Question 1

A wire is 12.00 m long and has a diameter of 1.50 mm. The elastic modulus of the wire is 7.00 × 1010 N/m2. If a force of 500 N is applied to end of the wire, then the increase in length of the wire is

Accepted Answer

A)  38.5 mm. 
B)  40.2 mm. 
C)  44.1 mm. 
D)  48.5 mm. 
E)  51.5 mm.

Question 2

A 100 N picture hangs from a nail in the wall. The diameter of the nail is 3.00 mm. The shear stress on the nail is

Accepted Answer

A)  1.98 × 107 N/m2. 
B)  1.86 × 107 N/m2. 
C)  1.62 × 107 N/m2. 
D)  1.41 × 107 N/m2. 
E)  1.34 × 107 N/m2.

Question 3

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 a hydrogen atom is 1.67 × 10−27 kg and the observed frequency of oscillation is 1.25 × 1014 Hz, what is the effective spring constant associated with the bond between the hydrogen atoms?

Accepted Answer

A)  1030 N/m 
B)  515 N/m 
C)  164 N/m 
D)  82 N/m 
E)  13 N/m

Question 4

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

Accepted Answer

A)  2.78 × 105 N/m2. 
B)  3.37 × 105 N/m2. 
C)  4.73 × 105 N/m2. 
D)  5.34 × 105 N/m2. 
E)  6.37 × 105 N/m2.

Question 5

A pendulum consists of a 4.00 kg mass suspended at the end of a 75.0 cm thin, massless rod. The pendulum is released from an angle of 20.0 degrees with the vertical. What is the velocity of the pendulum as it passes through the origin?

Accepted Answer

A)  98.9 cm/s 
B)  94.2 cm/s 
C)  89.2 cm/s 
D)  82.1 cm/s 
E)  79.5 cm/s

Question 6

A force of 15.0 N is applied to a wire with a diameter of 2.00 mm, causing its length to change by 1.20 mm. What is the stress on the wire?

Accepted Answer

A)  4.77 × 106 N/m2. 
B)  5.38 × 106 N/m2. 
C)  6.73 × 106 N/m2. 
D)  7.27 × 106 N/m2. 
E)  8.75 × 106 N/m2.

Question 7

A 1.00 kg mass is connected to a spring with a spring constant of 9.00 N/m. If the initial velocity is 4.00 cm/s and the initial displacement is 0.00 cm, then what is the maximum elastic potential energy of the spring?

Accepted Answer

A)  9.10 × 10-4 J 
B)  8.00 × 10-4 J 
C)  7.50 × 10-4 J 
D)  6.70 × 10-4 J 
E)  5.00 × 10-4 J

Question 8

A vertical spring system with a bob having mass M is set into motion with amplitude A. When the bob replaced by one having mass 2M, the following can be concluded:

Accepted Answer

A)  The period is about 0.7 times as large as before 
B)  The period is unaffected 
C)  The period is twice as large as before 
D)  The period is half as large as before 
E)  The period is about 1.4 times as large as before

Question 9

A 4.00 kg mass is connected to a spring with a spring constant of 9.00 N/m. If the initial velocity is 12.0 cm/s and the initial displacement is 4.00 cm, then what is the maximum velocity of the mass?

Accepted Answer

A)  20.3 cm/s 
B)  19.8 cm/s 
C)  15.5 cm/s 
D)  13.4 cm/s 
E)  11.5 cm/s

Question 10

A rod is 2.40 m long and has a diameter of 2.50 mm. A force of 2000 N is applied to the end, stretching the rod by 1.40 mm. What is the elastic modulus for this rod?

Accepted Answer

A)  6.98 × 1011 N/m2 
B)  1.75 × 1011 N/m2 
C)  4.07 × 108 N/m2 
D)  1.43 × 106 N/m2 
E)  5.83 × 10−4 N/m2

Question 11

A 1.0 kg mass is connected to a spring with a spring constant of 9.00 N/m. If the initial velocity is 0.0 cm/s and the initial displacement is 2.0 cm, then what is the maximum kinetic energy of the mass?

Accepted Answer

A)  0.014 J 
B)  0.0090 J 
C)  0.0075 J 
D)  0.0018 J 
E)  0.0012 J

Question 12

A wire is 1.50 m long and has a diameter of 1.50 mm. The elastic modulus of the wire is 6.20 × 1010 N/m2. If a force of 400 N is applied to end of the wire, then the increase in length of the wire is

Accepted Answer

A)  5.48 mm. 
B)  4.28 mm. 
C)  3.95 mm. 
D)  3.84 mm. 
E)  3.45 mm.

Question 13

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

Accepted Answer

A)  13.6 cm 
B)  19.2 cm 
C)  35.3 cm 
D)  40.4 cm 
E)  45.5 cm

Question 14

A mass is suspended vertically from a spring so it is at rest at the equilibrium position. The mass is pulled a short distance straight down and released so that it oscillates about the equilibrium position. The acceleration is greatest in magnitude and directed downward when the mass is

Accepted Answer

A)  at its highest point. 
B)  at the equilibrium position. 
C)  at its lowest point. 
D)  somewhere between the equilibrium point and maximum extension.

Question 15

A pendulum is made by attaching a 4.00 kg mass to the end of a thin, massless rod. The period of small-amplitude oscillations of the pendulum is 1.00 sec. What is the length of the rod?

Accepted Answer

A)  24.8 cm 
B)  29.7 cm 
C)  31.4 cm 
D)  34.1 cm 
E)  36.2 cm

Question 16

A nail projects 25.0 mm horizontally outward from a wall. A picture is hung from the end of the nail and the nail deflects downward by 2.00 × 10−6 m. The shear strain of the nail is

Accepted Answer

A)  7.00 × 10−5. 
B)  8.00 × 10−5. 
C)  9.00 × 10−5. 
D)  10.0 × 10−5. 
E)  12.0 × 10−5.

Question 17

A ball is subjected to a pressure of 2.0 atmospheres. The original diameter of the ball is 10.0 cm. The squeezed diameter of the ball is 9.999 cm. The volume strain of the ball is

Accepted Answer

A)  3.00 × 10-4. 
B)  3.30 × 10-4. 
C)  3.50 × 10-4. 
D)  3.70 × 10-4. 
E)  3.90 × 10-4.

Question 18

A cube of aluminum is at a depth of 1.00 km under seawater whose density is 1,025 kg/m3. Atmospheric pressure is 101.3 kPa. What is the volume stress on the cube? Use g = 9.80 m/s2.

Accepted Answer

A)  3.01 × 107 Pa. 
B)  2.60 × 107 Pa. 
C)  1.00 × 107 Pa. 
D)  1.34 × 107 Pa. 
E)  1.01 × 107 Pa.

Question 19

A nail projects 25.0 mm horizontally outward from a wall. A 400 N picture is hung from the end of the nail, and the nail deflects downward by 2.00 × 10-5 m. If the shear modulus is 3.40 × 1010 N/m2, then what is the radius of the nail?

Accepted Answer

A)  1.60 mm 
B)  1.86 mm 
C)  2.16 mm 
D)  2.44 mm 
E)  2.65 mm

Question 20

A 10.0 kg mass is attached to the end of a 2.00 m long brass rod, which has a diameter of 1.00 mm and negligible mass. The mass at the end is pulled, stretching the rod slightly, and then released. If the elastic modulus of brass is 9.10 × 1010 N/m2, then the period of the resulting oscillations is

Accepted Answer

A)  0.175 sec. 
B)  0.105 sec. 
C)  0.133 sec. 
D)  0.145 sec. 
E)  0.167 sec.

Exam 10: Elasticity and Oscillations

A wire is 12.00 m long and has a diameter of 1.50 mm. The elastic modulus of the wire is 7.00 × 10¹⁰ N/m². If a force of 500 N is applied to end of the wire, then the increase in length of the wire is

A 100 N picture hangs from a nail in the wall. The diameter of the nail is 3.00 mm. The shear stress on the nail is

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

A pendulum consists of a 4.00 kg mass suspended at the end of a 75.0 cm thin, massless rod. The pendulum is released from an angle of 20.0 degrees with the vertical. What is the velocity of the pendulum as it passes through the origin?

A force of 15.0 N is applied to a wire with a diameter of 2.00 mm, causing its length to change by 1.20 mm. What is the stress on the wire?

A 1.00 kg mass is connected to a spring with a spring constant of 9.00 N/m. If the initial velocity is 4.00 cm/s and the initial displacement is 0.00 cm, then what is the maximum elastic potential energy of the spring?

A vertical spring system with a bob having mass M is set into motion with amplitude A. When the bob replaced by one having mass 2M, the following can be concluded:

A 4.00 kg mass is connected to a spring with a spring constant of 9.00 N/m. If the initial velocity is 12.0 cm/s and the initial displacement is 4.00 cm, then what is the maximum velocity of the mass?

A rod is 2.40 m long and has a diameter of 2.50 mm. A force of 2000 N is applied to the end, stretching the rod by 1.40 mm. What is the elastic modulus for this rod?

A 1.0 kg mass is connected to a spring with a spring constant of 9.00 N/m. If the initial velocity is 0.0 cm/s and the initial displacement is 2.0 cm, then what is the maximum kinetic energy of the mass?

A wire is 1.50 m long and has a diameter of 1.50 mm. The elastic modulus of the wire is 6.20 × 10¹⁰ N/m². If a force of 400 N is applied to end of the wire, then the increase in length of the wire is

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

A mass is suspended vertically from a spring so it is at rest at the equilibrium position. The mass is pulled a short distance straight down and released so that it oscillates about the equilibrium position. The acceleration is greatest in magnitude and directed downward when the mass is

A pendulum is made by attaching a 4.00 kg mass to the end of a thin, massless rod. The period of small-amplitude oscillations of the pendulum is 1.00 sec. What is the length of the rod?

A nail projects 25.0 mm horizontally outward from a wall. A picture is hung from the end of the nail and the nail deflects downward by 2.00 × 10⁻⁶ m. The shear strain of the nail is

A ball is subjected to a pressure of 2.0 atmospheres. The original diameter of the ball is 10.0 cm. The squeezed diameter of the ball is 9.999 cm. The volume strain of the ball is

A cube of aluminum is at a depth of 1.00 km under seawater whose density is 1,025 kg/m³. Atmospheric pressure is 101.3 kPa. What is the volume stress on the cube? Use g = 9.80 m/s².

A nail projects 25.0 mm horizontally outward from a wall. A 400 N picture is hung from the end of the nail, and the nail deflects downward by 2.00 × 10^-5 m. If the shear modulus is 3.40 × 10¹⁰ N/m², then what is the radius of the nail?