Question 1

A cable is 10.0 m long and has a diameter of 2.00 mm. A force of 45.0 N is applied to the end of the cable and the cable stretches by 3.00 mm. What is the elastic modulus?

Accepted Answer

A)   3.05 × 1010 N/m2
B)   3.67 × 1010 N/m2
C)   3.98 × 1010 N/m2
D)   4.26 × 1010 N/m2
E)   4.77 × 1010 N/m2 E

Question 2

A rod with a diameter of 3.00 mm, projects 2.0 cm horizontally outward from a wall. A 50.0 N weight is hung from the end of the rod and the rod deflects downward by 2.00 × 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. A

Question 3

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 upward 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. C

Question 4

An astronaut measures her mass by means of a device consisting of a chair attached to a large spring. Her mass can be determined from the period of the oscillations she undergoes when set into motion. If the spring constant is 1250 N/m and 27.0 seconds are required for her to undergo 10 full oscillations, what is the combined mass of the astronaut and chair?

Accepted Answer

A)   231 kg
B)   537 kg
C)   85.5 kg
D)   171 kg

Question 5

Consider a physical pendulum constructed by attaching a thin, massless rod to the center of a uniform disc of mass 500 g and radius 4.00 cm. The disc has a moment of inertia of ½ MR2 about an axis perpendicular to the plane of the disc, through its center. With the rod hung from one end (the pivot), the plane of the disc (attached to the other end) is vertical. If the rod has a length of 50.0 cm, then the period of (small amplitude) oscillations of the pendulum will be

Accepted Answer

A)   1.24 sec.
B)   1.42 sec.
C)   1.74 sec.
D)   1.90 sec.
E)   2.25 sec.

Question 6

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 frequency of the resulting oscillations is

Accepted Answer

A)   6.20 Hz.
B)   7.51 Hz.
C)   7.95 Hz.
D)   8.21 Hz.
E)   9.51 Hz.

Question 7

A pendulum with a bob of mass 150 g has the same period as a thin rod of the same mass and length 42 cm when the rod is pivoted about its end. What is the length of the pendulum?

Accepted Answer

A)   13 cm
B)   14 cm
C)   21 cm
D)   28 cm

Question 8

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 modulus of the rod is

Accepted Answer

A)   2.28 × 1010 N/m2.
B)   1.99 × 1010 N/m2.
C)   1.67 × 1010 N/m2.
D)   1.59 × 1010 N/m2.
E)   1.42 × 1010 N/m2.

Question 9

A force of 100 N is applied to a rod with a diameter of 6.00 mm. The stress on the rod is

Accepted Answer

A)   5.47 × 106 N/m2.
B)   4.15 × 106 N/m2.
C)   3.54 × 106 N/m2.
D)   2.64 × 106 N/m2.
E)   2.03 × 106 N/m2.

Question 10

A 20.0 kg mass is attached to the end of a 1.00 m long steel 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 steel is 2.00 × 1011 N/m2, then the frequency of the resulting oscillations is

Accepted Answer

A)   37.2 Hz.
B)   30.4 Hz.
C)   24.5 Hz.
D)   20.1 Hz.
E)   14.1 Hz.

Question 11

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 to stretch the rod by 1.00 mm. What is the elastic modulus for this rod?

Accepted Answer

A)   4.17 × 10−4 N/m2
B)   2.00 × 106 N/m2
C)   4.07 × 108 N/m2
D)   2.44 × 1011 N/m2
E)   9.78 × 1011 N/m2

Question 12

A nail projects 40.0 mm horizontally outward from a wall. A 25.0 N coat is hung from the end of the nail and the nail deflects downward by 2.50 × 10−6 m. The shear strain of the nail is

Accepted Answer

A)   4.00 × 10−5.
B)   4.75 × 10−5.
C)   5.01 × 10−5.
D)   5.75 × 10−5.
E)   6.25 × 10−5.

Question 13

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

Accepted Answer

A)   1.79 × 10-5
B)   2.09 × 10-5
C)   2.55 × 10-5
D)   2.94 × 10-5
E)   3.21 × 10-5

Question 14

A cube is subjected to a pressure of 12 atmospheres. The original length of one side of the cube is 10.0 cm. The squeezed length of one side of the cube is 9.999 cm. The volume strain of the cube is

Accepted Answer

A)   2.00 × 10-4.
B)   2.20 × 10-4.
C)   2.40 × 10-4.
D)   2.60 × 10-4.
E)   3.00 × 10-4.

Question 15

An astronaut measures her mass by means of a device consisting of a chair attached to a large spring. Her mass can be determined from the period of the oscillations she undergoes when set into motion. If her mass together with the chair is 170 kg, and the spring constant is 1250 N/m, what time is required for her to undergo 10 full oscillations?

Accepted Answer

A)   3.7 s
B)   8.6 s
C)   170 s
D)   23 s

Question 16

A ball of aluminum is at a depth of 100.0 m under water whose density is 1,000 kg/m3. Atmospheric pressure is 101.3 kPa. What is the volume stress on the ball? Use g = 9.80 m/s2.

Accepted Answer

A)   9.80 × 105 Pa.
B)   1.08 × 106 Pa.
C)   1.28 × 105 Pa.
D)   2.13 × 106 Pa.
E)   2.33 × 106 Pa.

Question 17

An astronaut measures her mass by means of a device consisting of a chair attached to a large spring. Her mass can be determined from the period of the oscillations she undergoes when set into motion. If her mass together with the chair is 172 kg, and the time required for her to undergo 10 full oscillations is 27.0 seconds, what is the spring constant?

Accepted Answer

A)   400 N/m
B)   931 N/m
C)   148 N/m
D)   467 N/m

Question 18

A disk is suspended by a nail such that it pivots in a vertical plane about a point on the edge of the disk. If the period of oscillation of the disk is 1.25 s, what is the disk's radius?

Accepted Answer

A)   26 cm
B)   78 cm
C)   Cannot answer without knowing the disk's mass
D)   51 cm

Question 19

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 speed of the mass is greatest 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 20

A cable is 50.0 m long and has a diameter of 2.50 cm. A force of 10,000 N is applied to the end of the cable. If the maximum stretch allowed in the cable is 2.00 mm, then what is the minimum elastic modulus allowed?

Accepted Answer

A)   5.09 × 1011 N/m2
B)   1.27 × 1011 N/m2
C)   3.52 × 109 N/m2
D)   2.04 × 107 N/m2
E)   5.00 × 106 N/m2

Exam 10: Elasticity and Oscillations

A cable is 10.0 m long and has a diameter of 2.00 mm. A force of 45.0 N is applied to the end of the cable and the cable stretches by 3.00 mm. What is the elastic modulus?

A rod with a diameter of 3.00 mm, projects 2.0 cm horizontally outward from a wall. A 50.0 N weight is hung from the end of the rod and the rod deflects downward by 2.00 × 10^-6 m. The shear strain of the rod is

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 upward when the mass is

A pendulum with a bob of mass 150 g has the same period as a thin rod of the same mass and length 42 cm when the rod is pivoted about its end. What is the length of the pendulum?

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 modulus of the rod is

A force of 100 N is applied to a rod with a diameter of 6.00 mm. The stress on the rod is

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 to stretch the rod by 1.00 mm. What is the elastic modulus for this rod?

A nail projects 40.0 mm horizontally outward from a wall. A 25.0 N coat is hung from the end of the nail and the nail deflects downward by 2.50 × 10⁻⁶ m. The shear strain of the nail is

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

A cube is subjected to a pressure of 12 atmospheres. The original length of one side of the cube is 10.0 cm. The squeezed length of one side of the cube is 9.999 cm. The volume strain of the cube is

A ball of aluminum is at a depth of 100.0 m under water whose density is 1,000 kg/m³. Atmospheric pressure is 101.3 kPa. What is the volume stress on the ball? Use g = 9.80 m/s².

A disk is suspended by a nail such that it pivots in a vertical plane about a point on the edge of the disk. If the period of oscillation of the disk is 1.25 s, what is the disk's radius?

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 speed of the mass is greatest when the mass is

A cable is 50.0 m long and has a diameter of 2.50 cm. A force of 10,000 N is applied to the end of the cable. If the maximum stretch allowed in the cable is 2.00 mm, then what is the minimum elastic modulus allowed?