chapter 10 physics

A 2.0-kg mass is attached to a spring with a spring constant of 800 N/m and oscillates with an amplitude of 50 cm. What is the ratio of the potential energy to the total energy when the displacement is 10 cm?

(1/5)2

A 2.0-kg mass is attached to a spring with a spring constant of 800 N/m and oscillates with an amplitude of 50 cm. By what factor does to the total energy of oscillation change if the amplitude of oscillation is tripled?

(3)2

What is the compressive stress at the bottom of a column of height h, cross-sectional area A, and mass m?

mg/A

How is stress defined?

As force per unit cross-sectional area

The compressive stress at the bottom of a column must be less than what quantity to prevent it from being crushed under its own weight?

Compressive strength

Where does the loudspeaker have the largest x-component of the velocity?

D

You have three uniform shapes of equal mass with which to construct a physical pendulum. They are a hoop (rotational inertia about the center of mass equals mR2) with the axis at the edge, a disk (rotational inertia about the center of mass equals 12 mR2) with the axis at the edge, and a rod of length L = 2R with the axis at its end (rotational inertia about the end of a rod equals 13 mL2). Which shape will have the largest period?

the hoop

Physical pendulums are studied on the Earth and on the Moon. The magnitude of the free-fall acceleration on the Moon is about one-sixth that on the Earth. Rank the periods of the pendulums from greatest at the top to least on the bottom. Assume that the distance from the rotation axis to the center of mass of the object is constant.

10 moon 10 earth 1 moon 1 earth

If the period is 10 ms, then what is the frequency?

100 Hz

A mass-spring system oscillates in simple harmonic motion with a frequency of 2.0 kHz. If both the mass and the spring constant are doubled, then what is the frequency?

2.0 kHz

A steel guitar string of length L0 and cross-sectional area A0 is subject to a tension of magnitude F0, which causes the string to stretch by an amount ΔL0. If you apply a tension of magnitude of 2F0 to a string made of the same material and length but with twice the cross-sectional area (2A0), that string will stretch by an amount ΔL. Determine the ratio ΔLΔL0 .

1

By what factor does the period change if the amplitude is tripled?

1

Rank the following periods in terms of their corresponding frequencies, with the largest frequency at the top and the smallest at the bottom.

1 ms 1s 1 min 1 hr 1 day

A mass-spring system oscillates in simple harmonic motion with a period of 2.0 s. If the spring constant is doubled, then what is the period?

1.4s

A steel guitar string of length L0 and cross-sectional area A0 is subject to a tension of magnitude F0, which causes the string to stretch by an amount ΔL0. What force magnitude is needed to stretch a string of the same cross-sectional area and material but twice as long (L = 2L0) by the same amount (ΔL = ΔL0)?

1/2 F0

Simple pendulums are studied on the earth and on the moon. The magnitude of the free-fall acceleration on the moon is about 1/6 that on the earth. Rank the periods of the pendulums from greatest at the top to least on the bottom.

36L moon 36L earth L moon L earth

An object resting on a flat, horizontal, frictionless surface is connected to a spring, displaced from equilibrium, and then released. The other end of the spring is connected to a massive, immovable object. Rank the following cases according to the maximum acceleration magnitude of the object, with the largest maximum acceleration magnitude at the top and the smallest at the bottom. Ignore air resistance.

50 50 50 100 25 100 25 200

An object resting on a flat, horizontal, frictionless surface is connected to a spring, displaced from equilibrium, and then released. The other end of the spring is connected to a massive, immovable object. Rank the following cases according to the maximum speed of the object, with the largest maximum speed at the top and the smallest at the bottom. Ignore air resistance.

50 50 50 100 25 50 25 100

How far does a spring with a spring constant of 10 N/m stretch if an object of mass 10 g is attached to the lower end of the spring and the upper end of the spring is attached to the ceiling?

9.8 mm

Engineers test two gaskets of identical shape but made of two different materials to be used in a submersible diving bell. Gasket A undergoes a volume compression of 0.5% at a depth of 2000 m, and gasket B undergoes a 1% volume compression at the same depth. Which of the two materials has a larger bulk modulus?

A

Select all of the following situations in which a solid object deforms.

A cable lengthens when a heavy sign is attached to it. A block of ice contracts just before it melts. A baseball bat bends upon contact with a fast-moving baseball.

Select all of the following situations in which a solid object acts elastically.

A sponge is squeezed and then released. A rubber band is removed from a stack of papers.

Select all of the following forces that could cause damping.

Air resistance Drag Kinetic friction

Select all of the following that correspond to the meaning of the minus sign in Hooke's law for volume deformation. Assume that the bulk modulus is positive.

An increase in pressure causes a decrease in volume. An decrease in pressure causes a increase in volume.

Engineers test two rectangular beams of identical shape but made of two different materials to be used in a skyscraper. Beam A deforms twice as much as beam B when identical shear forces are applied. Which of the two materials has the larger shear modulus?

B

Select all of the lettered points on the graph where the loudspeaker has the most negative x-component of the velocity.

B F

Select all of the following that would increase the stiffness of a cylindrical block of wood.

Decrease its length. Increase its cross-sectional area

Which types of forces cause damping?

Dissipative forces

Select all of the following statements that are true regarding the maximum speed for simple harmonic motion.

Doubling the amplitude doubles the maximum speed. Quadrupling the spring constant doubles the maximum speed.

Select all of the following statements that are true regarding the maximum acceleration magnitude for simple harmonic oscillators.

Doubling the spring constant doubles the maximum acceleration magnitude. Doubling the amplitude doubles the maximum acceleration magnitude.

What kind of material will continue to stretch beyond its ultimate tensile strength?

Ductile

Match the items in the right and left columns.

Ductile material Soft metals Brittle material Thin ice Permanent deformation Exceeding the elastic limit Breaking Exceeding the ultimate strength

What type of objects return to their original shape and size after a deformation?

Elastic

For very small displacements greater than zero, select all of the following functions of force magnitude versus displacement from equilibrium that could result in simple harmonic motion. The equilibrium point is x = 0.

F = tanx F = sinx

What magnitude of force is needed to produce the same amount of stretch (ΔL = ΔL0) in a string made of the same material, but having twice the cross-sectional area and twice the length (i.e., A = 2 A0 and L = 2L0)?

Fo

Which of the following forces could result in an object moving with simple harmonic motion?

Force of magnitude kx, opposite the direction of the displacement

Where does the loudspeaker have a positive x-component of the displacement and a positive x-component of the velocity?

G

What are the units of stress?

It has units of pressure.

What are the units of strain?

It is dimensionless.

How does the k constant in Hooke's law depend on the dimensions of the deformed object when generalizing from springs to elastic media?

It is directly proportional to the cross-sectional area and inversely proportional to the length.

A mass and spring system oscillate in the vertical direction. Select all of the following quantities that, if changed, would affect the frequency of oscillation.

Mass Spring constant

Select all of the following that are SI units of Young's modulus.

N/m2 Pa

Select all of the following that are SI units of shear modulus.

N/m2 Pa

Select all of the following that are SI units of bulk modulus.

Pa N/m2

The bulk modulus of a material has the same units as which quantities?

Pressure Volume Stress

The Young's modulus of a material has the same units as which quantity?

Stress Pressure

If the following quantities of a physical pendulum were changed, which would cause the frequency to change?

The distance between the axis and the center of mass The rotational inertia

Select all of the following statements that are true when a system is at resonance.

The driving force is always in the same direction as the velocity. The amplitude is as large as possible. The frequency of the driving force is equal to the natural frequency of the system.

Why does the amplitude in an oscillator reach a maximum when the driving force is at resonance?

The force is always in the direction of the velocity and is always doing positive work.

Which of the following is true regarding Hooke's law for objects other than springs?

The magnitude of the tensile or compressive force is directly proportional to the change in the length of the object.

Which of the following statements is true for simple harmonic motion?

The maximum acceleration magnitude is directly proportional to the amplitude.

Which of the following statements is true for simple harmonic motion?

The maximum speed is directly proportional to the amplitude.

Select all of the following that are true for simple harmonic motion.

The net force is directly proportional to the displacement from equilibrium. The net force is in the opposite direction of the displacement from equilibrium. The graph of net force versus displacement from equilibrium is a straight line.

Select all of the following statements that apply to an object moving with simple harmonic motion.

The net force is not constant. Its displacement is not constant. Its acceleration is not constant.

The shear modulus of a material has the same units as which quantities?

The shear modulus of a material has the same units as which quantities?

Select all of the following that are necessary for an object to move with simple harmonic motion.

There must be a point of stable equilibrium. A restoring force must act on the object. The object must at some time be displaced from its equilibrium position.

In Hooke's law for shear deformation, how are the relative displacement and the separation of the two surfaces oriented?

They are perpendicular.

Which one of the following types of motion can be related to simple harmonic motion?

Uniform circular motion

Select all of the following statements that are true regarding uniform circular motion and simple harmonic motion.

Uniform circular motion is similar to simple harmonic motion if the radius of the circle is equal to the amplitude of the oscillator. The angular speed of uniform circular motion is similar to the angular frequency of simple harmonic motion. Uniform circular motion is two-dimensional, while simple harmonic motion is one-dimensional.

At which point is x < 0, vx < 0, and ax > 0?

b

Select all of the lettered points on the graph where the loudspeaker has zero x-component of the velocity.

c a e

Select all of the following sets of three vectors for an object in uniform circular motion, shown in the image, that are consistent with simple harmonic motion.

c d a

Six different simple pendulums are shown. The mass and length are indicated for each lettered case. Rank the frequency of oscillation from greatest at the top to least at the bottom. If there are ties, then order the cases alphabetically.

e f a b c d

Select all of the following that are units of Young's modulus.

lb/in2 psi

Newton's second law applied to simple harmonic motion has which of the following mathematical forms?

m a→ = -k x→