Deck 13: Elasticity and Vibrations

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.

Answer 1

The material cannot be easily compressed in volume.

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.

Answer 2

A large force is required for a small amount of twisting.

Question 3

What type of units are used when measuring strain?

A)length
B)volume
C)angle
D)Strain is a dimensionless quantity.

Answer 3

Strain is a dimensionless quantity.

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

Question 5

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

A)force
B)pressure
C)length
D)volume

Question 6

Which of the following quantities does tensile stress correspond to?

A)pressure
B)force
C)energy
D)volume

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

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

Question 9

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

A)pressure
B)force
C)length
D)area

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

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

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

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.

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.

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.

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)

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

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)

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%

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

Question 21

The total energy of a body attached on a horizontal spring is largest in equilibrium.

Question 22

The highest speed an object achieves in oscillatory motion is reached when it is the farthest from equilibrium.

Question 23

A Blue Elgiloy wire with a Young's modulus of Y = 1.6 × 10¹¹ Pa is used to press a tooth for correction of position. The wire is 3 cm long, has a diameter of 0.2 mm, bends under an angle of 140° where it presses the tooth, and stretches by 0.08 mm. What is the force exerted on the tooth? Assume that that tooth width is negligible so that the wire bends making an angle 140°.

Question 24

Angular frequency (the change of angle in an interval of time) is expressed in either degrees per second or radians per second.

Question 25

Both elastic and plastic deformations are reversible. The only difference between the two is that elastic material responds to stress in a linear fashion, and plastic responds in a non-linear fashion.

Question 26

The oscillatory motions of a mass on a horizontal spring and on an identical vertical spring are NOT the same because the force of gravity (weight) is acting in a vertical motion.

Question 27

An object of mass m = 700 g is attached to a spring. Its position is described by x = (0.15 m)cos(0.8ðt). What is the spring constant?

A)1.76 N/m
B)4.42 N/m
C)44.2 N/m
D)4420 N/m

Question 28

During a fast chase, at a speed of 60 km/h, a horse falls and hits a railing with its front leg cannon bone. The circumference of the bone is 23 cm. The horse comes to rest in 2.0 m. If that part of the leg has an effective mass of 5.0 kg, and bone withstands a maximum compressional stress of 1.6 × 10⁸ Pa, will the bone break?

Question 29

Stress, twisting, and hydraulic stress, all three apply only to solids and liquids.

Question 30

The meaning of a large Young's modulus is that a small force can produce large deformation of a material.

Question 31

A simple harmonic system and a particle moving in uniform circular motion have the same period. The angular frequency of the oscillating system is the same as the angular velocity of the rotational system.

Question 32

A force that causes an oscillating system to slow down is called a

A)restoring force.
B)Hooke's force.
C)damping force.
D)driving force.

Question 33

A restoring force is always directed opposite to displacement.

Question 34

The unit of tensile stress is the newton.

Question 35

The period of harmonic motion is independent of amplitude.

Question 36

The bulk modulus is a unitless coefficient.

Question 37

A horse with a mass of 520 kg has a front leg cannon bone that is 38 cm long. The bone has a circumference of 23 cm. The two front legs support 65% of the horse's weight. If the Young's modulus of a bone is 1.5 × 10¹⁰ Pa, what is the compression of the bone due to the horse's weight?

Question 38

A system is in resonance when an external harmonic excitation causes it to respond with maximum __________.

A)amplitude
B)frequency
C)wavelength
D)period

Question 39

Resonance occurs in a system with no damping when the frequency of the driving force is the same as the natural frequency of the system

Question 40

A simple harmonic system maintains constant frequency, whereas a dumped system's frequency decreases.

Question 41

You want to measure the weight of a bag of fruit. When you place the bag on a scale, it shows harmonic oscillation around 29.4 N, 3 oscillations per second. What is the spring constant of the scale?

Question 42

An object with a mass of 1.2 kg is pushed down on a vertical spring, compressing it 20 cm. When we release the spring, the object will fly up to a height of 2 m. What is the spring constant?

Question 43

A 30 kg block is at rest while attached to a spring with a spring constant of k = 1500 N/m. A 4 g bullet hits the block and remains in the block. As a result of the collision, the block compresses the spring by 1.8 cm. What was the speed of the bullet?

Question 44

Figure 13.2 Stress-strain relation for compact bone. The graph includes both tensile stress (the bone is stretched) and compressive stress (the bone is compressed).
Fig. 13.2 shows the stress-strain curve for compact bone. In addition to the coordinate system origin (0,0), the graph includes four points, (i) to (iv), along the curve. Describe the response of the compact bone in each interval, that is, whether it is elastic or not fully elastic.

Question 45

The total energy of a water molecule in the ground state is 9.2 × 10^-20 J. Find the amplitude and maximal velocity of vibration of a hydrogen atom. Compare the amplitude to the length of the O-H bond (9.6 × 10^-11 m). The mass of a hydrogen atom is m = 1.67 × 10^-27 kg. The spring constant for the H-O bond is k = 780 N/m.

Question 46

An object of mass 20 g is attached to a horizontal spring with a spring constant of 150 N/m. What is the speed of the object at 1/3 the amplitude? The spring was initially stretched by 4 cm.

Question 47

Figure 13.3 The figure shows a relaxed spring and a body sliding down an incline.
See Fig. 13.3. A crate of a mass 0.5 kg slides down a 30° incline and compresses a spring having a spring constant k = 150 N/m by 20 cm, coming to a stop. What is the length of the sliding path of the crate along the incline?

Question 48

Calculate the period of oscillation of a hydrogen atom in a water molecule (H₂O). The mass of a hydrogen atom is m = 1.67 × 10^-27 kg. The spring constant for the H-O bond is k = 780 N/m.

Question 49

Figure 13.4
The amplitude as a function of driving frequency for three oscillators.
Figure 13.4 shows the response of three oscillators to a driving frequency. The amplitudes are plotted as a function of frequency. If each of these three oscillators is started and then left as a free oscillator, discuss which will oscillate longest, which shortest, and why?