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.If the wire changed length by 1.20 mm,then the stress in the wire is

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

Answer 1

4.77 $\times$ 10⁶ N/m².

Question 2

A cable is 5.00 m long and has a diameter of 1.50 mm.The tensile modulus of the cable is 2.50 $\times$ 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 2

26.5 N

Question 3

A cable has a strain of 2.0 $\times$ 10^-3.If the un-stretched 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.

Answer 3

48 mm.

Question 4

A 2.00 m brass rod with a 1.00 mm diameter is used as a spring by stretching the rod.If the tensile modulus of brass is 9.10 $\times$ 10¹⁰ N/m²,then the spring constant of the rod is

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

Question 5

A wire is 12.00 m long and has a diameter of 1.50 mm.The tensile modulus of the wire is 7.00 $\times$ 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) 51.50 mm.

Question 6

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 tensile modulus for this rod?

A) 7.50 $\times$ 10¹⁰ N/m²
B) 8.70 $\times$ 10¹⁰ N/m²
C) 9.78 $\times$ 10¹⁰ N/m²
D) 10.2 $\times$ 10¹⁰ N/m²
E) 10.8 $\times$ 10¹⁰ N/m²

Question 7

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 $\times$ 10^-6 m.The shear strain of the nail is

A) 4.00 $\times$ 10^-5.
B) 4.75 $\times$ 10^-5.
C) 5.01 $\times$ 10^-5.
D) 5.75 $\times$ 10^-5.
E) 6.25 $\times$ 10^-5.

Question 8

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

A) 2.0 $\times$ 10^-4.
B) 4.0 $\times$ 10^-4.
C) 6.0 $\times$ 10^-4.
D) 8.0 $\times$ 10^-4.
E) 10 $\times$ 10^-4.

Question 9

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 tensile modulus?

A) 3.05 $\times$ 10¹⁰ N/m²
B) 3.67 $\times$ 10¹⁰ N/m²
C) 3.98 $\times$ 10¹⁰ N/m²
D) 4.26 $\times$ 10¹⁰ N/m²
E) 4.77 $\times$ 10¹⁰ N/m²

Question 10

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

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

Question 11

A spring-powered launcher has a spring with a spring constant of 150 N/cm.The launcher is prepared to launch a projectile by compressing the spring by 5.00 cm.If the mass of the projectile is 5.00 grams,then what is the velocity of the projectile when it is launched from the launcher?

A) 90.6 m/s
B) 86.6 m/s
C) 75.5 m/s
D) 60.3 m/s
E) 56.6 m/s

Question 12

A spring-powered launcher has a spring with a spring constant of 50.0 N/cm.The launcher is prepared to launch a projectile by compressing the spring by 5.00 cm.If the mass of the projectile is 10.0 grams,then what is the velocity of the projectile when it is launched from the launcher?

A) 65.4 m/s
B) 52.8 m/s
C) 45.7 m/s
D) 40.5 m/s
E) 35.4 m/s

Question 13

A wire is 1.50 m long and has a diameter of 1.50 mm.The tensile modulus of the wire is 6.20 $\times$ 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 14

A force of 15.0 N is applied to a wire with a diameter of 2.00 mm.If the wire changed length by 1.20 mm,then the stress in the wire is

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

Question 15

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

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

Question 16

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 tensile modulus allowed?

A) 1.02 $\times$ 10⁹ N/m²
B) 2.04 $\times$ 10⁹ N/m²
C) 2.55 $\times$ 10⁹ N/m²
D) 3.06 $\times$ 10⁹ N/m²
E) 3.52 $\times$ 10⁹ N/m²

Question 17

A force of 15.0 N is applied to a wire with an un-stretched 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 $\times$ 10^-4.
B) 2.00 $\times$ 10^-4.
C) 3.00 $\times$ 10^-4.
D) 4.00 $\times$ 10^-4.
E) 5.00 $\times$ 10^-4.

Question 18

A force of 10.0 N is applied to a wire with an un-stretched length of 4.00 m and a diameter of 5.00 mm.If the wire changed length by 1.20 mm,then the stress in the wire is

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

Question 19

A wire has a strain of 0.10%.If the wire has an un-stretched 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 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 to stretch the rod by 1.40 mm.What is the tensile modulus for this rod?

A) 6.99 $\times$ 10¹⁰ N/m²
B) 6.05 $\times$ 10¹⁰ N/m²
C) 5.54 $\times$ 10¹⁰ N/m²
D) 4.90 $\times$ 10¹⁰ N/m²
E) 4.02 $\times$ 10¹⁰ N/m²

Question 21

A cube of aluminum is at a depth of 1.00 km under water whose density is 1,000 kg/m³.The bulk stress on the cube due to the water is

A) 6.90 $\times$ 10⁶ Pa.
B) 7.50 $\times$ 10⁶ Pa.
C) 8.70 $\times$ 10⁶ Pa.
D) 9.90 $\times$ 10⁶ Pa.
E) 10.5 $\times$ 10⁶ Pa.

Question 22

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 $\times$ 10¹⁰ N/m²,then how much does the nail deflect downward?

A) 37.5 $\times$ 10^-6 m
B) 44.5 $\times$ 10^-6 m
C) 47.8 $\times$ 10^-6 m
D) 56.5 $\times$ 10^-6 m
E) 78.5 $\times$ 10^-6 m

Question 23

A 150 N picture hangs from a nail in the wall.The maximum shear stress the nail can sustain is 2.00 $\times$ 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 24

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 $\times$ 10^-6 m.The shear stress of the rod is

A) 2.78 $\times$ 10⁶ N/m².
B) 3.37 $\times$ 10⁶ N/m².
C) 4.73 $\times$ 10⁶ N/m².
D) 5.34 $\times$ 10⁶ N/m².
E) 6.37 $\times$ 10⁶ N/m².

Question 25

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 $\times$ 10^-5 m.If the shear modulus is 3.40 $\times$ 10¹⁰ N/m²,then what is the diameter of the nail?

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

Question 26

A ball is subjected to a pressure of 25.0 atmospheres.The un-squeezed diameter of the ball is 4.00 cm.The squeezed diameter of the ball is 3.99 cm.The bulk strain on the ball is

A) 5.00 $\times$ 10^-3.
B) 5.75 $\times$ 10^-3.
C) 6.53 $\times$ 10^-3.
D) 7.48 $\times$ 10^-3.
E) 8.68 $\times$ 10^-3.

Question 27

A 120.0 N picture hangs from a nail in the wall.The maximum shear stress the nail can sustain is 1.000 $\times$ 10⁶ N/m².The smallest diameter the nail can be is

A) 10.46 mm.
B) 12.36 mm.
C) 14.84 mm.
D) 16.67 mm.
E) 18.35 mm.

Question 28

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 $\times$ 10⁷ N/m².
B) 1.86 $\times$ 10⁷ N/m².
C) 1.62 $\times$ 10⁷ N/m².
D) 1.41 $\times$ 10⁷ N/m².
E) 1.34 $\times$ 10⁷ N/m².

Question 29

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 $\times$ 10⁶ N/m².
B) 6.24 $\times$ 10⁶ N/m².
C) 5.65 $\times$ 10⁶ N/m².
D) 4.37 $\times$ 10⁶ N/m².
E) 4.02 $\times$ 10⁶ N/m².

Question 30

A cube of aluminum is at a depth of 1.00 km under water whose density is 1,000 kg/m³.The bulk stress on the cube due to the water is

A) 1.95 $\times$ 10⁷ Pa.
B) 1.01 $\times$ 10⁷ Pa.
C) 1.32 $\times$ 10⁷ Pa.
D) 1.55 $\times$ 10⁷ Pa.
E) 1.61 $\times$ 10⁷ Pa.

Question 31

A cube is subjected to a pressure of 12 atmospheres.The un-squeezed length of one side of the cube is 10.000 cm.The squeezed length of one side of the cube is 9.999 cm.The bulk strain on the cube is

A) 2.0 $\times$ 10^-4.
B) 2.2 $\times$ 10^-4.
C) 2.4 $\times$ 10^-4.
D) 2.6 $\times$ 10^-4.
E) 3.0 $\times$ 10^-4.

Question 32

A nail projects 25.00 mm horizontally outward from a wall.A picture is hung from the end of the nail and the nail deflects downward by 2.00 $\times$ 10^-6 m.The shear strain of the nail is

A) 7.00 $\times$ 10^-5.
B) 8.00 $\times$ 10^-5.
C) 9.00 $\times$ 10^-5.
D) 10.0 $\times$ 10^-5.
E) 12.0 $\times$ 10^-5.

Question 33

A 120 N picture hangs from a nail in the wall.The maximum shear stress the nail can sustain is 1.00 $\times$ 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 34

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 $\times$ 10^-6 m.The shear strain of the rod is

A) 1.00 $\times$ 10^-4.
B) 1.50 $\times$ 10^-4.
C) 2.00 $\times$ 10^-4.
D) 2.50 $\times$ 10^-4.
E) 3.00 $\times$ 10^-4.

Question 35

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 $\times$ 10^-6 m.The shear modulus of the rod is

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

Question 36

A cube is subjected to a pressure of 10.0 atmospheres.The un-squeezed 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 bulk strain on the cube is

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

Question 37

A cube of aluminum is at a depth of 1.000 km under seawater whose density is 1,025 kg/m³.The bulk stress on the cube due to the seawater is

A) 3.015 $\times$ 10⁷ Pa.
B) 2.601 $\times$ 10⁷ Pa.
C) 2.405 $\times$ 10⁷ Pa.
D) 1.345 $\times$ 10⁷ Pa.
E) 1.005 $\times$ 10⁷ Pa.

Question 38

A ball of aluminum is at a depth of 100.0 m under water whose density is 1,000 kg/m³.The bulk stress on the ball due to the water is

A) 1.001 $\times$ 10⁶ Pa.
B) 1.081 $\times$ 10⁶ Pa.
C) 1.284 $\times$ 10⁶ Pa.
D) 2.131 $\times$ 10⁶ Pa.
E) 2.326 $\times$ 10⁶ Pa.

Question 39

A ball is subjected to a pressure of 2.0 atmospheres.The un-squeezed diameter of the ball is 10.0 cm.The squeezed diameter of the ball is 9.999 cm.The bulk strain on the ball is

A) 3.0 $\times$ 10^-4.
B) 3.3 $\times$ 10^-4.
C) 3.5 $\times$ 10^-4.
D) 3.7 $\times$ 10^-4.
E) 3.9 $\times$ 10^-4.

Question 40

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 $\times$ 10^-6 m.The shear strain of the rod is

A) 1.00 $\times$ 10^-4.
B) 1.50 $\times$ 10^-4.
C) 2.00 $\times$ 10^-4.
D) 2.50 $\times$ 10^-4.
E) 3.00 $\times$ 10^-4.

Question 41

A copper ball with a diameter of 5.00 cm is subjected to a pressure of 2.50 $\times$ 10⁶ Pa.The bulk modulus for copper is 14.00 $\times$ 10¹⁰ N/m².What is the bulk strain?

A) 1.79 $\times$ 10^-5
B) 2.09 $\times$ 10^-5
C) 2.55 $\times$ 10^-5
D) 2.94 $\times$ 10^-5
E) 3.21 $\times$ 10^-5

Question 42

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 simple harmonic motion?

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 43

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( $\omega$ t).What is the maximum acceleration of the simple harmonic motion?

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 44

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 16.0 $\times$ 10¹⁰ N/m².What is the pressure?

A) 2.4 $\times$ 10⁷ N/m²
B) 2.1 $\times$ 10⁷ N/m²
C) 1.9 $\times$ 10⁷ N/m²
D) 1.6 $\times$ 10⁷ N/m²
E) 1.2 $\times$ 10⁷ N/m²

Question 45

An aluminum ball is subjected to a pressure of 7.00 $\times$ 10⁶ Pa.The bulk strain is 1.0 $\times$ 10^-4.What is the bulk modulus?

A) 5.8 $\times$ 10¹⁰ N/m²
B) 6.1 $\times$ 10¹⁰ N/m²
C) 6.3 $\times$ 10¹⁰ N/m²
D) 7.0 $\times$ 10¹⁰ N/m²
E) 8.1 $\times$ 10¹⁰ N/m²

Question 46

A mass is suspended vertically from a spring so it is at rest at the equilibrium position.The mass is pulled straight down to an extension x 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 maximum upward travel.
B) at the equilibrium point.
C) at its maximum lower travel.
D) somewhere between the equilibrium point and maximum extension.

Question 47

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) = 8.00 cm/s sin( $\omega$ t)+ 10.0 cm/s cos( $\omega$ t).What is the maximum velocity of the simple harmonic motion?

A) 41.0 cm/s
B) 32.8 cm/s
C) 24.5 cm/s
D) 20.5 cm/s
E) 12.8 cm/s

Question 48

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) = 10.0 cm/s sin( $\omega$ t)+ 8.00 cm/s cos( $\omega$ t).What is the maximum displacement of the simple harmonic motion?

A) 25.1 cm
B) 30.5 cm
C) 35.3 cm
D) 40.4 cm
E) 45.5 cm

Question 49

A 1.0 kg mass is connected to a spring with a spring constant of 9.00 N/m.If the initial velocity is 4.0 cm/s and the initial displacement is 2.0 cm,then what is the maximum spring potential energy of the simple harmonic motion?

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

Question 50

A mass is suspended vertically from a spring so it is at rest at the equilibrium position.The mass is pulled straight down to an extension x and released so that it oscillates about the equilibrium position.The acceleration of the mass is zero when the mass is

A) at its maximum upward travel.
B) at the equilibrium point.
C) at its maximum lower travel.
D) somewhere between the equilibrium point and maximum extension.

Question 51

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( $\omega$ t).What is the maximum velocity the simple harmonic motion?

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 52

Seawater has a density of 1,025 kg/m³ at the surface.The bulk modulus of seawater is 0.2100 $\times$ 10¹⁰ N/m².What is the density of seawater at a depth of 10.00 km?

A) 1074 kg/m³
B) 1230 kg/m³
C) 1574 kg/m³
D) 1764 kg/m³
E) 1973 kg/m³

Question 53

An equation that describes the displacement in Simple Harmonic Motion is: x(t) = 1.20 m sin(2.40 rad/s t).What is the maximum velocity of the SHM?

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 54

A 1.0 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 2.00 cm,then what is the maximum kinetic energy of the simple harmonic motion?

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

Question 55

A mass is suspended vertically from a spring so it is at rest at the equilibrium position.The mass is pulled straight down to an extension x and released so that it oscillates about the equilibrium position.The speed of the mass is greatest when the mass is

A) at its maximum upward travel.
B) at the equilibrium point.
C) at its maximum lower travel.
D) somewhere between the equilibrium point and maximum extension.

Question 56

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) = 10.0 cm/s sin( $\omega$ t).What is the maximum velocity of the simple harmonic motion?

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

Question 57

A copper ball with a diameter of 5.00 cm is subjected to a pressure of 2.50 $\times$ 10⁶ Pa.The bulk modulus for copper is 14.00 $\times$ 10¹⁰ N/m².What is the change in the volume?

A) 1.01 $\times$ 10^-3 cm³
B) 1.17 $\times$ 10^-3 cm³
C) 1.20 $\times$ 10^-3 cm³
D) 1.58 $\times$ 10^-3 cm³
E) 1.70 $\times$ 10^-3 cm³

Question 58

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) = 8.00 cm/s sin( $\omega$ t)+ 10.0 cm/s cos( $\omega$ t).What is the maximum acceleration of the simple harmonic motion?

A) 10.0 cm/s²
B) 16.2 cm/s²
C) 19.2 cm/s²
D) 20.2 cm/s²
E) 24.5 cm/s²

Question 59

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) = 12.0 cm sin( $\omega$ t).What is the maximum displacement of the simple harmonic motion?

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

Question 60

A mass is suspended vertically from a spring so it is at rest at the equilibrium position.The mass is pulled straight down to an extension x 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 maximum upward travel.
B) at the equilibrium point.
C) at its maximum lower travel.
D) somewhere between the equilibrium point and maximum extension.

Question 61

A pendulum is made with a 4.00 kg mass suspended at the end of a 75.0 cm thin rod.The pendulum is started at 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 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( $\omega$ 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

A physical pendulum is composed of a disc whose center of gravity is attached to a thin rod.The disc has a moment of inertia of 1/2 MR².The mass of the disc is 500 gm and has a radius of 4.00 cm.The length of the rod is 50.0 cm.The period of the physical pendulum is

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

Question 64

A physical pendulum is composed of a sphere whose center of gravity is attached to a thin rod.The sphere has a moment of inertia of 2/5 MR².The mass of the sphere is 2.00 kg and has a radius of 30.0 cm.The length of the rod is 50.0 cm.The period 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 65

An astronaut measures her mass by means of a device consisting of a chair attached to a large spring.The period of oscillation she undergoes when set into motion is used to determine her mass.If the spring constant is 1250 N/m and 27 seconds is required for her to undergo 10 full oscillations what is the mass of the astronaut and chair?

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

Question 66

A pendulum is made with a 4.00 kg mass suspended at the end of a 75.0 cm thin rod.The period of the small motion simple harmonic motion is

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

Question 67

Diatomic molecules such as H₂ and O₂ undergo simple harmonic motion with frequencies that obey Hooke's Law with the effective mass being half the atomic mass.If the mass of an oxygen atom is 2.66 $\times$ 10^-26 kg,and the observed frequency of oscillation is 4.66 $\times$ 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) 2290 N/m

Question 68

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( $\omega$ 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 69

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 simple harmonic motion?

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

Question 70

A physical pendulum is composed of a disc whose center of gravity is attached to a thin rod.The disc has a moment of inertia of 1/2 MR².The mass of the disc is 1.00 kg and has a radius of 40 cm.The length of the rod is 50.0 cm.The period of the physical pendulum is

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

Question 71

A 10 kg mass is attached to the end of a 2.00 m brass rod with a 1 mm diameter.If the tensile modulus of brass is 9.10 $\times$ 10¹⁰ N/m²,then the frequency of the simple harmonic motion of the mass is

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

Question 72

A 10.0 kg mass is attached to the end of a 2.00 m brass rod with a 1.00 mm diameter.If the tensile modulus of brass is 9.10 $\times$ 10¹⁰ N/m²,then the period of the simple harmonic motion of the mass is

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

Question 73

An astronaut measures her mass by means of a device consisting of a chair attached to a large spring.The period of oscillation she undergoes when set into motion is used to determine her mass.If her mass together with the chair is 172 kg and the time required for her to undergo 10 full oscillations is 27 seconds,what is the spring constant?

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

Question 74

A 20.0 kg mass is attached to the end of a 1.00 m steel rod with a 1.00 mm diameter.If the tensile modulus of steel is 20.0 $\times$ 10¹⁰ N/m²,then the frequency of the simple harmonic motion of the mass is

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

Question 75

A pendulum is made with a 4.00 kg mass suspended at the end of a thin rod.The period of the small motion simple harmonic motion is 1.00 sec.What is the length of the thin rod?

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

Question 76

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 spring potential energy of the simple harmonic motion?

A) 9.10 $\times$ 10^-4 J
B) 8.00 $\times$ 10^-4 J
C) 7.50 $\times$ 10^-4 J
D) 6.70 $\times$ 10^-4 J
E) 5.00 $\times$ 10^-4 J

Question 77

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 displacement of the simple harmonic motion?

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

Question 78

Diatomic molecules such as H₂ and O₂ undergo simple harmonic motion with frequencies that obey Hooke's Law with the effective mass being half the atomic mass.If the mass of a hydrogen atom is 1.627 $\times$ 10^-27 kg and that of fluorine is 3.17 $\times$ 10^-26 kg,what is the ratio of oscillation frequencies of H₂ to that of F₂,assuming that the bond strength between the atoms of hydrogen is the same as that between fluorine atoms?

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

Question 79

Diatomic molecules such as H₂ and O₂ undergo simple harmonic motion with frequencies that obey Hooke's Law with the effective mass being half the atomic mass.If the mass of a hydrogen atom is 1.67 $\times$ 10^-27 kg and the observed frequency of oscillation is 125 $\times$ 10¹² Hz,what is the effective spring constant associated with the bond between the hydrogen atoms?

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

Question 80

An astronaut measures her mass by means of a device consisting of a chair attached to a large spring.The period of oscillation she undergoes when set into motion is used to determine her mass.If her mass together with the chair is 172 kg,and the spring constant is 1250 N/m,what is the time required for her to undergo 10 full oscillations?

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