Question 1

Which of these statements applies to a material with a large bulk modulus?
A)The material cannot be easily compressed in volume.
B)The material can be easily compressed in volume.
C)The material cannot be easily compressed in length.
D)The material can be easily compressed in length.

Accepted Answer

The bulk modulus is a measure of a material's resistance to uniform compression. A large bulk modulus indicates that the material is resistant to compression in volume, meaning it cannot be easily compressed.

Question 2

What does it mean to say that the value for the shear modulus of a material is large?
A)A small force can cause a large amount of twisting.
B)A large force is required for a small amount of twisting.
C)A small force can cause large linear expansion.
D)A large force is required to produce a small increase in length.

Accepted Answer

A large shear modulus means that the material is very rigid in response to shear stress, so a large force is needed to produce a small amount of twisting or shear deformation.

Question 3

What type of units are used when measuring strain?
A)length
B)volume
C)angle
D)Strain is a dimensionless quantity.

Accepted Answer

Strain is a measure of deformation representing the displacement between particles in the material body. It is a dimensionless quantity because it is defined as the ratio of change in length to the original length, thus cancelling out any units of measurement.

Question 4

Which of these quantities does NOT have to be conserved in the process of stretching of an extended object?
A)volume
B)mass
C)length
D)density

Accepted Answer

During the stretching of an extended object, its length changes as it is either increased or decreased based on the direction of the applied force, indicating that length does not have to be conserved. Mass, volume, and density are properties that are not inherently altered by simply stretching the object, assuming no material is added or removed.

Question 5

Which of these types of units is used when measuring hydraulic stress?
A)force
B)pressure
C)length
D)volume

Accepted Answer

Hydraulic stress is measured in terms of pressure, which is the force per unit area applied in a direction perpendicular to the surface of an object.

Question 6

Which of the following quantities does tensile stress correspond to?
A)pressure
B)force
C)energy
D)volume

Accepted Answer

Tensile stress is defined as the force per unit area applied to a material, which is similar to the concept of pressure, as both are force per unit area.

Question 7

If you double the amplitude of a simple harmonic oscillator, how is maximum velocity going to change?
A)double
B)increase by 4 times
C)decrease by 2 times
D)decrease by 4 times

Accepted Answer

The maximum velocity in a simple harmonic oscillator is directly proportional to the amplitude. Therefore, if the amplitude is doubled, the maximum velocity will also double.

Question 8

For an object attached to a horizontal spring, what is the relationship between kinetic (E_kin) and potential (E_pot) energy of the object when positioned at the point where displacement is exactly half the amplitude? A)E_kin = 3E_pot B)E_pot = 3E_kin C)E_kin = 2E_pot D)E_pot = 2E_kin

Accepted Answer

At half the amplitude, the potential energy is one-fourth of its maximum value, while the kinetic energy is three-fourths of the maximum, making the kinetic energy three times the potential energy at this point.

Question 9

Which of these types of units is used when measuring Young's modulus?
A)pressure
B)force
C)length
D)area

Accepted Answer

Young's modulus is a measure of the stiffness of a material and is defined as stress over strain. Since stress is measured in units of pressure (Pascals in the SI system), Young's modulus is also expressed in units of pressure.

Question 10

For an object oscillating on a spring, when is the velocity of the object the largest?
A)when potential energy is minimal
B)when potential energy is maximal
C)when displacement is farthest away from equilibrium
D)when acceleration is maximal

Accepted Answer

The velocity of an object oscillating on a spring is largest when its potential energy is minimal because at this point, most of the energy is kinetic, indicating maximum velocity. This typically occurs at the equilibrium position where the spring is neither compressed nor stretched.

Question 11

If the amplitude of a simple harmonic oscillator is tripled, which of these quantities does NOT change?
A)total energy
B)frequency
C)maximum speed
D)kinetic energy

Accepted Answer

The frequency of a simple harmonic oscillator is determined by its mass and the stiffness of the spring (or the force constant), not by the amplitude of the oscillation. Tripling the amplitude affects energy, speed, and kinetic energy, but not the frequency of oscillation.

Question 12

You attach a mass to a spring and let it oscillate. If you attach the same mass to another spring that has a spring constant that is 4 times larger than the first spring, how does the linear frequency of oscillations change?
A)increases by 2 times
B)increases by 4 times
C)increases by  times
D)decreases by 2 times

Accepted Answer

The answer of You attach a mass to a spring...

Question 13

If you increase the displacement of a spring from an equilibrium position by 2 times, how will its elastic potential energy change?
A)It will increase by 2 times.
B)It will decrease by 2 times.
C)It will increase by 4 times.
D)It will decrease by 4 times.

Accepted Answer

The elastic potential energy stored in a spring is given by the formula $E_p = \frac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is the displacement from the equilibrium position. If the displacement is doubled, the energy will increase by $2^2 = 4$ times, according to the square of the displacement increase.

Question 14

Figure 13.1
​  ​
The figure shows the elastic potential energy of an object attached to a horizontal spring. The object slides on a table without friction.
-In Fig. 13.1, at which position does the object reach minimum total energy?
A)(i)
B)(ii)
C)(iii)
D)The total energy is constant, the same everywhere.

Accepted Answer

The total energy of an object in motion, especially in contexts like pendulums or objects in gravitational fields, remains constant if we ignore air resistance and friction. This is because the total energy is the sum of kinetic energy and potential energy, which convert into each other without loss in an ideal system.

Question 15

Which of these statements can be applied to plastic deformation of an object?
A)It permanently changes the shape of an object.
B)The object returns to the original shape once the pressure stops.
C)It always occurs just before the object breaks.
D)A material experiencing it responds to stress in a linear fashion.

Accepted Answer

Plastic deformation refers to the permanent change in the shape of an object when a stress is applied and removed. Unlike elastic deformation, where the object returns to its original shape after the stress is removed, plastic deformation leaves lasting changes.

Question 16

Figure 13.1
​  ​
The figure shows the elastic potential energy of an object attached to a horizontal spring. The object slides on a table without friction.
-In Fig. 13.1, at which position does the object reach minimum potential energy?
A)(i)
B)(ii)
C)(iii)
D)(iv)

Accepted Answer

The answer of Figure 13.1
​  ​
The figure shows the...

Question 17

At what point can we say that the response of an object to stretching is elastic?
A)when the object starts oscillating
B)when the object remains stretched
C)when strain and stress are proportional
D)when strain and stress are inversely proportional

Accepted Answer

Elastic behavior is characterized by a proportional relationship between stress and strain, meaning the object returns to its original shape after the force causing the deformation is removed. This is described by Hooke's Law for elastic materials.

Question 18

Figure 13.1
​  ​
The figure shows the elastic potential energy of an object attached to a horizontal spring. The object slides on a table without friction.
-In Fig. 13.1, at which position does the object reach maximum kinetic energy?
A)(i)
B)(ii)
C)(iii)
D)(iv)

Accepted Answer

At position (ii), the object is at the lowest point in its trajectory, meaning all potential energy has been converted to kinetic energy, making it the point of maximum kinetic energy.

Question 19

For an object oscillating while attached to a horizontal spring, at what fraction of maximal velocity is it moving when it passes exactly half way from the equilibrium toward maximum extension?
A)25%
B)50%
C)75%
D)87%

Accepted Answer

The velocity is maximum at the equilibrium point and zero at the maximum extension. So, at half way from the equilibrium toward maximum extension, the velocity is half of the maximum velocity.

Question 20

An object with a mass of 200 g is attached to a horizontal spring having a spring constant of 1500 N/m. What is the maximum speed the mass can achieve if it is initially displaced 25 cm from equilibrium?
A)0.1 m/s
B)2.2 m/s
C)22 m/s
D)68 m/s

Accepted Answer

The answer of An object with a mass of 200...

Quiz 13: Elasticity and Vibrations

Which of these statements applies to a material with a large bulk modulus?

What does it mean to say that the value for the shear modulus of a material is large?

What type of units are used when measuring strain?

Which of these quantities does NOT have to be conserved in the process of stretching of an extended object?

Which of these types of units is used when measuring hydraulic stress?

Which of the following quantities does tensile stress correspond to?

If you double the amplitude of a simple harmonic oscillator, how is maximum velocity going to change?

For an object attached to a horizontal spring, what is the relationship between kinetic (E_kin) and potential (E_pot) energy of the object when positioned at the point where displacement is exactly half the amplitude?

Which of these types of units is used when measuring Young's modulus?

For an object oscillating on a spring, when is the velocity of the object the largest?

If the amplitude of a simple harmonic oscillator is tripled, which of these quantities does NOT change?

You attach a mass to a spring and let it oscillate. If you attach the same mass to another spring that has a spring constant that is 4 times larger than the first spring, how does the linear frequency of oscillations change?

If you increase the displacement of a spring from an equilibrium position by 2 times, how will its elastic potential energy change?

Figure 13.1 The figure shows the elastic potential energy of an object attached to a horizontal spring. The object slides on a table without friction. -In Fig. 13.1, at which position does the object reach minimum total energy?

Which of these statements can be applied to plastic deformation of an object?

Figure 13.1 The figure shows the elastic potential energy of an object attached to a horizontal spring. The object slides on a table without friction. -In Fig. 13.1, at which position does the object reach minimum potential energy?

At what point can we say that the response of an object to stretching is elastic?

Figure 13.1 The figure shows the elastic potential energy of an object attached to a horizontal spring. The object slides on a table without friction. -In Fig. 13.1, at which position does the object reach maximum kinetic energy?

For an object oscillating while attached to a horizontal spring, at what fraction of maximal velocity is it moving when it passes exactly half way from the equilibrium toward maximum extension?

An object with a mass of 200 g is attached to a horizontal spring having a spring constant of 1500 N/m. What is the maximum speed the mass can achieve if it is initially displaced 25 cm from equilibrium?