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physics
mechanics
Questions and Answers of
Mechanics
A position-versus-time plot for an object undergoing simple harmonic motion is given in FIGURE 13-30. Rank the six points indicated in the figure in order of increasing(a) Speed,(b) Velocity,(c)
A mass on a spring oscillates with simple harmonic motion of amplitude A about the equilibrium position x = 0. Its maximum speed is vmax and its maximum acceleration is amax.(a) What is the speed of
A mass oscillates on a spring with a period of 0.63 s and an amplitude of 4.4 cm. Write an equation giving x as a function of time, assuming the mass starts at x = A at time t = 0.
An atom in a molecule oscillates about its equilibrium position with a frequency of 2.00 × 1014 Hz and a maximum displacement of 3.50 nm.(a) Write an expression giving x as a function of time for
A mass oscillates on a spring with a period T and an amplitude 0.48 cm. The mass is at the equilibrium position x = 0 at t = 0, and is moving in the positive direction. Where is the mass at the
The position of a mass on a spring is given by x = (3.8 cm) cos[2πt/10.88 s)].(a) What is the period, T, of this motion?(b) Where is the mass at t = 0.55 s?(c) Show that the mass is at the same
A mass attached to a spring oscillates with a period of 3.35 s.(a) If the mass starts from rest at x = 0.0440 m and time t = 0, where is it at time t = 6.37 s?(b) Is the mass moving in the positive
A lawn sprinkler oscillates with simple harmonic motion of period T = 52.0 s, and sprays water with an angle to the vertical (θ = 0) that varies from θ = - 45° to θ = 45°, as shown in
While fishing for catfish, a fisherman suddenly notices that the bobber (a floating device) attached to his line is bobbing up and down with a frequency of 1.8 Hz. What is the period of the bobber's
A ball rolls on a circular track of radius 0.62 m with a constant angular speed of 1.3 rad/s in the counterclockwise direction. If the angular position of the ball at t = 0 is θ = 0, find the x
An object executing simple harmonic motion has a maximum speed of 4.1 m/s and a maximum acceleration of 0.85 m / s2. Find(a) The amplitude(b) The period of this motion.
A child rocks back and forth on a porch swing with an amplitude of 0.204 m and a period of 2.80 s. Assuming the motion is approximately simple harmonic, find the child's maximum speed.
A 30.0-g goldfinch lands on a slender branch, where it oscillates up and down with simple harmonic motion of amplitude 0.0335 m and period 1.65 s.(a) What is the maximum acceleration of the finch?
Tuning forks are used in the diagnosis of nervous afflictions known as large-fiber polyneuropathies, which are often manifested in the form of reduced sensitivity to vibrations. Disorders that can
A vibrating structural beam in a spacecraft can cause problems if the frequency of vibration is fairly high. Even if the amplitude of vibration is only a fraction of a millimeter, the acceleration of
A peg on a turntable moves with a constant tangential speed of 0.82 m/s in a circle of radius 0.33 m. The peg casts a shadow on a wall. Find the following quantities related to the motion of the
The pistons in an internal combustion engine undergo a motion that is approximately simple harmonic motion. If the amplitude of the motion is 3.5 cm, and the engine runs at 1700 rev/min, find(a) The
NASA trains astronauts to deal with weightlessness (and its associated nausea) by flying them in the "vomit comet," a modified KC-135 airplane that flies in an oscillating path with a period of 72
A 0.84-kg air cart is attached to a spring and allowed to oscillate. If the displacement of the air cart from equilibrium is x = (10.0 cm) cos[(2.00 s-1)t + p], find(a) The maximum kinetic energy of
If you dribble a basketball with a frequency of 1.9 Hz, how much time does it take for you to complete 12 dribbles?
A person rides on a mechanical bucking horse (see FIGURE 13-33) that oscillates up and down with simple harmonic motion. The period of the bucking is 0.74 s and the amplitude is slowly increasing. At
An object moves with simple harmonic motion of period T and amplitude A. During one complete cycle, for what length of time is the speed of the object greater than vmax/2?
An object executing simple harmonic motion has a maximum speed vmax and a maximum acceleration amax. Find(a) The amplitude(b) The period of this motion. Express your answers in terms of vmax and amax.
If a mass m is attached to a given spring, its period of oscillation is T. If two such springs are connected end to end and the same mass m is attached,(a) Is the resulting period of oscillation
An old car with worn-out shock absorbers oscillates with a given frequency when it hits a speed bump. If the driver adds a couple of passengers to the car and hits another speed bump,(a) Is the car's
The two blocks in FIGURE 13-34 have the same mass, m. All the springs have the same force constant, k, and are at their equilibrium length. When the blocks are set into oscillation,(a) Is the period
A 0.49-kg mass attached to a spring undergoes simple harmonic motion with a period of 0.67 s. What is the force constant of the spring?
A freshly caught catfish is placed on a spring scale, and it oscillates up and down with a period of 0.204 s. If the spring constant of the scale is 2160 N/m, what is the mass of the catfish?
System A consists of a mass m attached to a spring with a force constant k; system B has a mass 2m attached to a spring with a force constant k; system C has a mass 3m attached to a spring with a
Find the periods of block 1 and block 2 in Figure 13-34, given that k = 49.2 N/m and m = 1.25 kg.
You take your pulse and observe 74 heartbeats in a minute. What are the period and frequency of your heartbeat?
When a 0.62-kg mass is attached to a vertical spring, the spring stretches by 12 cm. How much mass must be attached to the spring to result in a 0.67-s period of oscillation?
A spring with a force constant of 82 N/m is attached to a 0.47-kg mass. Assuming that the amplitude of motion is 3.4 cm, determine the following quantities for this system:(a) v,(b) vmax,(c) T.
A bunch of grapes is placed in a spring scale at a supermarket. The grapes oscillate up and down with a period of 0.48 s, and the spring in the scale has a force constant of 650 N/m. What are (a) The
Two people with a combined mass of 125 kg hop into an old car with worn-out shock absorbers. This causes the springs to compress by 8.00 cm. When the car hits a bump in the road, it oscillates up and
A 0.95-kg mass attached to a vertical spring of force constant 130 N/m oscillates with a maximum speed of 0.45 m/s. Find the following quantities related to the motion of the mass:(a) The period,(b)
When a 0.184-kg mass is attached to a vertical spring, it causes the spring to stretch a distance d. If the mass is now displaced slightly from equilibrium, it is found to make 25.0 oscillations in
The springs of a 511-kg motorcycle have an effective force constant of 9130 N/m. (a) If a person sits on the motorcycle, does its period of oscillation increase, decrease, or stay the same? (b) By
If a mass m is attached to a given spring, its period of oscillation is T. If two such springs are connected end to end, and the same mass m is attached,(a) Is its period greater than, less than, or
A 0.285-kg mass is attached to a spring with a force constant of 53.4 N/m. If the mass is displaced 0.180 m from equilibrium and released, what is its speed when it is 0.135 m from equilibrium?
A 1.6-kg mass attached to a spring oscillates with an amplitude of 7.3 cm and a frequency of 2.8 Hz. What is its energy of motion?
A frame-by-frame analysis of slow-motion video shows that a hovering dragonfly takes 7 frames to complete one wing beat. If the video is shot at 240 frames per second, (a) What is the period of the
A 0.40-kg mass is attached to a spring with a force constant of 26 N/m and released from rest a distance of 3.2 cm from the equilibrium position of the spring. (a) Give a strategy that allows you to
(a) What is the maximum speed of the mass in the previous problem?(b) How far is the mass from the equilibrium position when its speed is half the maximum speed?
An astronaut uses a Body Mass Measurement Device to measure her mass. If the force constant of the spring is 2700 N/m, her mass is 75 kg, and the amplitude of her oscillation is 1.9 cm, what is her
A 0.505-kg block slides on a frictionless horizontal surface with a speed of 1.18 m/s. The block encounters an unstretched spring and compresses it 23.2 cm before coming to rest. (a) What is the
A 3.55-g bullet embeds itself in a 1.47-kg block, which is attached to a spring of force constant 825 N/m. If the maximum compression of the spring is 5.88 cm, find(a) The initial speed of the bullet
Metronomes, such as the penguin shown in FIGURE 13-35, are useful devices for music students. If it is desired to have the metronome tick with a greater frequency, should the penguin's bow tie be
A grandfather clock keeps correct time at sea level. If the clock is taken to the top of a nearby mountain, (a) Would you expect it to keep correct time, run slow, or run fast? (b) Choose the best
An observant fan at a baseball game notices that the radio commentators have lowered a microphone from their booth to just a few inches above the ground, as shown in FIGURE 13-36. The microphone is
A simple pendulum of length 2.3 m makes 5.0 complete swings in 37 s. What is the acceleration of gravity at the location of the pendulum?
A large pendulum with a 200-lb gold-plated bob 12 inches in diameter is on display in the lobby of the United Nations building. The pendulum has a length of 75 ft. It is used to show the rotation of
(a) Your heart beats with a frequency of 1.45 Hz. How many beats occur in a minute? (b) If the frequency of your heartbeat increases, will the number of beats in a minute increase, decrease, or stay
If the pendulum in the previous problem were to be taken to the Moon, where the acceleration of gravity is g/6, (a) Would its period increase, decrease, or stay the same? (b) Check your result in
A Hula Hoop hangs from a peg. Find the period of the hoop as it gently rocks back and forth on the peg. (For a hoop with axis at the rim I = 2mR2, where R is the radius of the hoop.)
A fireman tosses his 0.98-kg hat onto a peg, where it oscillates as a physical pendulum (FIGURE 13-37). If the center of mass of the hat is 8.4 cm from the pivot point, and its period of oscillation
Consider a meterstick that oscillates back and forth about a pivot point at one of its ends. (a) Is the period of a simple pendulum of length L = 1.00 m greater than, less than, or the same as the
On the construction site for a new skyscraper, a uniform beam of steel is suspended from one end. If the beam swings back and forth with a period of 2.00 s, what is its length?
(a) Find the period of a child's leg as it swings about the hip joint. Assume the leg is 0.55 m long and can be treated as a uniform rod.(b) Estimate the child's walking speed.
Suspended from the ceiling of an elevator is a simple pendulum of length L. What is the period of this pendulum if the elevator (a) Accelerates upward with an acceleration a, (b) Accelerates downward
An object undergoes simple harmonic motion with a period T. In the time 3T/2 the object moves through a total distance of 12D. In terms of D, what is the object's amplitude of motion?
If the amplitude of a simple harmonic oscillator is doubled, by what multiplicative factor do the following quantities change: (a) Angular frequency, (b) Frequency, (c) Period, (d) Maximum speed, (e)
A mass m is suspended from the ceiling of an elevator by a spring of force constant k. When the elevator is at rest, the period of the mass is T. Does the period increase, decrease, or remain the
You rev your car's engine to 3300 rpm (rev/min). (a) What are the period and frequency of the engine? (b) If you change the period of the engine to 0.033 s, how many rpms is it doing?
A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest, the period of the pendulum is T. Does the period increase, decrease, or remain the same when the
A 1.3-kg mass is attached to a spring with a force constant of 52 N/m. If the mass is released with a speed of 0.28 m/s at a distance of 8.1 cm from the equilibrium position of the spring, what is
An astronaut uses a Body Mass Measurement Device (BMMD) to determine her mass. What is the astronaut's mass, given that the force constant of the BMMD is 2600 N/m and the period of oscillation is
Sunspots vary in number as a function of time, exhibiting an approximately 11-year cycle. Galileo made the first European observations of sunspots in 1610, and daily observations were begun in Zurich
Scientists are using tiny, nanoscale cantilevers 4 micrometers long and 500 nanometers wide-essentially miniature diving boards-as a sensitive way to measure mass. An example is shown in FIGURE
An object undergoing simple harmonic motion with a period T is at the position x = 0 at the time t = 0. At the time t = 0.25T the position of the object is positive. State whether x is positive,
The maximum speed of a 4.1-kg mass attached to a spring is 0.78 m/s, and the maximum force exerted on the mass is 13 N.(a) What is the amplitude of motion for this mass?(b) What is the force constant
The acceleration of a block attached to a spring is given by a = - (0.302 m/s2) cos([2.41 rad/s]t). (a) What is the frequency of the block's motion? (b) What is the maximum speed of the block? (c)
In 1962, physicists at Cal Tech discovered that the surface of the Sun vibrates due to the violent nuclear reactions that roil within its core. This has led to a new field of solar science known as
A 9.50-g bullet, moving horizontally with an initial speed v0, embeds itself in a 1.45-kg pendulum bob that is initially at rest. The length of the pendulum is L = 0.745 m. After the collision, the
A mass moves back and forth in simple harmonic motion with amplitude A and period T. (a) In terms of A, through what distance does the mass move in the time T? (b) Through what distance does it move
A 1.44-g spider oscillates on its web, which has a damping constant of 3.30 × 10-5 kg/s. How much time does it take for the spider's amplitude of oscillation to decrease by 10.0 percent?
A service dog tag (FIGURE 13-40) is a circular disk of radius 1.9 cm and mass 0.013 kg that can pivot about a small hole near its rim. Refer to Table 10-1 to determine the moment of inertia about the
Calculate the ratio of the kinetic energy to the potential energy of a simple harmonic oscillator when its displacement is half its amplitude.
A 0.340-kg mass slides on a frictionless floor with a speed of 1.34 m/s. The mass strikes and compresses a spring with a force constant of 53.4 N/m.(a) How far does the mass travel after contacting
A shock absorber is designed to quickly damp out the oscillations that a car would otherwise make because it is suspended on springs.(a) Find the period of oscillation of a 1610-kg car that is
FIGURE 13-41 shows a displacement-versus-time graph of the periodic motion of a 3.8-kg mass on a spring.(a) Referring to the figure, do you expect the maximum speed of the mass to be greater than,
A 3.2-kg mass on a spring oscillates as shown in the displacement-versus-time graph in Figure 13-41.(a) Referring to the graph, at what times between t = 0 and t = 6.0 s does the mass experience a
A 0.45-kg crow lands on a slender branch and bobs up and down with a period of 1.5 s. An eagle flies up to the same branch, scaring the crow away, and lands. The eagle now bobs up and down with a
A mass m is connected to the bottom of a vertical spring whose force constant is k. Attached to the bottom of the mass is a string that is connected to a second mass m, as shown in FIGURE 13-42. Both
Consider the pendulum shown in FIGURE 13-43. Note that the pendulum's string is stopped by a peg when the bob swings to the left, but moves freely when the bob swings to the right.(a) Is the period
A mass moves back and forth in simple harmonic motion with amplitude A and period T.(a) In terms of T, how much time does it take for the mass to move through a total distance of 2A?(b) How much time
An object undergoes simple harmonic motion of amplitude A and angular frequency ω about the equilibrium point x = 0. Use energy conservation to show that the speed of the object at the general
A physical pendulum consists of a light rod of length L suspended in the middle. A large mass m1 is attached to one end of the rod, and a lighter mass m2 is attached to the other end, as illustrated
A vertical hollow tube is connected to a speaker, which vibrates vertically with simple harmonic motion (FIGURE 13-45). The speaker operates with constant amplitude, A, but variable frequency, Æ’.
If the temperature is increased by 10 degrees Fahrenheit, how many additional chirps are heard in a 13-s interval?A. 5B. 10C. 13D. 39
What is the temperature in degrees Fahrenheit if a cricket is observed to give 35 chirps in 13 s?A. 13 °FB. 35 °FC. 74 °FD. 90 °F
What is the frequency of the cricket's chirping (in Hz) when the temperature is 68 °F?A. 0.45 HzB. 2.2 HzC. 5.2 HzD. 29 Hz
Suppose the temperature decreases uniformly from 75 °F to 63 °F in 12 minutes. How many chirps does the cricket produce during this time?A. 28B. 1700C. 3800D. 22,000
Suppose we can change the plane's period of oscillation, while keeping its amplitude of motion equal to 30.0 m.(a) If we want to reduce the maximum acceleration of the plane, should we increase or
Suppose the force constant of the spring is doubled, but the mass and speed of the block are still 0.980 kg and 1.32 m/s, respectively.(a) By what multiplicative factor do you expect the maximum
(a) If the block's initial speed is increased, does the total time the block is in contact with the spring increase, decrease, or stay the same?(b) Find the total time of contact for v0 = 1.65 m/s, m
Describe how the sound of a symphony played by an orchestra would be altered if the speed of sound depended on the frequency of sound.
When you drive a nail into a piece of wood, you hear a tone with each blow of the hammer. In fact, the tone increases in pitch as the nail is driven farther into the wood. Explain.
On a guitar, some strings are single wires, others are wrapped with another wire to increase the mass per length. Which type of string would you expect to be used for a low-frequency note? Explain.
A wave travels along a stretched horizontal rope. The vertical distance from crest to trough for this wave is 16 cm and the horizontal distance from crest to trough is 22 cm. What are(a) The
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