...

A dog running in an open field has components of velocity v, = 2.6 m/s and Vy = -1.8 m/s at t, = 10.0 s. For the time interval from f, = 10.0 s to 12 = 20.0 s, the average acceleration of the dog has...

Two identical taut strings under the same tension F produce a note of the same fundamental frequency fo The tension in one of them is now increased by a very small amount F. (a) If they are played...

In the ammonia (NH3) molecule of Figure, three hydrogen (H) atoms form an equilateral triangle, with the center of the triangle at distance d = 9.40 x 10-11 m from each hydrogen atom. The nitrogen...

A particle moves along the x axis. Its position is given by the equation x = 2 x 3t - 4t2 with x in meters and t in seconds. Determine (a) Its position when it changes direction and (b) Its velocity...

A fireman clings to a vertical ladder and directs the nozzle of a hose horizontally toward a burning building. The rate of water flow is 6.31 kg/s, and the nozzle speed is 12.5 m/s. The hose passes...

A blockspring system oscillates with an amplitude of 3.50 cm. If the spring constant is 250 N/m and the mass of the block is 0.500 kg, determine (a) The mechanical energy of the system, (b) The...

A variable air capacitor used in a radio tuning circuit is made of N semicircular plates each of radius R and positioned a distance d from its neighbors, to which it is electrically connected. As...

A Machinist is using a wrench to loosen a nut. The wrench is 25.0 cm long, and be exerts a 17.O-N force at the end of the handle at 37° with the handle (Fig. 10.41). (a) What torque does the...

The two strands of the helix-shaped DNA molecule are held together by electrostatic forces as shown in Fig. 16-44. Assume that the net average charge (due to electron sharing) indicated on H and N...

Consider a projectile fired vertically in a constant gravitational field. For the same initial velocities, compare the times required for the projectile to reach its maximum height (a) For zero...

For the three hydrogen transitions indicated below, with n being the initial state and n being the final state, is the transition an absorption or an emission? Which is higher, the initial state...

In Figure, a small block is sent through point A with a speed of 7.0 m/s. Its path is without friction until it reaches the section of length L = 12 m, where the coefficient of kinetic friction is...

A light bar AB supports a 15-kg block at its midpoint C. Rollers at A and B rest against frictionless surfaces, and a horizontal cable AD is attached at A. Determine (a) The tension in cable AD, (b)...

Determine the velocity of each block 2 s after the blocks are released from rest. Neglect the mass of the pulleys and cord. 10 lb 50 lb B.

A 1.5D-m string of weight 1.25 N is tied to the ceiling at its upper end, and the lower end supports a weight W. When you pluck the string slightly, the waves traveling up the string obey the...

Two protons are aimed directly toward each other by a cyclotron accelerator with speeds of 1000 km/s, measured relative to the earth. Find the maximum electrical force that these protons will exert...

Capacitance of a Thundercloud The charge center of a thundercloud, drifting 3.0 km above the earth's surface, contains 20 C of negative charge. Assuming the charge center has a radius of 1.0 km, and...

A rectangular loop with width L and a slide wire with mass m are as shown in Fig. 29.53. A uniform magnetic field B is directed perpendicular to the plane of the loop into the plane of the figure....

A 140 kg hoop rolls along a horizontal floor so that the hoop's center of mass has a speed of 0.150 m/s. How much work must be done on the hoop to stop it?

The systems shown in Figure P5.21 are in equilibrium. If the spring scales are calibrated in newtons, what do they read? (Neglect the masses of the pulleys and strings, and assume the incline in part...

A long solenoid, with its axis along the x axis, consists of 200 turns per meter of wire that carries a steady current of 15.0 A. A coil is formed by wrapping 30 turns of thin wire around a circular...

A hunter on a frozen, essentially frictionless pond uses a rifle that shoots 4.20-g bullets at 965 m/s. The mass of the hunter (including his gun) is 72.5 kg, and the hunter holds tight to the gun...

A piece of wood is 0.600 m long, 0.250 m wide and 0.080 m thick. Its density is 600 kg/m3. What volume of lead must be fastened underneath it to sink the wood in calm water so that its top is just...

n idealized voltmeter is connected across the terminals of a 15.0-V battery, and a 75.0- appliance is also connected across its terminals. If the voltmeter reads 11.3 V: (a) How much power is being...

In earlier days, horses pulled barges down canals in the manner shown in Figure. Suppose the horse pulls on the rope with a force of 7900 N at an angle of = 18o to the direction of motion of the...

White light is spread out into its spectral components by a diffraction grating. If the grating has 2 000 grooves per centimeter, at what angle does red light of wavelength 640 nm appear in first...

A certain crude oil has an index of refraction of 1.25. A ship dumps 1.00 m3 of this oil into the ocean, and the oil spreads into a thin uniform slick. If the film produces a first-order maximum of...

A ball is thrown straight up from the ground with speed v0 At the same instant, a second ball is dropped from rest from a height H, directly above the point where the first ball was thrown upward....

Figure 34.57 shows an object and its image formed by a thin lens.(a) What is the focal length of the lens, and what type of lens (converging or diverging) is it?(b) What is the height of the image?...

An elevator cab that weighs 27.8kN moves upward. What is the tension in the cable if the cab's speed is? (a) Increasing at a rate of 1 .22 m/s2 and (b) Decreasing at a rate of 1 .22 m/s2?

A conservative force F(x) acts on a 2.0 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is graphed in Figure. When the particle is at x = 2.0m, its velocity is...

A disk, with a radius of 0.25 m, is to be rotated like a merry-go-round through 800 rad, starting from rest, gaining angular speed at the constant rate 1 through the first 400 rad and then losing...

A 200-mm lever and a 240-mm-diameter pulley are welded to the axle BE that is supported by bearings at C and D. If a 720-N vertical load is applied at A when the lever is horizontal, determine (a)...

A large 16.0-kg roll of paper with radius R = IS.O cm rests against the wall and is held in place by a bracket attached to a rod through the center of the 311 roll (Fig. 10.54). The rod turns without...

A disoriented physics professor drives 3.25 km north, then 4.75 km west, and then 1.50 km south. Find the magnitude and direction of the resultant displacement, using the method of components in a...

A uniform 3.00-kg rope 24.0 m long lies on the ground at the top of a vertical cliff. A mountain climber at the top lets down half of it to help his partier climb up the cliff. What was the change in...

A small sphere with mass m is attached to a mass less rod of length L that is pivoted at the top, forming a simple pendulum. The pendulum is pulled to one side that the rod is at an angle e from the...

A 5.00-kg block is set into motion up an inclined plane with an initial speed of 8.00 m/s (Fig. P8.33). The block comes to rest after traveling 3.00m along the plane, which is inclined at an angle of...

A transverse sinusoidal wave on a string has a period T = 25.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t = 0, a particle on the string at x = 0 has a transverse...

A wire having a uniform linear charge density A is bent into the shape shown in Figure P25.47. Find the electric potential at point O. 2R 2R

A .22 rifle bullet, traveling at 350 m/s, strikes a large tree, which it penetrates to a depth of 0.130 m. The mass of the bullet is 1.80 g. Assume a constant retarding force. (a) How much time is...

A ring-shaped conductor with radius a = 2.50 cm has a total positive charge Q = + 0.125 nC uniformly distributed around it, as shown in Fig. 21.24. The center of the ring is at the origin of...

Body A in Figure weighs 102 N, and body B weighs 32 N. The coefficients of friction between A and the incline are ? s = 0.56 and ? k = 0.25. Angle is 40 o . Let the positive direction of an x axis...

A potassium chloride crystal has an energy band gap of 7.6 eV above the topmost occupied band, which is full. Is this crystal opaque or transparent to light of wavelength 140 nm?

Figure shows an overhead view of a ring that can rotate about its center like a merry-go-round. Its outer radius R2 is 0.800 m, its inner radius R1 is R2/2.00, its mass M is 8.00 kg, and the mass of...

In Figure a light wave along ray r1 reflects once from a mirror and a light wave along ray r2 reflects twice from that same mirror and once from a tiny mirror at distance L from the bigger mirror....

A charge of -6.50 nC is spread uniformly over the surface of one face of a nonconducting disk of radius 1.25 cm. (a) Find the magnitude and direction of the electric field this disk produces at a...

A railroad freight car of mass 3.18 x 104 kg collides with a stationary caboose car. They couple together, and 27.0% of the initial kinetic energy is transferred to thermal energy, sound, vibrations,...

A 1.50-kg object is held 1.20 m above a relaxed mass less vertical spring with a force constant of 320 N/m. The object is dropped onto the spring. (a) How far does it compress the spring? (b) What...

A box of bananas weighing 40.0 N rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.40, and the coefficient of kinetic friction is 0.20. (a) If no...

A uniform thin rod of length 0.500 m and mass 4.00 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 3.00 g bullet traveling in the rotation...

Flying Leap of the Flea High-peed motion pictures (3500 frames/second) of a jumping, 21O-l-'g Ilea yielded the data used to plot the graph given in Fig. 2.42. (See "The Flying Leap of the Flea" by M....

124/55Cs has a half-life of 30.8s. (a) If we have 8.8g initially, how many Cs nuclei are present? (b) How many are present 2.0min later? (c) What is the activity at this time? (d) After how much time...

A football kicker can give the ball an initial speed of 25m/s. What are the (a) Least and (b) Greatest elevation angles at which he can kick the ball to score a field goal from a point 50 m in front...

Show that Equation 15.32 is a solution of Equation 15.31 provided that b2 < 4mk.

The reflecting surfaces of two intersecting flat mirrors are at an angle θ (0° For a light ray that strikes the horizontal mirror, show that the emerging ray will intersect the incident ray...

A claw hammer is used to pull a nail out of a board (Fig. 11.38). The nail is at an angle of 60° to the board, and a force F, of magnitude 500 N applied to the nail is required to pull it from...

An approximation for the potential energy of a KCl molecules U = A[(RJ/8r8 ) - l/r], where Ro = 2.67 X l0-l0 m and A = 2.31 X 10-28 J. m. Using this approximation: (a) Show that the radial component...

In 1 km races, runner 1 on track 1 (with time 2 min, 27 .95 s) appears to be faster than runner 2 on track 2 (2 min, 28.15 s). However, length L 2 of track 2 might be slightly greater than length L 1...

The L-shaped tank shown in Figure is filled with water and is open at the top. If d = 5.0 m, what is the force due to the water (a) On face A and (b) On faceB? 2d 3d B. 2d

Determine the precision of each measurement. 1. 536 ft 2. 307.3 mi 3. 5007 m 4. 5.00 cm 5. 0.0070 in. 6. 6.010 cm 7. 8400 km 8. 3000 ft 9. 187.40 m 10. 500 g

A rigid bar of weight W = 800 N hangs from three equally spaced vertical wires (length L = 150 mm, spacing a = 50 mm): two of steel and one of aluminum. The wires also support a load P acting on the...

A capacitor is charged to a potential of 12.0 V and is then connected to a voltmeter having an internal resistance of 3.40 M. After a time of 4.00 s the voltmeter reads 3.0 V. What are? (a) The...

In Fig. 2-28, a red car and a green car, identical except for the color, move toward each other in adjacent lanes and parallel to an x axis. At time t = 0, the red car is at xr = 0 and the green car...

The upward normal force exerted by the floor is 620 N on an elevator passenger who weighs 650 N. What are the reaction forces to these two forces? Is the passenger accelerating? If so, what are the...

Falling Hammer A hatumer with mass m is dropped from rest from a height h above the earth's surface. This height is not necessarily small compared with the radius RE of the earth. If you ignore air...

Maximum surface resistance considers a square sheet of side L, thickness d, and electrical resistivity p. The resistance measured between opposite edges of the sheet is called the surface resistance:...

A conducting rod of length moves with velocity v parallel to a long wire carrying a steady current I. The axis of the rod is maintained perpendicular to the wire with the near end a distance r away,...

To an order of magnitude, how many piano tuners are in New York City? The physicist Enrico Fermi was famous for asking questions like this on oral Ph.D. qualifying examinations. His own facility in...

You are a member of an Alpine Rescue Team. You must project a box of supplies up an incline of constant slope angle a so that it reaches a stranded skier who is a vertical distance h above the bottom...

A small winch is used to raise a 120-lb load. Find (a) the magnitude of the vertical force P that should be applied at C to maintain equilibrium in the position shown, (b) the reactions at A and B,...

A helicopter rotor blade can be considered a long thin rod, as shown in Fig. 8-46. (a) If each of the three rotor helicopter blades is 3.75m long and has a mass of 160kg. Calculate the moment of...

In demonstrating a dance step, a person moves in one dimension, as shown in Fig. 2.21. What are (a) The average speed and (b) The average velocity for each phase of the motion? (c) What are the...

Two racquetballs are placed in a glass jar, as shown in Figure P12.62. Their centers and the point A lie on a straight line. (a) Assume that the walls are frictionless, and determine P1, P2, and P3....

A particle with charge - 5.60 nC is moving in a uniform magnetic field B = -J 1.25 T) k. The magnetic force on the particle is measured to be F = - (3.40 X l0-7 N) i+ (7.40 X l0-7 N) j. (a) Calculate...

Suppose an electron was bound to a proton, as in the hydrogen atom, but by the gravitational force rather than by the electric force, what would be the radius and energy of the first Bohr orbit?

In Figure, an 817 kg construction bucket is suspended by a cable A that is attached at O to two other cables B and C, making angles 1 = 51.0? and 2 = 66.0? with the horizontal. Find the tensions in...

Two moles of an ideal gas are heated at constant pressure from T = 27C to T = 107C. (a) Draw a pV-diagram for this process. (b) Calculate the work done by the gas.

Expensive amplifier A is rated at 250 W, while the more modest amplifier B is rated at 40W. (a) Estimate the sound level in decibels you would expect at a point 3.5m from a loudspeaker connected in...

A particle of mass m moves in a potential given by V (r) = rk. Let the angular momentum be L. (a) Find the radius, r0, of a circular orbit. (b) If the particle is given a tiny kick so that the radius...

(Multiple choice) (1) True or False (a) The virtual image formed by a concave mirror is always smaller than the object. (b) A concave mirror always forms a virtual image. (c) A convex mirror never...

City A lies directly west of city B When there is no wind an airliner makes the 5550-kInround-trlp flight between them in 6.60h of flying time while traveling at the same speed in both directions....

(a) Derive an equation for the radial acceleration that includes v and Cd, but not r. (b) You are designing a merry-go-round for which a point on the rim will have a radial acceleration of 0.500 m/s2...

A car maintains a constant speed v as it traverses the hill and valley shown if Fig. 5-45. Both the hill and valley have radius of curvature R. (a) How do the normal forces acting on the car at A, B...

What are the shortest-wavelength X-rays emitted by electrons striking the face of a 33.5-kV TV picture tube? What are the longest wavelengths?

Classical Electron Spin (a) If you treat an electron as a classical spherical object with a radius of 1.0 x 10-17m, what angular speed is necessary to produce a spin angular momentum of magnitude h?...

A cart with mass 340 g moving on a frictionless linear air track at an initial speed of l- .2m/s undergoes an elastic collision with an initially stationary cart of unknown mass. After the collision,...

A thin, flat, uniform disk has mass M and radius R_ A circular hole of radius R/4, centered at a point R/2 from the disk's center, is then punched in the disk. (a) Find the moment of inertia of the...