Deck 10: Elasticity and Oscillations

Question 1

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) 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.

Answer 1

4.77 × 10⁶ N/m².

Question 2

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

Answer 2

8.0 × 10^-4.

Question 3

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

Answer 3

26.5 N

Question 4

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) 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 5

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

Question 6

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) 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 7

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) 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

Question 8

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?

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

Question 9

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

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 10

A force of 15.0 N is applied to a wire with an unstretched length of 4.00 m and a diameter of 5.00 mm. If the wire changed length by 1.20 mm, then the strain in the wire is

A) 1.00 × 10⁻⁴.
B) 2.00 × 10⁻⁴.
C) 3.00 × 10⁻⁴.
D) 4.00 × 10⁻⁴.
E) 5.00 × 10⁻⁴.

Question 11

A wire has a strain of 0.10%. If the wire has an unstretched length of 5.00 m, then the change in length of the wire is

A) 5.0 mm.
B) 7.0 mm.
C) 9.0 mm.
D) 10 mm.
E) 15 mm.

Question 12

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) 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 13

A cable has a strain of 2.0 × 10^-3. If the unstretched length of the cable is 24.0 m, then the change in length of the cable is

A) 35 mm.
B) 48 mm.
C) 52 mm.
D) 59 mm.
E) 67 mm.

Question 14

A force of 10.0 N is applied to a wire with an unstretched length of 4.00 m and a diameter of 5.00 mm. The wire changes length by 1.20 mm as a result of the applied force. What is the stress on the wire?

A) 3.67 × 10⁵ N/m².
B) 4.19 × 10⁵ N/m².
C) 4.67 × 10⁵ N/m².
D) 5.09 × 10⁵ N/m².
E) 6.55 × 10⁵ N/m².

Question 15

A force of 500 N is applied to a rod with a diameter of 4.00 mm. The stress on the rod is

A) 5.38 × 10⁷ N/m².
B) 4.66 × 10⁷ N/m².
C) 4.25 × 10⁷ N/m².
D) 3.98 × 10⁷ N/m².
E) 2.75 × 10⁷ N/m².

Question 16

A 2.00 m brass rod with a 1.00 mm diameter behaves like a spring under stretching or compression. If the elastic modulus of brass is 9.10 × 10¹⁰ N/m², then the spring constant of the rod is

A) 4.67 × 10⁴ N/m.
B) 4.22 × 10⁴ N/m.
C) 3.57 × 10⁴ N/m.
D) 2.47 × 10⁴ N/m.
E) 2.13 × 10⁴ N/m.

Question 17

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

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 18

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) 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 19

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

Question 20

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) 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 21

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) 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 22

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) 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 23

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

Question 24

A 120 N picture hangs from a nail in the wall. The maximum shear stress the nail can sustain is 1.00 × 10⁶ N/m². The smallest diameter the nail can be is

A) 10.5 mm.
B) 12.4 mm.
C) 13.7 mm.
D) 14.4 mm.
E) 15.9 mm.

Question 25

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) 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 26

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?

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

Question 27

A cube is subjected to a pressure of 10.0 atmospheres. The original length of one side of the cube is 1.20 cm. The squeezed length of one side of the cube is 1.18 cm. The volume strain of the cube is

A) 0.0362.
B) 0.0492.
C) 0.0534.
D) 0.0598.
E) 0.0645.

Question 28

A cube of aluminum is at a depth of 1.00 km under water whose density is 1,000 kg/m³. Atmospheric pressure is 101.3 kPa. What is the volume stress on the cube? Use g = 9.80 m/s².

A) 9.60 × 10⁶ Pa.
B) 9.70 × 10⁶ Pa.
C) 9.80 × 10⁶ Pa.
D) 9.90 × 10⁶ Pa.
E) 1.00 × 10⁷ Pa.

Question 29

An aluminum ball is subjected to a pressure of 7.00 × 10⁶ Pa. The volume strain is −1.0 × 10⁻⁴. What is the bulk modulus?

A) 5.8 × 10¹⁰ N/m²
B) 6.1 × 10¹⁰ N/m²
C) 6.3 × 10¹⁰ N/m²
D) 7.0 × 10¹⁰ N/m²
E) 8.1 × 10¹⁰ N/m²

Question 30

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

Question 31

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) 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 32

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) 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 33

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) 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 34

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) 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 35

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) 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 36

A steel ball with a diameter of 10 cm is subjected to a pressure that causes the volume of the ball to shrink by 0.01%. The bulk modulus for steel is 1.6 × 10¹¹ N/m². What is the pressure?

A) 2.4 × 10⁷ N/m²
B) 2.1 × 10⁷ N/m²
C) 1.9 × 10⁷ N/m²
D) 1.6 × 10⁷ N/m²
E) 1.2 × 10⁷ N/m²

Question 37

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) 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 38

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) 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 39

A nail with a diameter of 1.00 mm projects 25.0 mm horizontally outward from a wall. A 40.0 N picture is hung from the end of the nail. If the shear modulus is 3.40 × 10¹⁰ N/m², then how much does the nail deflect downward?

A) 3.74 × 10^-5 m
B) 4.45 × 10^-5 m
C) 4.78 × 10^-5 m
D) 5.65 × 10^-5 m
E) 7.85 × 10^-5 m

Question 40

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?

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 41

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) 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 42

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

Question 43

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

Question 44

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 amplitude of the oscillations?

A) 2.67 cm
B) 2.33 cm
C) 2.05 cm
D) 1.67 cm
E) 1.33 cm

Question 45

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

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

Question 46

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

Question 47

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

Question 48

A 3.0 kg mass is connected to a spring with a spring constant of 6.0 N/m. The velocity is given by the expression v(t) = (10 cm/s) sin(ω t). What is the maximum velocity of the mass?

A) 10 cm/s
B) 14 cm/s
C) 17 cm/s
D) 20 cm/s
E) 25 cm/s

Question 49

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) 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 50

A 2.0 kg mass is connected to a spring with a spring constant of 9.0 N/m. The displacement is given by the expression x(t) = (12 cm) sin(ω t). What is the amplitude of the motion?

A) 8.0 cm
B) 12 cm
C) 20 cm
D) 24 cm
E) 30 cm

Question 51

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 of the mass is zero when the mass is

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 52

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

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

Question 53

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) 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 54

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) 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 55

A 1.0 kg mass is connected to a spring with a spring constant of 9.0 N/m. If the initial velocity is 4.0 cm/s and the initial displacement is 2.0 cm, then what is the maximum kinetic energy of the mass?

A) 0.0023 J
B) 0.0078 J
C) 0.0026 J
D) 0.0020 J
E) 0.0012 J

Question 56

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?

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

Question 57

A 2.00 kg mass is connected to a spring with a spring constant of 6.00 N/m. The displacement is given by the expression x(t) = (12.0 cm) sin(ω t). What is the maximum velocity of the mass?

A) 34.8 cm/s
B) 30.7 cm/s
C) 25.6 cm/s
D) 20.8 cm/s
E) 17.5 cm/s

Question 58

A 2.00 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) = (10.0 cm/s) sin(ω t). What is the maximum acceleration of the mass?

A) 17.5 cm/s²
B) 21.2 cm/s²
C) 25.2 cm/s²
D) 30.5 cm/s²
E) 36.7 cm/s²

Question 59

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

Question 60

A 1.0 kg mass is connected to a spring with a spring constant of 9.0 N/m. If the initial velocity is 4.0 cm/s and the initial displacement is 2.0 cm, then what is the maximum elastic potential energy of the spring?

A) 0.0026 J
B) 0.0059 J
C) 0.0035 J
D) 0.0067 J
E) 0.0060 J

Question 61

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

Question 62

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

Question 63

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

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

Question 64

A block on a frictionless, horizontal surface is attached to a spring that requires 125 N of force for the block to be stretched 15 cm away from equilibrium. From this position the block is released, and it begins to oscillate with a period of 0.25 s. What is the mass of the block?

A) 0.66 kg
B) 4.1 kg
C) 1.3 kg
D) 5.3 kg

Question 65

A physical pendulum is composed of a sphere whose center of gravity is attached to a thin rod of negligible mass. The sphere has a moment of inertia of 2/5 MR² about its center. The mass of the sphere is 2.00 kg, and it has a radius of 30.0 cm. The length of the rod is 50.0 cm. The period (for small-amplitude oscillations) of the physical pendulum is

A) 2.45 sec.
B) 2.02 sec.
C) 1.98 sec.
D) 1.52 sec.
E) 1.25 sec.

Question 66

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?

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

Question 67

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) 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 68

A pendulum, which has a period of 0.52 s on Earth, is taken to the surface of a large asteroid. There it is measured to have a period of 1.7 s. What is the value of the gravitational acceleration on the surface of that asteroid?

A) 5.78 m/s²
B) 0.48 m/s²
C) 3.0 m/s²
D) 0.92 m/s²

Question 69

Consider a physical pendulum constructed by attaching a thin, massless rod to the center of a uniform disc of mass 1.00 kg and radius 40.0 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

A) 2.22 sec.
B) 2.03 sec.
C) 1.89 sec.
D) 1.63 sec.
E) 1.32 sec.

Question 70

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

Question 71

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?

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

Question 72

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

Question 73

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?

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

Question 74

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

Question 75

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?

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

Question 76

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

Question 77

A block on a frictionless, horizontal surface is attached to one end of a spring that is also attached to the wall on the opposite end. When stretched away from equilibrium by 15 cm and released, the block oscillates with a period of 0.25 s. If the mass of the block is 15 kg, what force was required to stretch the spring by the initial 15 cm?

A) 230 N
B) 450 N
C) 710 N
D) 360 N
E) 1400 N

Question 78

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)?

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

Question 79

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?

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

Question 80

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

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