Deck 9: Elastic Properties of Matter: Stress and Strain

Question 1

A cable lifting a 4.00-lb bowling ball stretches by 3.00 mm. If the cable is cut in half and both halves are used together to lift the same bowling ball, each cable will stretch by

A) 0.50 mm.
B) 0.75 mm.
C) 1.00 mm.
D) 1.25 mm
E) 1.50 mm.

Answer 1

0.75 mm.

Question 2

The Young's modulus for aluminum is . If a 35.0-cm long aluminum bar is shortened by 4.00 mm under a certain load, what is the stress on this bar?

A) .
B) .
C) .
D) .
E) QUOTE 8.00×109 N/m2.

Answer 2

.

Question 3

A design project requires you to construct a crane to lift a maximum load of QUOTE 5.00×103kg and with a maximum upward acceleration of 2.00 m/s². What size diameter steel cable should you use if the cable is to have a safety factor of exactly 5?

A) 1.64 cm
B) 1.10 cm
C) 2.68 cm
D) 3.00 cm
E) 1.20 cm

Answer 3

2.68 cm

Question 4

A cable lifting a 4.00-lb bowling ball stretches by 3.00 mm. The same cable lifting a 5.00-lb bowling ball stretches by

A) 3.05 mm.
B) 3.50 mm.
C) 3.75 mm.
D) 4.00 mm.
E) 4.25 mm.

Question 5

Fill In the blank. If you double the radius of a steel cable without changing its length, you would __________ its elastic constant.

A) double
B) triple
C) quadruple
D) halve
E) not change

Question 6

A 3.00-m long wire with a diameter of 1.50 mm has Young's modulus of 9.00 x10¹⁰ N/m². What mass has to be attached to the wire so that it would extend it by 3.00 mm under its weight?

A) 159 kg
B) 5.16 kg
C) 16.2 kg
D) 64.8 kg
E) 48.6 kg

Question 7

A wire 2.5-m long has a cross-sectional area of 2.5 mm². It is hung vertically, and a 4.5-kg mass is attached to it. By how much does the wire stretch if Young's modulus for that material is 2.0 x10¹¹ N/m²?

A) 0.22 mm
B) 2.2 mm
C) 0.022 mm
D) 0.72 mm
E) 0.072 mm

Question 8

If you double the length of a bungee cord with no change in its cross-sectional area, its spring constant would

A) double.
B) triple.
C) cut in half.
D) quadruple.
E) not change.

Question 9

Young's modulus depends on the geometric shape of the object:

Question 10

An 800-kg mass is hung from a 1.50-m copper wire with a cross-sectional area of 0.350 cm². Young's modulus for copper is 1.10 x 10¹¹ N/m². How much does the wire stretch?

A) 2.56 mm
B) 2.97 mm
C) 3.14 mm
D) 3.86 mm
E) 4.13 mm

Question 11

An 800-kg mass is hung from a 2.00-m steel wire with a cross-sectional area of 0.250 cm². Young's modulus for steel is 2.0 *10¹¹ N/m². How much does the wire stretch?

A) 2.56 mm
B) 2.97 mm
C) 3.14 mm
D) 3.86 mm
E) 4.13 mm

Question 12

Fill in the blank. If you double the cross-sectional area of a steel rod, you would __________ the Young's modulus of steel.

A) double
B) triple
C) quadruple
D) cut in half
E) not change

Question 13

Young's modulus Y has units of

A) force.
B) mass density.
C) energy.
D) pressure.
E) mass per unit time.

Question 14

A spring is made of a wire of radius r and length L. If the radius of the wire and the length of the wire were doubled, the spring constant of the spring would

A) double.
B) quadruple.
C) halve.
D) quarter.
E) remain unchanged.

Question 15

When an object is under stress,

A) it deforms.
B) it undergoes strain.
C) it changes its shape or size.
D) All of the above.
E) None of these.

Question 16

A wire has a diameter of 0.75 mm. It is stretched 0.20% of its original length when a mass of 5.0 kg is hanging from it. What is the Young's modulus of the wire?

A) 1.4 x 10¹⁰ N/m²
B) 5.6 x 10¹⁰ N/m²
C) 1.7 x 10¹¹ N/m²
D) 5.6 x 10⁸ N/m²
E) 1.4 x 10⁸ N/m²

Question 17

If you measure the magnitude of the force required to stretch a typical laboratory spring as a function of the MAGNITUDE of stretch, which of the graphs shown would best represent your data?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 18

Which of the following statements are correct?

A) You apply tensile stress when you stretch an object along its length.
B) You apply volume stress when you squeeze an object on all sides.
C) You apply shear stress when you apply offset forces to deform an object.
D) All of the above statements are correct.
E) Only A and B are correct.

Question 19

If you grab each end of a pencil and try to pull the ends apart, you are putting the pencil under tension or tensile stress; if you push the ends toward each other, you are putting the pencil under

A) volume stress.
B) compressive stress.
C) shear stress.
D) Both A and B are correct.
E) Only C is correct.

Question 20

A design project requires you to construct a crane to lift a maximum of QUOTE 5.00×103 kg and with a maximum upward acceleration of 2.00 m/s², and with a safety factor of 5. If the cable is 20.0 m long, by how much does the cable stretch when the crane is operating at the design limits?

A) 2.80 cm
B) 1.05 cm
C) 6.21 cm
D) 0.84 cm
E) 5.22 cm

Question 21

True or false? Volume stress is equal to the pressure on the object.

Question 22

Use the following figure to answer the following question:
A steel wire and an aluminum wire of the same length L and diameter d are joined to form a wire of length 2L. The wire is fastened to the ceiling and a mass m is attached to the other end. If the masses of the wires are negligible relative to mass m, the ratio of the stress in the aluminum wire to the stress in the steel wire is

A) less than 1.
B) equal to 1.
C) greater than 1.
D) dependent on mass m.
E) impossible to determine.

Question 23

The bulk modulus of water is 2.00 x 10⁹ N/m². By how much must the pressure be increased to reduce the volume of 1.00 kg of water from 1.00 to 0.998 L?

A) 2.00 x10⁶ N/m²
B) 4.00 x 10⁶ N/m²
C) 2.00 x 10⁷ N/m²
D) 4.00 x 10⁷ N/m²
E) 8.00 x 10⁶ N/m²

Question 24

The graph shows force exerted by two springs with spring constants and , respectively, as a function of extension/compression. Which of the following statements is not true?

A) At the same extension force exerted by spring one is larger than force exerted by spring two
B) When the force exerted by spring one is the same as force exerted by spring two, the latter is extended more.
C) If both springs have the same dimensions, spring one is made from a stiffer material than spring two.
D) If the springs are made of the same material and have the same length, spring one has a smaller cross-sectional area than spring two.
E) If the springs are made of the same material and have the same cross-sectional areas, spring one is shorter than spring two.

Question 25

When you squeeze a small stress-ball on all sides in your palm you decrease its volume to ¾ of its original volume. What is the volume strain on the ball?

A)
B)
C)
D)
E)

Question 26

The bulk modulus of mercury is If a drop of benzene with a volume is moved from a vacuum chamber to a high-pressure chamber with , the volume of the droplet

A) increases by 1.14× 10^-4 mm³ .
B) increases by 1.14× 10^-7 mm³ .
C) doesn't change.
D) decreases by 1.14× 10^-4 mm³ .
E) decreases by 1.14× 10^-7 mm³ .

Question 27

A cube expands by 6.94 mm³ when moved from normal conditions to a vacuum chamber. If the bulk modulus of the material is 28.5 GPa, what is the length of the side of that cube?

A) 1.95 mm
B) 0.125 m
C) 4.42 cm
D) 12.5 m
E) 1.95 km

Question 28

A college student measures his height just before he goes to bed at night and also right after he gets up in the morning the next day. His measurements are 1.80 m, and 1.82 m, respectively. What is the compressive strain on his body due to the normal force and the gravity that are acting on him all day long?

A) 2/182
B) 2/180
C) 1.82 m-1.80 m
D) 182/180
E) 180/182

Question 29

A 4.00 m-long steel cable is used to support a church chandelier. After the 226-kg chandelier is attached to the cable hanging from the ceiling, the steel cable is lengthened by 3.00 mm. Calculate the tensile stress in the cable. The Young's modulus for steel is QUOTE 2.00×1011N/m2 .)

A)
B)
C)
D)
E)

Question 30

00x10¹⁰ N/m². Neglect any effect of the temperature difference.)

A) 3.35 x 10^-5 m³
B) 2.25 x 10^-4 m³
C) 1.18 x 10^-5 m³
D) 0.15 x 10^-4 m³
E) None of the above.

Question 31

A cube expands by 6.94 mm³ when moved from normal conditions to a vacuum chamber. If the bulk modulus of the material is 28.5 GPa, what is the length of the side of that cube?

A) 1.95 mm
B) 0.125 m
C) 4.42 cm
D) 12.5 m
E) 1.95 km

Question 32

A 4.00 m-long steel cable is used to support a church chandelier. After the 226-kg chandelier is hung from the ceiling, the steel cable is lengthened by 3.00 mm. Calculate the diameter of the cable in millimeters. The Young's modulus for steel is .)

A) 1.48
B) 2.17
C) 3.84
D) 4.34E. 6.51

Question 33

A laboratory experiment on stress-strain shows the following quantitative results: , , , , Which one of the above values represents a possible value for a tensile strain?

A)
B)
C)
D)
E)

Question 34

The bulk modulus B has units of

A) force.
B) energy.
C) pressure.
D) mass per unit time.
E) mass density.

Question 35

A 1.83 m-long aluminum "singing" rod is vertically balanced on the floor on one of its ends. Calculate the pressure on the ground exerted by the road due to the weight of the road. The density of Al is QUOTE 2.70×10³ kg/m3 and the diameter of the rod is 1.27 cm.

A) 2.7 N/m²
B) 8.4 N/m²
C) 2.7×10⁴ N/m²
D) 4.8×10⁴ N/m²
E) 4.94×10³ N/m²

Question 36

Use the following figure to answer the following question:
A steel wire and an aluminum wire of the same length L and diameter d are joined to form a wire of length 2L. The wire is fastened to the ceiling and a mass m is attached to the other end. If the masses of the wires are negligible relative to mass m, the ratio of the strain in the aluminum wire to the strain s in the steel wire is

A) less than 1.
B) equal to 1.
C) greater than 1.
D) dependent on mass m.
E) impossible to determine.

Question 37

Which of the following graphs shows the change in pressure as a function of change in volume for an object with initial volume V?

A) A)
B) B)
C) C)
D) D)
E) E)

Question 38

During exercise the volume of a human lung can increase by as much as 15%. If the bulk modulus for a lung is 3.00 kN/m², what is the change in the pressure?

A) +0.450 Pa
B) -0.450 Pa
C) 0
D) -450 Pa
E) +450 Pa

Question 39

The bulk modulus for steel is . If a solid steel ball of radius 2.00 cm is taken from Cape Canaveral to the Moon, what is the change in its volume in cubic meters?

A)
B)
C)
D)
E)

Question 40

A 1.00 m-high retaining wall is built out of concrete blocks. Each block weighs 22.2 N and has dimensions of 20.3 cm 9.20 cm 5.60 cm. Estimate the minimum volume stress on a block at the very bottom layer of the wall. Assume that the largest surface areas of blocks are facing each other, the height of the wall cannot exceed 1.00 m, and ignore the thin layer of cement between those faces.

A) 2.0210⁴ N/m²
B) 1.9010⁴ N/m²
C) 2.1410⁴ N/m²
D) 3.4510⁵ N/m²
E) 1.87 N/m²

Question 41

All elastic materials obey Hooke's law in the region of small strain.

A) True
B) False

Question 42

The point that identifies the proportional limit of the material whose graph of stress as a function of strain is shown is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 43

The point that identifies the elastic limit of the material whose graph of stress as a function of strain is shown is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 44

Which of the following could not have units of N/m²?

A) Young's modulus
B) shear modulus
C) bulk modulus
D) stress
E) strain

Question 45

The point that identifies the fracture point of the material whose graph of stress as a function of strain is shown is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 46

When pressure changes by value of Δp the change in volume of sphere of side a is . If the volume is , the change in the radius Δr is

A) 0.125r.
B) 0.500r.
C) 0.0435r.
D) 0.0646r.
E) 0.250r.

Question 47

The table below shows ultimate tensile strengths ) and Young's moduli ) for tungsten W) and silicon Si). Based on the information in the table, what is the ratio of ultimate tensile strains for these materials, namely .

A) 0.0980
B) 10.2
C) 0.0459
D) 2.77
E) 0.457

Question 48

The ultimate tensile strength of monocrystalline silicon is , while its Young's modulus of . What is the maximum extension that 1.35 cm silicon piece can withstand without breaking?

A) 0.503 cm
B) 0.363 cm
C) 0.0503 cm
D) 0.0503 m
E) 0.394 cm

Question 49

The form of Hooke's law relating shear stress to shear strain is F/A = E $\Delta$ s/h.The figure shows a block subjected to shear stress. Which number corresponds to the surface area A in the equation just given?

A) 1
B) 2
C) 3
D) 4
E) 5