Question 1

A 150 N picture hangs from a nail in the wall. The maximum shear stress the nail can sustain is 2.00 × 106 N/m2. The smallest diameter the nail can be is

Accepted Answer

A)  9.77 mm. 
B)  8.22 mm. 
C)  7.97 mm. 
D)  7.52 mm. 
E)  6.03 mm.

Question 2

Diatomic molecules such as H2 and F2 undergo simple harmonic motion with frequencies that obey Hooke's Law, with an effective mass equal to half the atomic mass. If the mass of a hydrogen atom is 1.627 × 10−27 kg and the mass of a fluorine atom is 3.17 × 10−26 kg, what is the approximate ratio of the oscillation frequency of H2 to that of F2, assuming the bond strengths are the same?

Accepted Answer

A)  360 
B)  19 
C)  38 
D)  4.4 
E)  9.5

Question 3

A 24.0 N picture hangs from a nail in the wall. The diameter of the nail is 2.00 mm. The shear stress on the nail is

Accepted Answer

A)  7.64 × 106 N/m2. 
B)  6.24 × 106 N/m2. 
C)  5.65 × 106 N/m2. 
D)  4.37 × 106 N/m2. 
E)  4.02 × 106 N/m2.

Question 4

A particular pendulum on Earth has a period of 1.00 s. When transported to the moon, where the gravitational acceleration is 1/6 that on Earth, the period of the pendulum would be

Accepted Answer

A)  0.41 
B)  1.00 s 
C)  2.4 s 
D)  4.1 s 
E)  6.0 s

Question 5

A rod with a diameter of 2.00 mm, projects 20.0 mm horizontally outward from a wall. A 10.0 N weight is hung from the end of the rod and the rod deflects downward by 4.00 × 10-6 m. The shear strain of the rod is

Accepted Answer

A)  1.00 × 10-4. 
B)  1.50 × 10-4. 
C)  2.00 × 10-4. 
D)  2.50 × 10-4. 
E)  3.00 × 10-4.

Question 6

Diatomic molecules such as H2 and O2 undergo simple harmonic motion with frequencies that obey Hooke's Law, with an effective mass equal to half the atomic mass. If the mass of an oxygen atom is 2.66 × 10−26 kg and the observed frequency of oscillation is 4.66 × 1013 Hz, what is the effective spring constant associated with the bond between the atoms in an oxygen molecule (O2)?

Accepted Answer

A)  1140 N/m 
B)  182 N/m 
C)  116 N/m 
D)  29 N/m 
E)  2280 N/m

Question 7

Seawater has a density of 1,025 kg/m3 at the surface. The bulk modulus of seawater is 2.100 × 109 N/m2. What is the density of seawater at a depth of 10.00 km? (Use g = 9.8 m/s2 and ignore any change in density with depth when calculating the pressure.)

Accepted Answer

A)  1076 kg/m3 
B)  1230 kg/m3 
C)  1574 kg/m3 
D)  1764 kg/m3 
E)  1973 kg/m3

Question 8

A 125 g pendulum bob hung on a string of length 35 cm has the same period as when the bob is hung from a spring and caused to oscillate. What is the spring constant?

Accepted Answer

A)  1.9 N/m 
B)  3.5 N/m 
C)  5.2 N/m 
D)  27 N/m

Question 9

A ball is subjected to a pressure of 25.0 atmospheres. The original diameter of the ball is 4.00 cm. The squeezed diameter of the ball is 3.99 cm. The volume strain of the ball is

Accepted Answer

A)  5.00 × 10-3. 
B)  5.75 × 10-3. 
C)  6.53 × 10-3. 
D)  7.48 × 10-3. 
E)  8.68 × 10-3.

Question 10

A 2.00 kg mass is connected to a spring with a spring constant of 9.00 N/m. The displacement is given by the expression x(t) = (12.0 cm) sin(ω t). What is the period of the simple harmonic motion?

Accepted Answer

A)  4.75 sec 
B)  4.27 sec 
C)  3.95 sec 
D)  3.36 sec 
E)  2.96 sec

Question 11

A 4.00 kg mass is connected to a spring with a spring constant of 9.00 N/m. The velocity is given by the expression v(t) = (12.8 cm/s) cos(ω t + π/4). What is the maximum velocity of the mass?

Accepted Answer

A)  41.0 cm/s 
B)  32.8 cm/s 
C)  19.2 cm/s 
D)  12.8 cm/s 
E)  9.05 cm/s

Question 12

A cable is 5.00 m long and has a diameter of 1.50 mm. The elastic modulus of the cable is 2.50 × 1010 N/m2. A force is applied to the end of the cable and the cable stretches by 3.00 mm. What is the applied force?

Accepted Answer

A)  16.5 N 
B)  20.5 N 
C)  26.5 N 
D)  32.6 N 
E)  36.6 N

Question 13

A pendulum is made by attaching a 4.00 kg mass to the end of a thin, 75.0 cm long, massless rod. The period of (small amplitude) oscillations of the pendulum is

Accepted Answer

A)  2.45 sec. 
B)  2.01 sec. 
C)  1.74 sec. 
D)  1.33 sec. 
E)  1.04 sec.

Question 14

A 2.00 kg mass is connected to a spring with a spring constant of 900 N/m. The displacement is given by the expression x(t) = (12.0 cm) sin(ω t). What is the frequency of the simple harmonic motion?

Accepted Answer

A)  5.02 Hz 
B)  4.21 Hz 
C)  3.38 Hz 
D)  2.56 Hz 
E)  2.05 Hz

Question 15

A grandfather clock keeps time using a pendulum whose length is finely adjustable. If you have a grandfather clock that is running fast, should you shorten or lengthen the pendulum?

Accepted Answer

A)  Shorten it 
B)  Lengthen it 
C)  You should reduce its mass 
D)  You should add mass to it

Question 16

A 4.00 kg mass is connected to a spring with a spring constant of 9.00 N/m. The velocity is given by the expression v(t) = (12.8 cm/s) cos(ω t + π/4). What is the maximum acceleration of the mass?

Accepted Answer

A)  13.6 cm/s2 
B)  16.2 cm/s2 
C)  19.2 cm/s2 
D)  20.2 cm/s2 
E)  24.5 cm/s2

Question 17

A force of 20 N is applied to a wire with an unstretched length of 2.5 m. The wire gets 2.00 mm longer. The strain in the wire is

Accepted Answer

A)  2.0 × 10-4. 
B)  4.0 × 10-4. 
C)  6.0 × 10-4. 
D)  8.0 × 10-4. 
E)  10 × 10-4.

Question 18

A 75 g block is placed into oscillation as it hangs from a vertical spring. If the amplitude of the motion is 22 cm and the block is observed to have a maximum speed of 14 m/s (as it passes through the equilibrium position), what is the spring constant?

Accepted Answer

A)  300 N/m 
B)  22 N/m 
C)  4.8 N/m 
D)  1200 N/m

Question 19

A copper ball with a diameter of 5.00 cm is subjected to a pressure increase of 2.50 × 106 Pa. The bulk modulus for copper is 1.40 × 1011 N/m2. What is the magnitude of the resulting change in the volume?

Accepted Answer

A)  1.01 × 10-3 cm3 
B)  1.17 × 10-3 cm3 
C)  1.20 × 10-3 cm3 
D)  1.58 × 10-3 cm3 
E)  1.70 × 10-3 cm3

Question 20

An equation that describes the displacement of an object moving in simple harmonic motion is x(t) = (1.20 m) sin[(2.40 rad/s) t]. What is the maximum velocity of the object?

Accepted Answer

A)  5.32 m/s 
B)  4.82 m/s 
C)  3.68 m/s 
D)  2.88 m/s 
E)  2.03 m/s

Exam 10: Elasticity and Oscillations

A 150 N picture hangs from a nail in the wall. The maximum shear stress the nail can sustain is 2.00 × 10⁶ N/m². The smallest diameter the nail can be is

A 24.0 N picture hangs from a nail in the wall. The diameter of the nail is 2.00 mm. The shear stress on the nail is

A particular pendulum on Earth has a period of 1.00 s. When transported to the moon, where the gravitational acceleration is 1/6 that on Earth, the period of the pendulum would be

A rod with a diameter of 2.00 mm, projects 20.0 mm horizontally outward from a wall. A 10.0 N weight is hung from the end of the rod and the rod deflects downward by 4.00 × 10^-6 m. The shear strain of the rod is

Seawater has a density of 1,025 kg/m³ at the surface. The bulk modulus of seawater is 2.100 × 10⁹ N/m². What is the density of seawater at a depth of 10.00 km? (Use g = 9.8 m/s² and ignore any change in density with depth when calculating the pressure.)

A 125 g pendulum bob hung on a string of length 35 cm has the same period as when the bob is hung from a spring and caused to oscillate. What is the spring constant?

A ball is subjected to a pressure of 25.0 atmospheres. The original diameter of the ball is 4.00 cm. The squeezed diameter of the ball is 3.99 cm. The volume strain of the ball is

A 2.00 kg mass is connected to a spring with a spring constant of 9.00 N/m. The displacement is given by the expression x(t) = (12.0 cm) sin(ω t) . What is the period of the simple harmonic motion?

A 4.00 kg mass is connected to a spring with a spring constant of 9.00 N/m. The velocity is given by the expression v(t) = (12.8 cm/s) cos(ω t + π/4) . What is the maximum velocity of the mass?

A cable is 5.00 m long and has a diameter of 1.50 mm. The elastic modulus of the cable is 2.50 × 10¹⁰ N/m². A force is applied to the end of the cable and the cable stretches by 3.00 mm. What is the applied force?

A pendulum is made by attaching a 4.00 kg mass to the end of a thin, 75.0 cm long, massless rod. The period of (small amplitude) oscillations of the pendulum is

A 2.00 kg mass is connected to a spring with a spring constant of 900 N/m. The displacement is given by the expression x(t) = (12.0 cm) sin(ω t) . What is the frequency of the simple harmonic motion?

A grandfather clock keeps time using a pendulum whose length is finely adjustable. If you have a grandfather clock that is running fast, should you shorten or lengthen the pendulum?

A 4.00 kg mass is connected to a spring with a spring constant of 9.00 N/m. The velocity is given by the expression v(t) = (12.8 cm/s) cos(ω t + π/4) . What is the maximum acceleration of the mass?

A force of 20 N is applied to a wire with an unstretched length of 2.5 m. The wire gets 2.00 mm longer. The strain in the wire is

A 75 g block is placed into oscillation as it hangs from a vertical spring. If the amplitude of the motion is 22 cm and the block is observed to have a maximum speed of 14 m/s (as it passes through the equilibrium position) , what is the spring constant?

A copper ball with a diameter of 5.00 cm is subjected to a pressure increase of 2.50 × 10⁶ Pa. The bulk modulus for copper is 1.40 × 10¹¹ N/m². What is the magnitude of the resulting change in the volume?

An equation that describes the displacement of an object moving in simple harmonic motion is x(t) = (1.20 m) sin[(2.40 rad/s) t]. What is the maximum velocity of the object?