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college physics reasoning

Questions and Answers of College Physics Reasoning

An aluminum bar has a length of 2.0 m and a rectangular cross section with sides of 3.5 mm and 6.9 mm. (a) What force is required to stretch the bar 1.2 mm? (b) What is the strain for this
Consider one of the children in Figure P11.28. If she is swinging with a typical amplitude, what is her approximate maximum kinetic energy? Figure P11.28 ?
A mass-on-a-spring oscillator has m = 7.0 kg and k = 300 N/m and is oscillating with an amplitude of 12 cm. (a) If the value of the mass is increased by a factor of two but the amplitude is kept
Consider a simple pendulum with L = 5.2 m and m = 3.3 kg. It is given an initial displacement y = +0.15 m (as measured along the circular arc along which it moves) and an initial velocity of +0.20
A simple pendulum has a length L and a mass m. At its highest point, the pendulum mass is 0.25L above its lowest point (Fig. P11.42). What is the speed of the mass when it is at its lowest point?
Consider a simple pendulum with L = 1.2 m and m = 2.0 kg. Suppose the mass is initially at rest at the lowest point on its trajectory when it is given an impulse such that it then has a velocity of
Consider a simple pendulum of length 1.2 m with m 2.0 kg. If the amplitude of the oscillation is 0.15 m (as measured along the circular arc along which it moves), what is the total mechanical energy
The position of a simple harmonic oscillator is given by y = A sin(2pft), with f = 400 Hz. Find a value of t at which the potential energy is one quarter of its maximum value.
Consider a simple harmonic oscillator whose position as a function of time is given by Figure P11.38. At what times in this plot is the kinetic energy a maximum? At what time(s) is the potential
A particle attached to a spring with k = 50 N/m is undergoing simple harmonic motion, and its position is described by the equation x = (5.7 m)cos(7.5t), with t measured in seconds. (a) What is
The position of a mass-on-a-spring oscillator is given by y = A sin(25t), where the value of t is in seconds and A = 0.35 m. (a) What is the maximum kinetic energy of an oscillator of mass 1.7
Discuss the difference between the Young’s modulus of a material and the strength of a material. Does a large value of Y guarantee a strong material?
Arrange these materials according to their Young’s modulus from smallest to largest: (a) Jell-O, (b) steel, (c) wood, (d) diamond.
The windshield wipers on your car are an example of periodic motion. What is the approximate period of the motion?
In Chapter 3, we learned how the apparent weight of a person in an elevator depends on the acceleration of the elevator. Consider a simple pendulum that is placed in an elevator. Does the
Many musicians use a metronome to help keep time when playing music. Some metronomes use a simple pendulum. If a metronome clicks 100 times per minute, what is the length of the pendulum?
Pendulum clocks use a pendulum to keep time (Fig. Q11.15). This type of clock can be adjusted by varying the length of the pendulum. How should the length be adjusted in the following cases? Figure
Derive the frequency of oscillation of a torsional oscillator, Equation 11.20. Consider how the restoring force depends on the twist angle and use Newton?s second law for rotational motion (? = I?).
Use energy considerations to derive the oscillation frequency for a mass-on-a-spring oscillator. The maximum potential energy stored in the spring must be equal to the maximum kinetic energy of the
In Section 11.3, we discussed the total mechanical energy of a mass-on-a-spring oscillator. The result in Equation 11.21 shows that the total energy is proportional to the square of the amplitude.
Make a sketch of how the position and kinetic energy of a harmonic oscillator vary with time. The period of the oscillations of KE can be determined from the separation in time of adjacent maxima in
Two solid rods are made of the same material and have the same cross-sectional areas, and their lengths differ by a factor of two. If a compressive force F is applied to both, what is the ratio of
Two metal rods with the same length and cross-sectional area are both subjected to a compressive force F. If the length of rod 1 changes by more than the length of rod 2, which one has the larger
When a group of marching soldiers reach a bridge, they often “break stride” and do not walk “in step” across the bridge. Explain why.
A basketball player dribbles the ball as she moves along the court. What is a typical value for the frequency of this oscillatory motion?
A car mounted on struts is like a mass on a spring. If you ignore damping, how will the frequency of the oscillations change if passengers (or a heavy load) are added to the car? Will the frequency
If a spring with spring constant k0 is cut in half, what is the spring constant of one of the pieces?
Consider a simple pendulum that is used as a clock. (a) What should the length of the pendulum be to make one oscillation (one “tick” of the clock) every second when it is at sea
Design an experiment to measure the torsion constant k of a torsion fiber. The value of k is needed in the analysis of the Cavendish experiment
A mass hangs from a vertical spring and is initially at rest. A person then pulls down on the mass, stretching the spring. Does the total mechanical energy of this system (the mass plus the spring)
A friend of yours is asked to design a swing using two ropes attached to the branch of a tree, and he shows you the design as sketched in Figure Q11.1. Explain why this design will not work very
A mass-on-a-spring system has spring constant k = 400 N/m and mass m = 0.50 kg. (a) If it is given an initial displacement of 0.25 m and then released, what is the initial potential energy of
Figure P11.4 shows the position as a function of time for a mass attached to a spring. At what points are? Figure P11.4 ? (a) The magnitude of the momentum of the mass largest,? (b) The kinetic
The cone of a loudspeaker oscillates with an amplitude of 2.0 mm. If the frequency is 2.5 kHz, what are the maximum velocity and the maximum acceleration of the cone? Assume the speaker cone moves as
Figure P11.32 shows the displacement of a mass on a spring as a function of time.? Figure P11.32 ? (a) At what point is the acceleration positive and the velocity negative?? (b) Are there any times
Consider a torsional oscillator like the one in Figure P11.30 and suppose it has a frequency of 0.045 Hz. If the length of the rod is increased by a factor of three, what is the new frequency of the
Consider the torsional oscillator in Figure P11.30. The rotating mass consists of two small spheres, each of mass m = 2.0 kg, that are attached to the ends of a mass less rod of length L = 1.5 m. The
A torsional oscillator has a moment of inertia of 4.5 kg · m2 and a torsion constant k = 0.15 N · m. What is the frequency of the oscillator?
What is the approximate period of one of the swings in Figure P11.28? Figure P11.28 ?
The length of a simple pendulum is increased by a factor of three. By what factor does the frequency change?
A simple pendulum uses a steel wire as the “string.” The length of this wire is 1.5 m at room temperature. If the temperature is increased by 10°C, the length of the wire increases by 0.18 mm.
A simple pendulum has a period of 2.5 s on the Earth. An astronaut then takes it to the surface of the Moon. What period does the astronaut measure there?
A simple pendulum has a length of 2.5 m and is pulled a distance y = 0.25 m to one side and then released (Fig. P11.24).? Figure P11.24 ? (a) What is the speed of the pendulum when it passes through
A simple pendulum oscillates with a period of 3.5 s. What is its length?
Consider a simple pendulum that consists of a rock of mass 3.5 kg tied to the end of a (massless) string of length 1.5 m.(a) What is the frequency of the pendulum?(b) What is the period of the
Estimate the maximum acceleration of a bungee jumper. Is it larger or smaller than the acceleration due to gravity during free fall? Example 11.3 gives values for several quantities that may be
Consider the mass-on-a-spring system in Figure P11.20. Three identical springs, with the same spring constant k = 40 N/m, are used to connect the mass (m = 20 kg) to a ceiling. What is the frequency
A mass-on-a-spring system has m = 50 kg and k = 200 N/m. The mass is pulled a distance 0.25 m from its equilibrium position and then released. (a) What is the maximum acceleration of the
Estimate the spring constant for a trampoline. Assume a person is standing on the trampoline and oscillating up and down without leaving the trampoline. Begin by estimating the mass of the oscillator
A mass m = 2.4 kg is attached to two springs as it slides along a friction less floor, while the springs are fastened to two walls as shown in Figure P11.17. The springs both have k = 400 N/m and are
A mass m = 4.5 kg is attached to a vertical spring with k = 200 N/m and is set into motion. (a) What is the frequency of the oscillation? (b) If the amplitude of the oscillation is 3.5 cm,
Suppose Figure P11.3 describes the displacement of a masson- a-spring harmonic oscillator.? Figure P11.3 ? (a) If the mass is m = 2.0 kg, what is the spring constant?? (b) Estimate the velocity at t
A child plays on a bungee cord and oscillates with a certain frequency f. An adult with a mass that is five times greater than that of the child then uses the same bungee cord. What is the ratio of
Consider the mass on a spring in Figure 11.6. If the spring constant is k = 30 N/m and the mass is m = 2.5 kg, what is the period? Figure 11.6 0 Wall x =" alt = "Consider the mass on a spring in
The period of oscillation for a mass-on-a-spring system is 0.22 s. If m = 3.5 kg, what is the spring constant of the spring?
Figure P11.11 shows the velocity of a simple harmonic oscillator as a function of time.? (a) Estimate the position when v = 0.? (b) Estimate the frequency. Figure P11.11 ? v (m/s) +5 0.1 0.2 t 0.3 -5
A simple harmonic oscillator has a frequency of 300 Hz and an amplitude of 0.10 m. What is the maximum velocity of the oscillator?
Figure P11.9 shows the velocity as a function of time for an oscillator. Is it a simple harmonic oscillator? Explain why or why not. What is its frequency? Figure P11.9 ? Li (ms) 5 6 1 234
The displacement of a harmonic oscillator is given by y = 7.1 sin(48t), where the units of y are meters and t is measured in seconds. Give three values of t at which the oscillator has (a) Its
The displacement of a harmonic oscillator is given by y = 9.4 sin(15t), where the units of y are meters and t is measured in seconds. What is its maximum velocity?
The displacement of a harmonic oscillator is given by y = 3.4 sin(25t), where the units of y are meters and t is measured in seconds. Find (a) The amplitude(b) The frequency.
(a) For the simple harmonic oscillator in Figure P11.3, estimate the velocity at t = 4.0 s and at 7.0 s.? Figure P11.3 ? (b) At what time(s) does the velocity have its largest positive value? у (cm)
Figure P11.4 shows a plot of the position as a function of time for a particle undergoing simple harmonic motion. Identify the following points on this graph:? (a) Where is the speed largest?? (b)
Figure P11.3 shows the displacement of a simple harmonic oscillator as a function of time. (a) Find the period, frequency, and amplitude of the oscillator.? (b) At what time(s) does the acceleration
A person’s heart beats 70 times in 1 minute. What is the average frequency of this oscillation?
A simple harmonic oscillator takes 15 seconds to undergo 25 complete oscillations. (a) What is the period of the oscillator? (b) What is the frequency of the oscillator?
Skee Ball amusement. The popular arcade sport of Skee Ball involves bowling a wooden ball 3 in. (7.6 cm) in diameter down an alley 9 ft long, where the ball is then launched off a short ramp as shown
Halley’s comet moves about the Sun in a highly elliptical orbit. At its closest approach, it is a distance of 8.9 × 1010 m from the Sun and has a speed of 54 km/s. When it is farthest from
A meteor with a volume of 1.0 km3 strikes the Earth at the equator as shown in Figure P9.48, and all the fragments stick to the surface.? (a) What is the magnitude of the change in the angular
Repeat Problem 43, but now assume the person is holding a 5.0-kg mass in each hand. Data from Problem 43 Consider a person who is sitting on a friction less rotating stool as in Figure P9.43. The
A child of mass 50 kg jumps onto the edge of a merry-go-round of mass 150 kg and radius 2.0 m that is initially at rest as sketched in Figure 9.12. While in the air (during her jump), the child?s
A bug of mass 3.0 g is sitting at the edge of a CD of radius 8.0 cm. If the CD is spinning at 300 rpm, what is the angular momentum of the bug?Concerned with the magnitude of the angular momentum,
A figure skater begins a spin at an angular velocity of 200 rpm with her arms and legs out away from her body (Fig. 9.11A). She then pulls her arms and legs in close to her body, and her angular
A puck (mass m1 = 0.50 kg) slides on a friction less table as shown in Figure P9.39. The puck is tied to a string that runs through a hole in the table and is attached to a mass m2 = 1.5 kg. The mass
A child (m = 40 kg) is playing on a merry-go-round (m = 200 kg, R = 2.0 m) that is initially at rest. The child then jumps off in a direction tangent to the edge of the merry-go-round as shown in
Estimate the angular momentum of a figure skater of mass 50 kg who is spinning at 300 rpm (Fig. 9.11). Assume her arms and legs are pulled in very close to her rotation axis. Concerned with the
An empty bookcase (total mass 10 kg) is accidentally tipped over (Fig. P9.30). If it is given only a very gentle initial push, what is the speed of the top edge of the bookcase just before it strikes
A cylinder of mass 7.0 kg and radius 0.25 m rolls without slipping along a level floor. Its center of mass has a speed of 1.5 m/s. Find (a) The kinetic energy of translation and (b) The
A rod of mass 4.0 kg and length 1.5 m hangs from a hinge as shown in Figure P9.28. The end of the rod is then given a ?kick? so that it is moving at a speed of 5 m/s. How high will the rod swing?
Suppose the table in Figure P9.26 is extremely slippery so that there is no friction between the table and the end of the pencil. As a result, the pencil slips as it tips over. Let ?no friction
A pencil (mass 10 g and length 15 cm) is initially balanced so that it is sitting vertically on a flat table as shown in Figure P9.26. If the pencil then falls, what is its angular velocity just
Repeat Problem 9.22(f) (i.e., find vf), but now assume the rod is initially oriented an angle of 30? above the horizontal. Data From Problem 9.22(f) ? -L- Hinge (pivot point)
A bucket filled with dirt of mass 20 kg is suspended by a rope that hangs over a pulley of mass 30 kg and radius 0.25 m (Fig. P9.31). Everything is initially at rest, but someone is careless and lets
A bicycle is moving at a speed of 15 m/s when the rider applies her brakes. The bicycle comes to a stop after moving forward another 20 m. Estimate the force of one of the bicycle brake pads on the
A bicycle is moving at a speed of 15 m/s when the rider applies her brakes. The bicycle comes to a stop after moving forward another 20 m. Estimate the force of one of the bicycle brake pads on the
Estimate the angular momentum of a DVD that is playing your favorite video. Assume an angular speed of 1000 rpm. The mass of a DVD is about 15 g.Concerned with the magnitude of the angular momentum,
A bowling ball has a mass of 6.0 kg and a radius of 22 cm. If it is rolling down a lane with a speed of 9.0 m/s, what is the angular momentum of the ball?Concerned with the magnitude of the angular
Consider the pencil in Problem 26. What is the angular momentum of the pencil just before it strikes the table? Concerned with the magnitude of the angular momentum, not its sign. Data from problem
Consider a person who is sitting on a friction less rotating stool as in Figure P9.43. The person initially has his arms outstretched and is rotating with an angular speed of 5.0 rad/s. He then pulls
Estimate the angular momentum of an airplane propeller that is spinning at 2000 rpm.Concerned with the magnitude of the angular momentum, not its sign.
Two disks are located on an axle as shown in Figure P9.46. The lower disk is initially spinning at 50 rad/s, and the upper one is not spinning. The upper disk then falls onto the lower disk, and they
A particle of mass 3.0 kg moves with a horizontal velocity of 20 m/s as shown in Figure P9.47.? (a) What is the angular momentum of the particle about an axis that runs through point P and is
A DVD (radius 6.0 cm) is spinning freely with an angular velocity of 1200 rpm when a bug drops onto and sticks to the DVD a distance 4.5 cm from the center. If the DVD slows to 800 rpm, what is the
Estimate the angular momentum associated with the Moon’s orbital motion around the Earth.
What is the ratio of the angular momentum of the Moon due to its orbital motion around the Earth to the Earth’s orbital angular momentum around the Sun?
For the particle in Problem 47, what is the direction of the angular velocity of the particle? Data from problem 47 A particle of mass 3.0 kg moves with a horizontal velocity of 20 m/s as shown in
Use the right-hand rule to find the direction of the orbital angular momentum of the Earth as it orbits the Sun as sketched in Figure 9.19.? Figure 9.19 ? 23.5 THE SEASONS ON EARTH -Plane of Earth's
Consider the rotational motion of the Earth as it spins about the axis that runs from the North Pole to the South Pole. Find the magnitude and direction of the angular momentum L(vector) associated
Consider the rotational motion of the wheels of a car when the car is in motion. Use a drawing to show the direction of the angular momentum of each wheel.
Consider the yo-yo in Figure 9.8. What is the direction of the angular momentum vector of the yo-yo? Figure 9.8 ? M R V; = 0 W; = 0 INITIAL POSITION Uf = ? Wf = ? FINAL POSITION

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