phys final
b.) What is the frequency of the interfering wave?
31.8 Hz
c.) Compute the kinetic and potential energies of the system when the position of the cart is 2.00 cm.
5 x 10^-3 J, 4 x 10^-3 J
c.) Find the amplitude of the motion.
5.1 cm
e.) Find the total length of the track
5367.6 m
c.) What is the angular speed of the wheel at t=2.00s?
9 rad/s
b.) What is the largest object mass for which standing waves could be observed?
900 kg
c.) If the original frequency is held constant and the tension in the wire is increased by a factor of 25, how many loops are present in the new pattern?
????
c.) What is the spatial length of such a pulse?
0.165 nm
b.) Through how many revolutions has the wheel turned during this time interval?
1.75 rev
c.) Find the kinetic energy when its position is 2.50 cm
12.2 mJ
When a 4.90 kg object is placed on top of a vertical spring, the spring compresses a distance of 2.86 cm. What is the force constant of the spring?
1679 Nm
A particle moves in simple harmonic motion with a frequency of 3.00 Hz and an amplitude of 4.60 cm. a.) Through what total distance does the particle move during one cycle of its motion?
18.4 cm
b.) What frequency does the driver detect after the police car passes him?
2075.72 Hz
b.) Determine the maximum speed of the block.
0.250 m/s
b.) What are the values of L for the next two resonance conditions?
0.270m, 0.450m
b.) What is the fundamental frequency of vibration of the wire?
13 Hz
b.) If the A and C strings have the same linear mass density and length L, determine the ratio of tensions in the two strings.
2.82??
An 80.0-kg hiker is trapped on a mountain ledge following a storm. A helicopter rescues the hiker by hovering above him and lowering a cable to him. The mass of the cable is 8.00 kg, and its length is 15.0 m. A sling of mass 70.0 kg is attached to the end of the cable. The hiker attaches himself to the sling, and the helicopter then accelerates upward. Terrified by hanging from the cable in midair, the hiker tries to signal the pilot by sending transverse pulses up the cable. A pulse takes 0.250 s to travel the length of the cable. What is the acceleration of the helicopter? Assume the tension in the cable is uniform.
3 m/s^2
A simple pendulum is 7.00 m long a.) What is the period of small oscillations for this pendulum if it is located in an elevator accelerating upward at 2.00 m/s2?
4.84 s
A taut string for which m = 5.00×10-2 kg/m is under a tension of 80.0 N. How much power must be supplied to the string to generate sinusoidal waves at a frequency of 60.0 Hz and an amplitude of 6.00 cm?
512 N
e.) What is the speed of propagation of this wave?
55 m/s
A simple apparatus for demonstrating resonance in an air column is shown. A vertical pipe open at both ends is partially submerged in water, and a tuning fork vibrating at an unknown frequency is placed near the top of the pipe. The length L of the air column can be adjusted by moving the pipe vertically. The sound waves generated by the fork are reinforced when L corresponds to one of the resonance frequencies of the pipe. For a certain pipe, the smallest value of L for which a peak occurs in the sound intensity is 9.00 cm. a.) What is the frequency of the tuning fork?
953 Hz
b.) What is the velocity of the cart when the position is 2.00 cm?
0.141 m/s
b.) Determine the phase constant and write a general expression for the wave function.
0.150cos(15.7x-50.3t)
A 0.500-kg cart connected to a light spring for which the force constant is 20.0 N/m oscillates on a frictionless, horizontal air track. a.) Calculate the maximum speed of the cart if the amplitude of the motion is 3.00 cm.
0.19 m/s
A star rotates with a period of 30 days about an axis through its center. The period is the time interval required for a point on the star's equator to make one complete revolution around the axis of rotation. After the star undergoes a supernova explosion, the stellar core, which had a radius of 1.0×104 km, collapses into a neutron star of radius 3.0 km. Determine the period of rotation of the neutron star.
0.23 seconds
Christian Huygens (1629-1695), the greatest clockmaker in history, suggested that an international unit of length could be defined as the length of a simple pendulum having a period of exactly 1 s. How much shorter would our length unit be if his suggestion had been followed?
0.248 m
b.) What is the net displacement if the end at which reflection occurs is free to slide up and down?
0.30 m
A steel wire of length 30.0 m and a copper wire of length 20.0 m, both with 1.00-mm diameters, are connected end to end and stretched to a tension of 150 N. During what time interval will a transverse wave travel the entire length of the two wires? (The density of steel and copper are 7860 and 8920 kg/m3, respectively.)
0.32 s
The fundamental frequency of an open organ pipe corresponds to the A above middle C (440 Hz on the chromatic musical scale). The third resonance of a closed organ pipe has the same frequency. (Assume that the speed of sound in air is 343 m/s.) a.) What is the length of the open pipe?
0.39 m
d.) What is the period of this wave?
0.4 s
b.) What should be the duration of the emitted pulse if it is to include 10 cycles of the ultrasonic wave?
0.476 us
b.) Find the total speed of the object when its position is 1.25 cm (Let 0 cm be the position of equilibrium)
1.02 m/s
c.) x = 0.500, t = 0
1.15 cm
A taut rope has a mass of 0.165 kg and a length of 3.50 m. What power must be supplied to the rope so as to generate sinusoidal waves having an amplitude of 0.110 m and a wavelength of 0.485 m and traveling with a speed of 29.0 m/s?
1.17 kW
A car with a mass of 1300 kg is constructed so that its frame is supported by four springs. Each spring has a force constant of 20 000 N/m. Two people riding in the car have a combined mass of 160 kg. Find the frequency of vibration of the car after it is driven over a pothole in the road.
1.18 Hz
c.) What is the maximum acceleration of the block?
1.25 m/s^2
A 200-g block connected to a light spring for which the force constant is 5.00 N/m is free to oscillate on a frictionless, horizontal surface. The block is displaced 5.00 cm from equilibrium and released from rest. a.) Find the period of its motion
1.26 seconds
Two identical loudspeakers placed 3.00 m apart are driven by the same oscillator. A listener is originally at point O, located 8.00 m from the center of the line connecting the two speakers. The listener then moves to point P, which is a perpendicular distance 0.350 m from O, and she experiences the first minimum in sound intensity. What is the frequency of the oscillator?
1.3 kHz
Consider the diatomic oxygen molecule O2, which is rotating in the xy plane about the z axis passing through its center, perpendicular to its length. The mass of each oxygen atom is 2.66×10-26 kg, and at room temperature, the average separation between the two oxygen atoms is d = 1.21×10-10 m. a.) Calculate the moment of inertia of the molecule about the z axis
1.96 x 10^-46 Kgm^2
A wheel rotates with a constant angular acceleration of 3.50 rad/s2. a.) If the angular speed of the wheel is 2.00 rad/s at t = 0, through what angular displacement does the wheel rotate in 2.00 s?
11 radians
A string with a mass m = 8.00 g and a length L = 5.00 m has one end attached to a wall; the other end is draped over a small, fixed pulley a distance d = 4.00 m from the wall and attached to a hanging object with a mass M = 4.00 kg as in the figure below. If the horizontal part of the string is plucked, what is the fundamental frequency of its vibration?
13.3 Hz
b.) The subs barely miss each other and pass. What frequency is detected by an observer riding on sub B as the subs recede from each other?
1385 Hz
A section of drainage culvert 1.23 m in length makes a howling noise when the wind blows across its open ends. a.) Determine the frequencies of the first three harmonics of the culvert if it is cylindrical in shape and open at both ends. Take v = 343 m/s as the speed of sound in air.
139 Hz, 279 Hz, 418 Hz
A submarine (sub A) travels through water at a speed of 8.00 m/s, emitting a sonar wave at a frequency of 1400 Hz. The speed of sound in the water is 1533 m/s. A second submarine (sub B) is located such that both submarines are traveling directly toward each other. The second submarine is moving at 9.00 m/s. a.) What frequency is detected by an observer riding on sub B as the subs approach each other?
1416 Hz
c.) While the subs are approaching each other, some of the sound from sub A reflects from sub B and returns to sub A. If this sound were to be detected by an observer on sub A, what is its frequency?
1432 Hz
Two sinusoidal waves traveling in opposite directions interfere to produce a standing wave with the wave function y = (1.50) sin(0.400x) cos(200t) where x and y are in meters and t is in seconds. a.) Determine the wavelength of the interfering waves.
15.7 m
A sinusoidal wave traveling in the positive x direction has an amplitude of 15.0 cm, a wavelength of 40.0 cm, and a frequency of 8.00 Hz. The vertical position of an element of the medium at t = 0 and x = 0 is also 15.0 cm. a.) Find the wave number k, period T, angular frequency, and speed v of the wave.
15.7 rad/s, 50.3 rad/s, 0.125 s, 3.20 m/s
d.) Find the potential energy when its position is 2.50 cm
15.8 mJ
c.) Find the maximum acceleration of the particle.
16.9 m/s^2
The fishing pole in the figure below makes an angle of 20.0° with the horizontal. What is the torque exerted by the fish about an axis perpendicular to the page and passing through the angler's hand if the fish pulls on the fishing line with a force = 100 N at an angle 37.0° below the horizontal? The force is applied at a point L = 2.00 m from the angler's hands.
167.8 Nm clockwise
A uniform string has a mass of 0.300 kg and a length of 6.00 m. The string passes over a pulley and supports a 2.00-kg object. Find the speed of a pulse traveling along this string.
19.8 m/s
d.) Assuming that the acceleration is constant, find the total angular displacement of the disc as it plays.
190,927 rad
Four people, each with a mass of 72.7 kg, are in a car with a mass of 1110 kg. An earthquake strikes. The driver manages to pull off the road and stop, as the vertical oscillations of the ground surface make the car bounce up and down on its suspension springs. When the frequency of the shaking is 1.60 Hz, the car exhibits a maximum amplitude of vibration. The earthquake ends and the four people leave the car as fast as they can. By what distance does the car's undamaged suspension lift the car's body as the people get out?
2 cm
b.) A typical angular speed of a molecule is 4.60´1012 rad/s. If the oxygen molecule is rotating with this angular speed about the z axis, what is its rotational kinetic energy?
2.06 x 10^-21 J
The angular position of a pendulum is represented by the equation θ = 0.0300 cos ωt, where θ is in radians and ω = 2.53 rad/s. Determine the period and length of the pendulum.
2.48s, 1.53m
b.) Suppose T1 = 5.0 N, R1 = 1.0 m, T2 = 15 N, and R2 = 0.50 m. What is the net torque about the rotation axis, and which way does the cylinder rotate starting from rest?
2.5Nm
Two waves are traveling in the same direction along a stretched string. The waves are 90.0° out of phase. Each wave has an amplitude of 2.00 cm. Find the amplitude of the resultant wave.
2.83 cm
b.) Find the angular speed at the end of the recording, where the spiral has a radius of 5.50 cm
21.82 rad/s
c.) What is the wavelength of this wave?
22 m
c.) Repeat parts (a) and (b) for the case when the police car is traveling northbound. while the police car overtakes: after the police car passes:
2623.8 Hz, 2402.1 Hz
A 50.0-g object connected to a spring with a force constant of 35.0 N/m oscillates with an amplitude of 4.00 cm on a frictionless, horizontal surface. a.) Find the total energy of the system
28 mJ
A 2.00-kg object attached to a spring moves without friction (b = 0) and is driven by an external force given by the expression F = 3.00sin(2πt), where F is in newtons and t is in seconds. The force constant of the spring is 20.0 N/m. a.) Find the resonance angular frequency of the system.
3.16 s^-1
A driver travels northbound on a highway at a speed of 25.0 m/s. A police car, traveling southbound at a speed of 40.0 m/s, approaches with its siren producing sound at a frequency of 2500 Hz. a.) What frequency does the driver observe as the police car approaches?
3036.3 Hz
A uniform horizontal beam with a length of L = 8.00 m and a weight of Wb = 200 N is attached to a wall by a pin connection. Its far end is supported by a cable that makes an angle of f = 53.0° with the beam. A person of weight Wp = 600 N stands a distance d = 2.00 m from the wall. Find the tension in the cable as well as the magnitude and direction of the force exerted by the wall on the beam.
313N, 581N
An electric motor turns a flywheel through a drive belt that joins a pulley on the motor and a pulley that is rigidly attached to the flywheel as shown in the figure below. The flywheel is a solid disk with a mass of 80.0 kg and a radius R = 0.625 m. It turns on a frictionless axle. Its pulley has much smaller mass and a radius of 0.230 m. The tension Tu in the upper (taut) segment of the belt is 153 N, and the flywheel has a clockwise angular acceleration of 1.67 rad/s2. Find the tension in the lower (slack) segment of the belt.
39.55N
An ultrasonic tape measure uses frequencies above 20 MHz to determine dimensions of structures such as buildings. It does so by emitting a pulse of ultrasound into air and then measuring the time interval for an echo to return from a reflecting surface whose distance away is to be measured. The distance is displayed as a digital read-out. A tape measure emits a pulse of ultrasound with a frequency of 21.0 MHz. a.) What is the distance to an object from which the echo pulse returns after 24 ms when the air temperature is 26°C?
4.16 m
Two waves traveling in opposite directions produce a standing wave The individual wave functions are: y1 = 4.0sin(3.0x - 2.0t) y2 = 4.0sin(3.0x + 2.0t) where x and y are measured in centimeters and t is in seconds. a.) Find the amplitude of the simple harmonic motion of the element of the medium located at x = 2.3 cm.
4.6 cm
In the arrangement shown below, an object can be hung from a string (with linear mass density μ = 0.002 00 kg/m) that passes over a light pulley. The string is connected to a vibrator (of constant frequency f), and the length of the string between point P and the pulley is L = 2.50 m. When the mass m of the object is either 25.0 kg or 36.0 kg, standing waves are observed; no standing waves are observed with any mass between these values, however. a.) What is the frequency of the vibrator? (Note: The greater the tension in the string, the smaller the number of nodes in the standing wave.)
420 Hz
b.) Determine the angle through which the drill rotates during this period
4205.57 rad
A standing-wave pattern is observed in a thin wire with a length of 5.00 m. The wave function is y = 0.003 00 sin (πx) cos (130πt) where x and y are in meters and t is in seconds. a.) How many loops does this pattern exhibit?
5 loops
During a certain time interval, the angular position of a swinging door is described by θ = 5.09 + 10.7t + 2.02t2, where θ is in radians and t is in seconds. Determine the angular position, angular speed, and angular acceleration of the door at the following times. a.) t= 0s
5.09 rad, 10.7 rad/s, 4.04rad/s^2
c.) What is the period of this pendulum if it is placed in a truck that is accelerating horizontally at 2.00 m/s2?
5.26 s
b.) What is the period of small oscillations for this pendulum if it is located in an elevator accelerating downward at 2.00 m/s2?
5.95 s
For the solid sphere shown, calculate the translational speed of the center of mass at the bottom of the incline and the magnitude of the translational acceleration of the center of mass.
5/7gsin(theta)
c.) Find the speed of the interfering waves.
500 m/s
A uniform ladder of length L, rests against a smooth, vertical wall. The mass of the ladder is m, and the coefficient of static friction between the ladder and the ground is ms = 0.40. Find the minimum angle qmin at which the ladder does not slip.
51 degrees
The middle C string on a piano has a fundamental frequency of 262 Hz, and the string for the first A above middle C has a fundamental frequency of 440 Hz. a.) Calculate the frequencies of the next two harmonics of the C string.
524 Hz, 786 Hz
b.) t= 3.10s
57.67 rad, 23.22 rad/s, 4.04 rad/s^2
b.) Find the angular frequency of the driven system.
6.28 s^-1
A playground merry-go-round of radius R = 1.40 m has a moment of inertia I = 245 kg · m2 and is rotating at 8.0 rev/min about a frictionless vertical axle. Facing the axle, a 22.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round?
6.8 rev/min
A digital audio compact disc carries data, each bit of which occupies 0.6 µm along a continuous spiral track from the inner circumference of the disc to the outside edge. A CD player turns the disc to carry the track counterclockwise above a lens at a constant speed of 1.20 m/s. a.) Find the required angular speed at the beginning of the recording, where the spiral has a radius of 1.90 cm.
63.16 rad/s
b.) What are the three lowest natural frequencies of the culvert if it is blocked at one end?
69.7 Hz, 209 Hz, 349 Hz
An Ethernet cable is 4.10 m long. The cable has a mass of 0.215 kg. A transverse pulse is produced by plucking one end of the taut cable. The pulse makes four trips down and back along the cable in 0.895 s. What is the tension in the cable?
70.4 N
Two vectors lying in the xy plane are given by the equations A=2i+3j and B=-i+2j. Find AxB and verify that AxB=-BxA
7k, -7k
A dentist's drill starts from rest. After 3.20 s of constant angular acceleration, it turns at a rate of 2.51 104 rev/min a.) Find the drill's angular acceleration
821.40 rad/s^2
b.) What is its maximum speed?
86.71 cm/s
c.) A full-length recording lasts for 74 min 33 s. Find the average angular acceleration of the disc.
-0.0092 rad/s^2
A transverse wave on a string is described by the following wave function. y=0.110sin(pi/11x+5pit) where x and y are in meters and t is in seconds. a.) Determine the transverse speed at t = 0.120 s for an element of the string located at x = 1.50 m.
-1.17 or -1.73
Two waves on one string are described by the wave functions y1 = 3.0 cos(4.0x − 1.6t) y2 = 4.0 sin(5.0x − 2.0t) where x and y are in centimeters and t is in seconds. Find the superposition of the waves y1 + y2 at the following points. (Remember that the arguments of the trigonometric functions are in radians.) a.) x = 1.00, t = 1.00
-1.65 cm
b.) Determine the transverse acceleration at t = 0.120 s for an element of the string located at x = 1.50 m.
-20 m/s^2
b.) x = 1.00, t = 0.500
-6.02 cm
A series of pulses, each of amplitude 0.150 m, are sent down a string that is attached to a post at one end. The pulses are reflected at the post and travel back along the string without loss of amplitude. When two waves are present on the same string, the net displacement of a particular element of the string is the sum of the displacements of the individual waves at that point. a.) What is the net displacement of an element at a point on the string where two pulses are crossing, if the string is rigidly attached to the post?
0 m
A pendulum with a length of 1.00 m is released from an initial angle of 15.0°. After 1 000 s, its amplitude has been reduced by friction to 5.50°. What is the value of b/2m?
0.001 s^-1
Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long with a mass of 300 kg, and a minute hand 4.20 m long with a mass of 100 kg (see figure below). Calculate the total rotational kinetic energy of the two hands about the axis of rotation. (You may model the hands as long, thin rods rotated about one end. Assume the hour and minute hands are rotating at a constant rate of one revolution per 12 hours and 60 minutes, respectively.)
0.009 J
d.) Express the position, velocity, and acceleration as functions of time in SI units.
0.05cos(5t), -0.25sin(5t), -1.25cos(5t)
b.) Write the expression for y as a function of x and t for the wave in part (a) assuming y(x, 0) = 0 at the point x = 10.0 cm. (Use the following as necessary: x and t.)
0.08sin(7.9x + 18.85t -0.79)
Write the expression for y as a function of x and t in SI units for a sinusoidal wave traveling along a rope in the negative x direction with the following characteristics: A = 8.00 cm, λ = 80.0 cm, f= 3.00 Hz, and y(0, t) = 0 at t = 0. (Use the following as necessary: x and t.)
0.08sin(7.9x + 18.85t)
b.) Find the positions of the nodes and antinodes if one end of the string is at x = 0.
n(pi/3), n(pi/6)
A one-piece cylinder is free to rotate about the central z axis. A rope wrapped around the drum, which has radius R1, exerts a force T1 to the right on the cylinder. A rope wrapped around the core, which has a radius R2, exerts a force T2 downward on the cylinder. a.) What is the net torque acting on the cylinder about the rotation axis?
R2T2-R1T1
