PLV's Modules 4-7

-6.25 × 105 J

A 2 000-kg car travelling at 25.0 m/s skids to halt on level ground. How much work was done by nonconservative forces in stopping the car?

Only if energy is somehow added to the ball.

A ball hangs on the end of a string that is connected to the ceiling so that it swings like a pendulum. You pull the ball up so that it nearly touches the end of your nose. You let the ball swing down (from rest), and then swing back, toward your face. Under which conditions will the ball strike your nose?

Gravitational, kinetic, and elastic

A ball is dropped from some height onto an unstrained vertical spring (mounted to a tabletop) and compresses it. Consider an instant where the spring has not yet brought the ball to a halt, but is still in the process of compressing. What types of energies are associated with the spring-ball system at that instant? Assume that the zero of gravitational energy is at the level of the tabletop.

Both conservative and nonconservative forces act on the ball.

A ball is dropped vertically from a height h. When it rebounds from the floor it attains a maximum height of 23⁢ h. What statement is true?

A nonconservative force does positive work on the ball.

A ball starts with an initial kinetic energy of 1000 J and zero gravitational energy potential. At some later time, the ball has zero kinetic energy and 1150 J of gravitational potential energy. Which of the following is true?

The amplitude remains the same, and the angular frequency increases. Correct answer iconCorrect. At the instant the top block is removed, the total mechanical energy of the remaining system is all elastic potential energy and is 12kA2 (see Equation 10.13), where A is the amplitude of the previous simple harmonic motion. This total mechanical energy is conserved, because friction is absent. Therefore, the total mechanical energy of the ensuing simple harmonic motion is also 12kA2, and the amplitude remains the same as it was previously. The angular frequency ω is given by Equation 10.11 as ω=km. Thus, when the mass m attached to the spring decreases, the angular frequency increases.

A block is attached to a horizontal spring. On top of this block rests another block. The two-block system slides back and forth in simple harmonic motion on a frictionless horizontal surface. At one extreme end of the oscillation cycle, when the blocks come to a momentary halt, the top block is lifted vertically upward, without disturbing the bottom block. What happens to the amplitude and the angular frequency of the ensuing motion?

130 rad/s

A car is moving with a constant speed of 70.0 mi/h (31.2 m/s). If its wheels have a radius of 24.1 cm, what is their angular speed?

The total kinetic energy before and after the collision is conserved.

A car of mass m moving with a speed v collides with an identical car that is at rest. After the collision, the cars stick together. Which of the following statements is false?

ultrasonic

A certain dog whistle simultaneously emits a range of frequencies above 50 kHz. How can this sound be characterized?

Greater than

A cloud of interstellar gas is rotating. Because the gravitational force pulls the gas particles together, the cloud shrinks, and, under the right conditions, a star may be formed. Would the angular velocity of the star be less than, greater than, or equal to the angular velocity of the rotating gas?

Gold

A common construction brick used in home building has a volume of 65 in3. Which of the following bricks of this size weighs the most?

The pressure in the fluid in section 1 is greater than in section 2.

A fluid flowing in a pipe with a uniform cross-sectional area changes elevation. Which of the following is true?

None of the above is true.

A group of particles has a net momentum equal to zero? Which of the following must be true?I. The speed of each particle is zero.II. The velocity of each particle is zero.III. The mass of each particle must be equal.IV. The kinetic energy of each particle must be zero.

The hoop

A hoop of mass M and radius R and a solid cylinder of mass M and radius R are rolling along level ground with the same translational speed. Which object has the greater total kinetic energy?

The solid sphere

A hoop, a solid cylinder, a spherical shell, and a solid sphere are placed at rest at the top of an inclined plane. All the objects have the same radius. They are all released at the same time and allowed to roll down the plane. Which object reaches the bottom first?

The frequency in the air is the same as the frequency in the water, and the wavelength in the air is smaller than the wavelength in the water.

A horn on a boat sounds a warning, and the sound penetrates the water. How does the frequency of the sound in the air compare to its frequency in the water? How does the wavelength in the air compare to the wavelength in the water?

Δx= 0 m; Δθ= 2π rad

A lawn mower blade of length 0.50 m rotates about its center. Are the magnitudes of the linear displacement (Δx) and angular displacement (Δθ) of one of the tips upon one complete rotation?

1 m

A meter stick rotates about one end through an angle of 57.3°. What is the arc length traced out by the opposite end?

the speed of the wave decreases.

A rope is attached to a hook in the ceiling and is hanging straight down. The rope has a mass m, and nothing is attached to the free end of the rope. As a transverse wave travels down the rope from the top, ________________.

The square.

A skateboarder wants to cross a large playground and notices that there are large shapes painted on its asphalt surface. One shape is a large circle that covers the entire playground. Inscribed in that circle is a square, with one point at the skateboarder's feet and the other at his destination. The surface is rough and, therefore, friction is present. What path does he follow in order to minimize the work done by nonconservative forces?

14 m/s

A stone is dropped from rest from the top of a cliff into a pond below. If its initial height is 10 m, what is its speed when it hits the water?

All of the above

A stone is projected at a 45° above the horizontal. At the peak of its trajectory, what types of energy does it possess?

1.23 × 104 J

A stone sphere of radius 7.00 m rests in a flat field. Relative to the ground, what is the gravitational potential energy of a 90.0-kg person sitting on the very top of the sphere?

All of the above must be true.

A uniform ladder is at rest leaning against a smooth wall (frictionless) as shown in the figure at the left. The base of the ladder is on rough ground (friction). The corresponding free-body diagram for the ladder is shown in the figure at the right. Which of the following must be true?

Compress the spring twice as much

A vertical spring is mounted to a table and compressed downward. A ball of mass m is placed on a spring (spring constant k), the spring is released, and the ball is projected vertically upward. In which case would you expect the ball to reach the greatest maximum height?

0.14 m

A wave has the mathematical form y=(0.2⁢ m)⁢ sin(2π⁢ f⁢t-2π⁢x/λ). What is the displacement of a particle at the origin after a time t=1/8⁢T?

0.24 m

A wave has the mathematical form y=(0.4⁢ m)⁢ sin(2π⁢ f⁢t-2π⁢x/λ) and has a wavelength of 0.90 m. What is the y-displacement of the wave at x=0.54 m at t=0 s?

Her angular speed decreases, and her angular momentum remains constant.

A woman is sitting on a spinning piano stool with her arms folded. Ignore any friction in the spinning stool. When she extends her arms outward, which of the following is true?

28 m/s2

An airplane prop has a radius of 1.5 m. If it starts from rest and accelerates uniformly to an angular speed of 55 rad/s in a time of 3.0 s, what is the tangential acceleration of the tip of the prop?

at different times, the echo under water returning more quickly.

An echo is sound that returns to you after being reflected from a distant surface (e.g., the side of a cliff). Assuming that the distances involved are the same, an echo under water and an echo in air return to you _____________________

All of these are true.

An object is floating in a fluid. Which of the following is true?

Your eardrums move outward as you climb up the mountain.

As you climb a mountain, your ears "pop" because of the changes in atmospheric pressure. Which of the following is true?

The magnitude of the force F2 is greater than F1.

Consider the two-piston system in the figure below. A force F1 is applied to the smaller piston. Which of the following is true?

II only

Exploding gunpowder in a cannon (mass M) propels a cannonball (mass m) forward. Simultaneously, the cannon recoils. Which of the following is true? Note that M>m.I. The speeds of the cannonball and cannon are equal.II. The magnitudes of the momentum of the cannonball and cannon are equal.III. The kinetic energy of the cannonball and cannon are equal.

B

Five simple pendulums are shown in the drawings. The lengths of the pendulums are drawn to scale, and the masses are either m or 2m, as shown. Which one has the smallest angular frequency of oscillation?

The sheets move toward each other and the gap narrows.

Hang two sheets of paper vertically from adjacent corners. The sheets should be parallel and close to each other with a small gap between them. Now gently blow down between the two sheets. What happens?

4.7 s

How long does it take the thunder from a lightening strike to travel one mile (in air)?

3600 J

How much energy is dissipated by a 60-W light bulb in one minute?

Thunder longitudinal, lightening transverse.

How would you describe thunder and the light from lightening as waves?

2.2 m/s

If the angular speed of a 1.1-m baseball bat is 2.0 rad/s, what is the tangential speed of the tip of the bat?

30.2 m/s

If the chemical energy stored in a 250-Calorie (1.0 × 106 J) energy bar were converted into the kinetic energy of a 2 200-kg car, what would be the speed of the car (assuming it started from rest)?

Increase the length by a factor of four

If you want to decrease the frequency of a simple pendulum by a factor of two you should ...

Both of these

In a famous demonstration in 1646, Pascal poured water into an already full barrel using a long narrow pipe. As he filled the extension tube higher and higher, the barrel eventually burst. Which of the following choices best explains why the barrel burst?

A 1-kg mass swinging freely at the end of a rope

In which of the following is a tangential acceleration involved in the motion?

1.5 m/s

It takes a wave traveling on a string 1.2 s to complete a full cycle. You measure the distance it takes to repeat itself to be 1.8 m. How fast is the wave moving?

The pressure at the bottom of the pool on the moon would be less than the pressure at the bottom of the pool on earth, since the pressure in a fluid also depends on the local acceleration due to gravity, which is less on the moon.

Let's say you could go swimming on the moon. How would the pressure at the bottom of a 3-m deep swimming pool compare with the pressure at the bottom of the same pool on earth?

The lift force on an airplane would be reduced, making it more difficult for takeoff.

Normal changes in weather can sometimes produce unusually low-density air near airports. Under these conditions, which of the following would be true?

The total momentum in the y-direction after the collision will be equal to zero.

Object 1 is moving in the positive x-direction. It collides with a second object that is initially at rest. The collision is not head-on, so the objects move off in different directions after the collision (see figure). What must be true about the total momentum of object 1 and object 2 in the y-direction after the collision?

10 psi + 1 atm

Specifications on a basketball suggest it be inflated to a pressure of 9-11 psi. You inflate the ball to a pressure of 10 psi. What is the absolute pressure in the ball?

40 rev

Staring from rest, a lawn mower blade undergoes a constant acceleration of 125.0 rad/s2. How many revolutions does it undergo in 2.0 s?

Divide the mass by four, or quadruple the spring constant.

Suppose a mass is attached to the end of a horizontal oscillating spring of spring constant k. Choose the answer that will double the frequency of oscillation.

4000 W/m2

Suppose a sound source uniformly delivers 40 W of power perpendicularly to a square surface of side 10 cm. What is the sound intensity on the surface?

10.4 m/s

Suppose that an object undergoes simple harmonic motion, and its displacement has an amplitude A= 15.0 cm and a frequency f= 11.0 cycles/s (Hz). What is the maximum speed (v) of the object?

25.0 rad/s2

Suppose the car now accelerates from 0 m/s to 30.0 m/s in 5.00 s. If the wheels have a radius of 24.1 cm, what is their angular acceleration?

45 dB

Suppose the intensity due to one source is 1.0 × 10-10 W/m2 and the other is 3.2 × 10-6 W/m2. What is the difference between their intensity levels in decibels (dB)?

East and west.

Suppose the longitudinal component of a wave created by an earthquake is travelling from east to west. As it passes through your position, how would you expect to move?

1350 N/m

Suppose you hang a mass m= 5.50 kg from a vertical spring and it stretches 4.00 cm from its unstrained length. What is the spring constant k of the spring?

0.08 rad/s

Suppose you have a simple pendulum that, on earth, has an angular frequency of 0.20 rad/s. What is its frequency on the moon, where gmoon=16gearth?

It is reduced by a factor of 2.

Suppose you replace a guitar string with another one. Assuming the length and the tension are identical to that of the original string, how does the velocity of the wave change if the mass of the new string is twice that of the original?

The pitch would get progressively lower (i.e., smaller frequency).

Suppose you were bungee jumping from a bridge while blowing a hand-held air horn. How would someone remaining on the bridge hear the pitch of the air horn as time increased?

Object A has a greater moment of inertia than Object B.

The drawing shows two objects rotating about a vertical axis. The mass of each object is given in terms of m0, and its perpendicular distance from the axis is given in terms of r0. Which of the following is true?

C

The figure below shows the top view of two balls colliding on a horizontal frictionless table. The path followed by the center of mass of this system is shown by the black vector. Which path, labeled A, B, C, or D, will the center of mass follow after the collision?

A

The figure shows an overhead view of a large door that is free to pivot on a hinge along its left edge. A force F is applied to the door in four different ways. The magnitude of the force is the same in each case. In which case is the torque on the door the largest?

-0.79 rad/s2

The initial angular velocity of a ceiling fan is 6.28 rad/s. It accelerates uniformly to 3.14 rad/s in 4.0 s. What is the angular acceleration?

4.0 W/m2

The intensity a distance r from a spherically symmetric sound source is 100 W/m2. What is the intensity at five times this distance from the source?

The smaller hoop; two times as great.

The same force F is applied to the edge of two hoops as the drawing below shows. The hoops have the same mass, whereas the radius of the larger hoop is twice the radius of the smaller one. The entire mass of each hoop is concentrated at its rim, so the moment of inertia is equal to Mr2, where M is the mass of the hoop, and r is the radius. Which hoop has the greater angular acceleration, and how many times as great is it compared to the other hoop?

99 dB

The sound intensity at the ear of passenger in a car with a damaged muffler is 8.0 × 10-3 W/m2. What is the intensity level of this sound in decibels? Use the threshold of hearing (1.0 × 10-12 W/m2) as the reference.

1.62 m

The speed of sound in air is 343 m/s. What is the wavelength of a sound wave with a frequency of 212 Hz?

C, A, B

Three solid objects are floating in a liquid as shown. Rank the densities of the objects, largest first.

False

True or False: In a two-dimensional collision, momentum can only be conserved in one dimension, not both.

False

True or False: In an elastic collision, the kinetic energy of each object is the same both before and after the collision.

False

True or false: Equal volumes of different materials will weigh the same.

The magnitude of the torque created by F1 must be equal in magnitude to the torque created by F2.

Two forces are applied to a ship's wheel. The wheel is not rotating. Which of the following must be true?

IV only

Two objects have the same momentum. Which of the following is true?I. The masses of the objects are equal.II. The speeds of the objects are equal.III. The velocities of the objects are equal.IV. The direction of motion of each object is the same.

B

Two particles are located on the x-axis as shown. Particle 1 has a mass 3m, and particle 2 has a mass of m. Where on the x-axis, as indicated by the letters A, B, C, and D, is closest to the center of mass of this system?

The pressure in the fluid in section 2 is greater than in section 1.

Water is flowing through a horizontal pipe. Which of the following is true?

ω= -0.10π rad/s

What is the average angular velocity of the seconds hand of a clock?

wavelength/2

What is the distance between the center of a condensation and the center of an adjacent rarefaction in a sound wave of wavelength λ?

1.25 N

What is the magnitude of the force F required to stretch or compress a spring of spring constant k= 50.0 N/m a distance x= 2.50 cm from its unstrained length?

151 m/s2

What is the magnitude of the total acceleration of the tip of a 1.20-m airplane propeller that is moving with an angular speed of 35.0 rad/s and undergoing an angular acceleration of 11.0 rad/s2?

18.4 m

What is the maximum height a 100-W engine can lift a 100-kg man in 3.00 minutes?

sqr root g/l

What is the natural frequency of a mass m hanging at the end of a massless string of length L?

The center of gravity.

What is the point at which the weight of rigid object can be considered to act when producing a torque on the object?

-60 J

What is the work done by the force of gravity when a 20.0-kg weight is displaced vertically upward a distance of 3.0 m?

1/2pi sqr root k/m

What should be the frequency of the driving force acting on a mass m attached to the end of a horizontal spring of spring constant k in order put the system into resonance?

The alcohol thermometer

Which of the following is not a common type of pressure gauge?

The body can have translational motion and rotational motion, as long as its translational and angular accelerations are equal to zero.

Which of the following is true about a rigid body in dynamic equilibrium?

ω0= 0 rad/s, ω= 5.0 rad/s, t= 3.0 s

Which of the following sets of variables are suitable for direct substitution into the angular kinematic equations?

C

Which of the letters below most closely matches the location of the center of gravity of the baseball bat?

f observer = f source (( 1 - (v observer/ v of sound)) / (1 + (V source / V of sound)))

Which one of the equations below would you use in the case of the observer moving to the left relative to a stationary medium, and the source moving to the right?

It decreases.

You are a passenger on a jetliner that is flying at constant velocity. You get up from your seat and walk toward the front of the plane. Because of this action, your forward momentum increases. What happens to the forward momentum of the plane itself?

It took the thunder a longer time to reached your ears on New Year's Eve.

You happen to observe lightning strike the same tree (a mile away) at two different times of the year. You recall the first one was on a hot summer night, and the second one was during a rare winter storm on New Year's Eve when the temperature was below zero. What statement is true? Assume the sound is moving in an ideal monatomic gas.

The object with the greater mass should be attached to the spring with the smaller spring constant.

You have two springs. One has a greater spring constant than the other. You also have two objects, one with a greater mass than the other. Which object should be attached to which spring, so that the resulting spring-object system has the greatest possible period of oscillation?

The nail hurts worse than the chalk, because the nail has a smaller cross-sectional area.

You push a piece of chalk and a nail into your hand with the same force. Which of the following is true?