Deck 10: Elasticity and Oscillations

Question 1

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

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

Answer 1

$8.0 \times 10^{-4}$ .

Question 2

A wire has a strain of $0.10 \%$ . If the wire has an unstretched length of $5.00 \mathrm{~m}$ , then the change in length of the wire is

A) $9.0 \mathrm{~mm}$ .
B) $15 \mathrm{~mm}$ .
C) $10 \mathrm{~mm}$ .
D) $5.0 \mathrm{~mm}$ .
E) $7.0 \mathrm{~mm}$ .

Answer 2

$5.0 \mathrm{~mm}$ .

Question 3

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

A) $5.00 \times 10^{-4}$ .
B) $2.00 \times 10^{-4}$ .
C) $3.00 \times 10^{-4}$ .
D) $1.00 \times 10^{-4}$ .
E) $4.00 \times 10^{-4}$ .

Answer 3

$3.00 \times 10^{-4}$ .

Question 4

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

A) $4.19 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ .
B) $4.67 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ .
C) $5.09 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ .
D) $6.55 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ .
E) $3.67 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ .

Question 5

A force of $100 \mathrm{~N}$ is applied to a rod with a diameter of $6.00 \mathrm{~mm}$ . The stress on the rod is

A) $2.03 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ .
B) $2.64 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ .
C) $3.54 \times 10^{6}\mathrm{~N} / \mathrm{m}^{2}$ .
D) $5.47 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ .
E) $4.15 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ .

Question 6

A force of $500 \mathrm{~N}$ is applied to a rod with a diameter of $4.00 \mathrm{~mm}$ . The stress on the rod is

A) $4.66 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$ .
B) $5.38 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$ .
C) $3.98 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
D) $2.75 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$ .
E) $4.25 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$ .

Question 7

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

A) $7.27 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ .
B) $5.38 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ .
C) $4.77 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ .
D) $6.73 \times10^{6}\mathrm{~N} / \mathrm{m}^{2}$ .
E) $8.75 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ .

Question 8

A $2.00 \mathrm{~m}$ brass rod with a $1.00 \mathrm{~mm}$ diameter behaves like a spring under stretching or compression. If the elastic modulus of brass is $9.10 \times 10^{10}\mathrm{~N} / \mathrm{m}^{2}$ , then the spring constant of the rod is

A) $4.67 \times 10^{4} \mathrm{~N} / \mathrm{m}$ .
B) $2.13 \times 10^{4} \mathrm{~N} / \mathrm{m}$ .
C) $4.22 \times 10^{4} \mathrm{~N} / \mathrm{m}$ .
D) $3.57 \times 10^{4} \mathrm{~N} / \mathrm{m}$ .
E) $2.47 \times 10^{4} \mathrm{~N} / \mathrm{m}$ .

Question 9

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

A) $6.98 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
B) $1.75 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
C) $1.43 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$
D) $5.83 \times 10^{-4} \mathrm{~N} / \mathrm{m}^{2}$
E) $4.07 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$

Question 10

A rod is $2.40 \mathrm{~m}$ long and has a diameter of $2.50 \mathrm{~mm}$ . A force of $2000 \mathrm{~N}$ is applied to the end to stretch the rod by $1.00 \mathrm{~mm}$ . What is the elastic modulus for this rod?

A) $2.44 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
B) $2.00 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$
C) $4.17 \times 10^{-4} \mathrm{~N} / \mathrm{m}^{2}$
D) $9.78 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
E) $4.07 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$

Question 11

A wire is $1.50 \mathrm{~m}$ long and has a diameter of $1.50 \mathrm{~mm}$ . The elastic modulus of the wire is $6.20 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ . If a force of $400 \mathrm{~N}$ is applied to end of the wire, then the increase in length of the wire is

A) $3.95 \mathrm{~mm}$ .
B) $5.48 \mathrm{~mm}$ .
C) $3.45 \mathrm{~mm}$ .
D) $3.84 \mathrm{~mm}$ .
E) $4.28 \mathrm{~mm}$ .

Question 12

A wire is $12.00 \mathrm{~m}$ long and has a diameter of $1.50 \mathrm{~mm}$ . The elastic modulus of the wire is $7.00 \times 10^{10}\mathrm{~N} / \mathrm{m}^{2}$ . If a force of $500 \mathrm{~N}$ is applied to end of the wire, then the increase in length of the wire is

A) $38.5 \mathrm{~mm}$ .
B) $51.5 \mathrm{~mm}$ .
C) $44.1 \mathrm{~mm}$ .
D) $40.2 \mathrm{~mm}$ .
E) $48.5 \mathrm{~mm}$ .

Question 13

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

A) $1.27 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
B) $2.04 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
C) $3.52 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$
D) $5.09 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$
E) $5.00 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$

Question 14

A cable is $5.00 \mathrm{~m}$ long and has a diameter of $1.50 \mathrm{~mm}$ . The elastic modulus of the cable is $2.50 \times 10^{10}\mathrm{~N} / \mathrm{m}^{2}$ . A force is applied to the end of the cable and the cable stretches by $3.00 \mathrm{~mm}$ . What is the applied force?

A) $26.5 \mathrm{~N}$
B) $32.6 \mathrm{~N}$
C) $20.5 \mathrm{~N}$
D) $36.6 \mathrm{~N}$
E) $16.5 \mathrm{~N}$

Question 15

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

A) $3.67 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
B) $3.05 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
C) $4.77 \times10^{10}\mathrm{~N} / \mathrm{m}^{2}$
D) $3.98 \times10^{10}\mathrm{~N} / \mathrm{m}^{2}$
E) $4.26 \times 10^{10}\mathrm{~N} / \mathrm{m}^{2}$

Question 16

A nail projects $40.0 \mathrm{~mm}$ horizontally outward from a wall. A $25.0 \mathrm{~N}$ coat is hung from the end of the nail and the nail deflects downward by $2.50 \times 10^{-6} \mathrm{~m}$ . The shear strain of the nail is

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

Question 17

A nail projects $25.0 \mathrm{~mm}$ horizontally outward from a wall. A picture is hung from the end of the nail and the nail deflects downward by $2.00 \times 10^{-6} \mathrm{~m}$ . 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) $12.0 \times 10^{-5}$ .
E) $10.0 \times 10^{-5}$ .

Question 18

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

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

Question 19

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

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

Question 20

Aball is subjected to a pressure of 25.0 atmospheres. The original diameter of the ball is $4.00 \mathrm{~cm}$ . The squeezed diameter of the ball is $3.99 \mathrm{~cm}$ . The volume strain of the ball is

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

Question 21

A ball is subjected to a pressure of 2.0 atmospheres. The original diameter of the ball is $10.0 \mathrm{~cm}$ . The squeezed diameter of the ball is $9.999 \mathrm{~cm}$ . The volume strain of the ball is

A) $3.50 \times 10^{-4}$ .
B) $3.00 \times 10^{-4}$ .
C) $3.30 \times 10^{-4}$ .
D) $3.90 \times 10^{-4}$ .
E) $3.70 \times 10-4$ .

Question 22

A $120 \mathrm{~N}$ picture hangs from a nail in the wall. The maximum shear stress the nail can sustain is $1.00 \times 10^{6}$ $\mathrm{N} / \mathrm{m}^{2}$ . The smallest diameter the nail can be is

A) $10.5 \mathrm{~mm}$ .
B) $13.7 \mathrm{~mm}$ .
C) $12.4 \mathrm{~mm}$ .
D) $15.9 \mathrm{~mm}$ .
E) $14.4 \mathrm{~mm}$ .

Question 23

A $24.0 \mathrm{~N}$ picture hangs from a nail in the wall. The diameter of the nail is $2.00 \mathrm{~mm}$ . The shear stress on the nail is

A) $5.65 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ .
B) $4.02 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ .
C) $4.37 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ .
D) $6.24 \times 10^{6}\mathrm{~N} / \mathrm{m}^{2}$ .
E) $7.64 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$ .

Question 24

A $100 \mathrm{~N}$ picture hangs from a nail in the wall. The diameter of the nail is $3.00 \mathrm{~mm}$ . The shear stress on the nail is

A) $1.62 \times 10^{7} \mathrm{~N} / \mathrm{m} 2$ .
B) $1.98 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$ .
C) $1.41 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$ .
D) $1.34 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$ .
E) $1.86 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$ .

Question 25

A $150 \mathrm{~N}$ picture hangs from a nail in the wall. The maximum shear stress the nail can sustain is $2.00 \times 10^{6}$ $\mathrm{N} / \mathrm{m}^{2}$ . The smallest diameter the nail can be is

A) $6.03 \mathrm{~mm}$ .
B) $8.22 \mathrm{~mm}$ .
C) $7.52 \mathrm{~mm}$ .
D) $9.77 \mathrm{~mm}$ .
E) $7.97 \mathrm{~mm}$ .

Question 26

A cube of aluminum is at a depth of $1.00 \mathrm{~km}$ under seawater whose density is $1,025 \mathrm{~kg} / \mathrm{m}^{3}$ . Atmospheric pressure is $101.3 \mathrm{kPa}$ . What is the volume stress on the cube? Use $g=9.80 \mathrm{~m} / \mathrm{s}^{2}$ .

A) $1.34 \times 10^{7} \mathrm{~Pa}$ .
B) $1.00 \times 10^{7} \mathrm{~Pa}$ .
C) $2.60 \times 10^{7} \mathrm{~Pa}$ .
D) $1.01 \times 10^{7} \mathrm{~Pa}$ .
E) $3.01 \times 10^{7} \mathrm{~Pa}$ .

Question 27

Aball of aluminum is at a depth of $100.0 \mathrm{~m}$ under water whose density is $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ . Atmospheric pressure is $101.3 \mathrm{kPa}$ . What is the volume stress on the ball? Use $\mathrm{g}=9.80 \mathrm{~m} / \mathrm{s}^{2}$ .

A) $2.13 \times 10^{6} \mathrm{~Pa}$ .
B) $1.08 \times 10^{6} \mathrm{~Pa}$ .
C) $1.28 \times 10^{5} \mathrm{~Pa}$ .
D) $2.33 \times 10^{6} \mathrm{~Pa}$ .
E) $9.80 \times 10^{5} \mathrm{~Pa}$ .

Question 28

A cube of aluminum is at a depth of $1.00 \mathrm{~km}$ under water whose density is $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ . Atmospheric pressure is $101.3 \mathrm{kPa}$ . What is the volume stress on the cube? Use $\mathrm{g}=9.80 \mathrm{~m} / \mathrm{s}^{2}$ .

A) $1.00 \times 10^{7} \mathrm{~Pa}$ .
B) $9.60 \times 10^{6} \mathrm{~Pa}$ .
C) $9.70 \times 10^{6} \mathrm{~Pa}$ .
D) $9.80 \times 10^{6} \mathrm{~Pa}$ .
E) $9.90 \times 10^{6} \mathrm{~Pa}$ .

Question 29

A rod with a diameter of $2.00 \mathrm{~mm}$ projects $20.0 \mathrm{~mm}$ horizontally outward from a wall. A $10.0 \mathrm{~N}$ weight is hung from the end of the rod and the rod deflects downward by $4.00 \times 10-6 \mathrm{~m}$ . The shear modulus of the rod is

A) $1.42 \times 10^{10}\mathrm{~N} / \mathrm{m}^{2}$ .
B) $2.28 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ .
C) $1.67 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ .
D) $1.99 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ .
E) $1.59 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ .

Question 30

A nail with a diameter of $1.00 \mathrm{~mm}$ projects $25.0 \mathrm{~mm}$ horizontally outward from a wall. A $40.0 \mathrm{~N}$ picture is hung from the end of the nail. If the shear modulus is $3.40 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ , then how much does the nail deflect downward?

A) $4.45 \times 10^{-5} \mathrm{~m}$
B) $3.74 \times 10^{-5} \mathrm{~m}$
C) $7.85 \times 10^{-5} \mathrm{~m}$
D) $4.78 \times 10^{-5} \mathrm{~m}$
E) $5.65 \times 10^{-5} \mathrm{~m}$

Question 31

A nail projects $25.0 \mathrm{~mm}$ horizontally outward from a wall. A $400 \mathrm{~N}$ picture is hung from the end of the nail, and the nail deflects downward by $2.00 \times 10^{-5} \mathrm{~m}$ . If the shear modulus is $3.40 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ , then what is the radius of the nail?

A) $2.16 \mathrm{~mm}$
B) $2.65 \mathrm{~mm}$
C) $1.86 \mathrm{~mm}$
D) $2.44 \mathrm{~mm}$
E) $1.60 \mathrm{~mm}$

Question 32

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

A) $3.37 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ .
B) $2.78 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ .
C) $6.37 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ .
D) $5.34 \times 10^{5}\mathrm{~N} / \mathrm{m}^{2}$ .
E) $4.73 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$

Question 33

An aluminum ball is subjected to a pressure of $7.00 \times 10^{6} \mathrm{~Pa}$ . The volume strain is $-1.0 \times 10^{-4}$ . What is the bulk modulus?

A) $8.1 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
B) $6.3 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
C) $5.8 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
D) $7.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
E) $6.1 \times 10^{10}\mathrm{~N} / \mathrm{m}^{2}$

Question 34

A copper ball with a diameter of $5.00 \mathrm{~cm}$ is subjected to a pressure of $2.50 \times 10^{6} \mathrm{~Pa}$ . The bulk modulus for copper is $1.40 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ . What is the magnitude of the volume strain?

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

Question 35

A copper ball with a diameter of $5.00 \mathrm{~cm}$ is subjected to a pressure increase of $2.50 \times 106 \mathrm{~Pa}$ . The bulk modulus for copper is $1.40 \times 10^{11}\mathrm{~N} / \mathrm{m}^{2}$ . What is the magnitude of the resulting change in the volume?

A) $1.70 \times 10^{-3} \mathrm{~cm}^{3}$
B) $1.01 \times 10^{-3} \mathrm{~cm}^{3}$
C) $1.58 \times 10^{-3} \mathrm{~cm}^{3}$
D) $1.17 \times 10^{-3} \mathrm{~cm}^{3}$
E) $1.20 \times 10^{-3} \mathrm{~cm}^{3}$

Question 36

A steel ball with a diameter of $10 \mathrm{~cm}$ is subjected to a pressure that causes the volume of the ball to shrink by $0.01 \%$ . The bulk modulus for steel is $1.6 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ . What is the pressure?

A) $1.6 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
B) $2.4 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
C) $1.2 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
D) $1.9 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
E) $2.1 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$

Question 37

Seawater has a density of $1,025 \mathrm{~kg} / \mathrm{m}^{3}$ at the surface. The bulk modulus of seawater is $2.100 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$ . What is the density of seawater at a depth of $10.00 \mathrm{~km}$ ? (Use $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$ and ignore any change in density with depth when calculating the pressure.)

A) $1230 \mathrm{~kg} / \mathrm{m}^{3}$
B) $1764 \mathrm{~kg} / \mathrm{m}^{3}$
C) $1076 \mathrm{~kg} / \mathrm{m}^{3}$
D) $1574 \mathrm{~kg} / \mathrm{m}^{3}$
E) $1973 \mathrm{~kg} / \mathrm{m}^{3}$

Question 38

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

A) $5.32 \mathrm{~m} / \mathrm{s}$
B) $4.82 \mathrm{~m} / \mathrm{s}$
C) $2.03 \mathrm{~m} / \mathrm{s}$
D) $3.68 \mathrm{~m} / \mathrm{s}$
E) $2.88 \mathrm{~m} / \mathrm{s}$

Question 39

A $4.00 \mathrm{~kg}$ mass is connected to a spring with a spring constant of $9.00 \mathrm{~N} / \mathrm{m}$ . The velocity is given by the expression $v(t)=(12.8 \mathrm{~cm} / \mathrm{s}) \cos (\omega t+\pi / 4)$ . What is the maximum acceleration of the mass?

A) $13.6 \mathrm{~cm} / \mathrm{s}^{2}$
B) $20.2 \mathrm{~cm} / \mathrm{s}^{2}$
C) $19.2 \mathrm{~cm} / \mathrm{s}^{2}$
D) $24.5 \mathrm{~cm} / \mathrm{s}^{2}$
E) $16.2 \mathrm{~cm} / \mathrm{s}^{2}$

Question 40

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

A) $15.5 \mathrm{~cm} / \mathrm{s}$
B) $19.8 \mathrm{~cm} / \mathrm{s}$
C) $11.5 \mathrm{~cm} / \mathrm{s}$
D) $20.3 \mathrm{~cm} / \mathrm{s}$
E) $13.4 \mathrm{~cm} / \mathrm{s}$

Question 41

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

A) $0.0020 \mathrm{~J}$
B) $0.0078 \mathrm{~J}$
C) $0.0026 \mathrm{~J}$
D) $0.0023 \mathrm{~J}$
E) $0.0012 \mathrm{~J}$

Question 42

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

A) $0.0059 \mathrm{~J}$
B) $0.0035 \mathrm{~J}$
C) $0.0060 \mathrm{~J}$
D) $0.0026 \mathrm{~J}$
E) $0.0067 \mathrm{~J}$

Question 43

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

A) $0.014 \mathrm{~J}$
B) $0.0018 \mathrm{~J}$
C) $0.0075 \mathrm{~J}$
D) $0.0012 \mathrm{~J}$
E) $0.0090 \mathrm{~J}$

Question 44

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

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

Question 45

A $1.00 \mathrm{~kg}$ mass is connected to a spring with a spring constant of $9.00 \mathrm{~N} / \mathrm{m}$ . If the initial velocity is $4.00 \mathrm{~cm} / \mathrm{s}$ and the initial displacement is $0.00 \mathrm{~cm}$ , then what is the amplitude of the oscillations?

A) $1.33 \mathrm{~cm}$
B) $1.67 \mathrm{~cm}$
C) $2.67 \mathrm{~cm}$
D) $2.05 \mathrm{~cm}$
E) $2.33 \mathrm{~cm}$

Question 46

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

A) $4.75 \mathrm{sec}$
B) $4.27 \mathrm{sec}$
C) $3.36 \mathrm{sec}$
D) $2.96 \mathrm{sec}$
E) $3.95 \mathrm{sec}$

Question 47

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

A) $1.74 \mathrm{sec}$ .
B) $2.01 \mathrm{sec}$ .
C) $1.04 \mathrm{sec}$ .
D) $1.33 \mathrm{sec}$ .
E) 2.45 sec.

Question 48

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

A) $29.7 \mathrm{~cm}$
B) $34.1 \mathrm{~cm}$
C) $36.2 \mathrm{~cm}$
D) $24.8 \mathrm{~cm}$
E) $31.4 \mathrm{~cm}$

Question 49

Consider a physical pendulum constructed by attaching a thin, massless rod to the center of a uniform disc of mass $500 \mathrm{~g}$ and radius $4.00 \mathrm{~cm}$ . The disc has a moment of inertia of $1 \frac{1}{2} \mathrm{MR}^{2}$ 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 $50.0 \mathrm{~cm}$ , then the period of (small amplitude) oscillations of the pendulum will be

A) $1.24 \mathrm{sec}$ .
B) $1.74 \mathrm{sec}$ .
C) 2.25 sec.
D) $1.42 \mathrm{sec}$ .
E) $1.90 \mathrm{sec}$

Question 50

Consider a physical pendulum constructed by attaching a thin, massless rod to the center of a uniform disc of mass $1.00 \mathrm{~kg}$ and radius $40.0 \mathrm{~cm}$ . The disc has a moment of inertia of $1 / 2 \mathrm{MR}^{2}$ 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 $50.0 \mathrm{~cm}$ , then the period of (small amplitude) oscillations of the pendulum will be

A) $1.63 \mathrm{sec}$ .
B) $2.03 \mathrm{sec}$ .
C) $1.89 \mathrm{sec}$ .
D) 2.22 sec.
E) $1.32 \mathrm{sec}$ .

Question 51

Diatomic molecules such as $\mathrm{H}_{2}$ and $\mathrm{O}_{2}$ 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 $1.67 \times 10^{-27} \mathrm{~kg}$ and the observed frequency of oscillation is $1.25 \times 10^{14} \mathrm{~Hz}$ , what is the effective spring constant associated with the bond between the hydrogen atoms?

A) $515 \mathrm{~N} / \mathrm{m}$
B) $13 \mathrm{~N} / \mathrm{m}$
C) $164 \mathrm{~N} / \mathrm{m}$
D) $82 \mathrm{~N} / \mathrm{m}$
E) $1030 \mathrm{~N} / \mathrm{m}$

Question 52

Diatomic molecules such as $\mathrm{H}_{2}$ and $\mathrm{O}_{2}$ 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 $2.66 \times 10^{-26} \mathrm{~kg}$ and the observed frequency of oscillation is $4.66 \times 1013 \mathrm{~Hz}$ , what is the effective spring constant associated with the bond between the atoms in an oxygen molecule $\left(\mathrm{O}_{2}\right)$ ?

A) $182 \mathrm{~N} / \mathrm{m}$
B) $1140 \mathrm{~N} / \mathrm{m}$
C) $29 \mathrm{~N} / \mathrm{m}$
D) $116 \mathrm{~N} / \mathrm{m}$
E) $2280 \mathrm{~N} / \mathrm{m}$

Question 53

Diatomic molecules such as $\mathrm{H}_{2}$ and $\mathrm{F}_{2}$ 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 $1.627 \times 10^{-27}$ $\mathrm{kg}$ and the mass of a fluorine atom is $3.17 \times 10^{-26} \mathrm{~kg}$ , what is the approximate ratio of the oscillation frequency of $\mathrm{H}_{2}$ to that of $\mathrm{F}_{2}$ , assuming the bond strengths are the same?

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