Deck 9: Static Equilibrium; Elasticity and Fracture

Question 1

Choose the one alternative that best completes the statement or answers the question.
A 25-kg piece of equipment can be hung by steel wires of length 1.00 m, 2.00 m, or 3.00 m. If all the wires have the same diameter, which one will stretch the greatest percent?

A) the 1.00-m wire
B) the 3.00-m wire
C) the 2.00-m wire
D) They will all stretch by the same percent.

Answer 1

They will all stretch by the same percent.

Question 2

Choose the one alternative that best completes the statement or answers the question.
A 25-kg piece of equipment can be hung by steel wires of length 1.00 m, 2.00 m, or 3.00 m. If all the wires have the same diameter, which one will stretch the greatest distance?

A) the 2.00-m wire
B) the 3.00-m wire
C) the 1.00-m wire
D) They will all stretch by the same distance.

Answer 2

the 3.00-m wire

Question 3

Choose the one alternative that best completes the statement or answers the question.
If the sum of the external forces on an object is zero, then the sum of the external torques on it
must also be zero.

Answer 3

False

Question 4

Choose the one alternative that best completes the statement or answers the question.
Two blocks are made of the same material, but one has twice the volume of the other block. Which block will have the greater shear modulus?

A) It will be the same for both of them.
B) the larger one
C) the smaller one

Question 5

Choose the one alternative that best completes the statement or answers the question.
Two solid spheres are made from the same material, but one has twice the diameter of the other. Which sphere will have the greater bulk modulus?

A) the larger one
B) the smaller one
C) It will be the same for both spheres.

Question 6

Choose the one alternative that best completes the statement or answers the question.
The graph in the figure shows the tensile stress as a function of the tensile strain in a certain wire. What does the slope of this graph give us for this wire?

A) the pressure in the wire
B) the tensile stress in the wire
C) Young's modulus for the material of the wire
D) the tension in the wire
E) the percent change in the length of the wire

Question 7

Choose the one alternative that best completes the statement or answers the question.
Tensile strain is

A) the stress per unit area.
B) the applied force per unit area.
C) the ratio of stress to elastic modulus.
D) the ratio of the change in length to the original length.

Question 8

Choose the one alternative that best completes the statement or answers the question.
Tensile stress is

A) applied force per cross-sectional area.
B) the strain per unit length.
C) the same as force.
D) the ratio of the change in length.

Question 9

Choose the one alternative that best completes the statement or answers the question.
If the sum of the external torques on an object is zero, then the sum of the external forces on it
must also be zero.

Question 10

Choose the one alternative that best completes the statement or answers the question.
Which of the following are SI units of Young's modulus? (There could be more than one correct choice.)

A) $\mathrm { kg } \cdot \mathrm { m } ^ { 2 } / \mathrm { s } ^ { 2 }$
B) $\mathrm { N } / \mathrm { m } \cdot \mathrm { s } ^ { 2 }$
C) $\mathrm { kg } \cdot \mathrm { m } / \mathrm { s } ^ { 2 }$
D) $\mathrm { kg } / \mathrm { m } \cdot \mathrm { s } ^ { 2 }$
E) $\mathrm { kg } / \mathrm { m } ^ { 2 }$

Question 11

Choose the one alternative that best completes the statement or answers the question.
A croquet mallet balances when suspended from its center of mass, as shown in the left part of the figure. If you cut the mallet into two pieces at its center of mass, as shown in the right part of the figure, how do the masses of the two pieces compare? (There could be more than one correct choice.)

A) The piece with the head of the mallet has the greater mass.
B) The masses are equal.
C) The piece with the head of the mallet has the smaller mass.
D) It is impossible to tell.

Question 12

Choose the one alternative that best completes the statement or answers the question.
Which one of the following would be expected to have the smallest bulk modulus?

A) helium vapor
B) solid iron
C) liquid water
D) liquid mercury
E) solid uranium

Question 13

Choose the one alternative that best completes the statement or answers the question.
Which one of the following is an accurate statement?

A) Tensile stress is measured in newtons.
B) The ratio of tensile stress to tensile strain is called Young's modulus.
C) Tensile strain is measured in meters.
D) "Stress" has a meaning very close to "stretch."
E) "Strain" has a meaning very close to "force."

Question 14

Choose the one alternative that best completes the statement or answers the question.
When a car is weighed, it is driven slowly on a horizontal floor over a scale that records a reading as the front wheels go over the scale, and then records a second reading as the rear wheels go over
The scale. The weight of the car is equal to

A) the weight under the rear wheels.
B) the difference of the two weights.
C) the weight under the front wheels.
D) the average of the two weights.
E) the sum of the two weights.

Question 15

Choose the one alternative that best completes the statement or answers the question.
Two wires are made out of the same metal, but one wire is twice as long as the other wire. Which wire will have the greatest elastic modulus?

A) the longer wire
B) the shorter wire
C) It will be the same for both wires.

Question 16

Choose the one alternative that best completes the statement or answers the question.
A piece of iron sinks to the bottom of a lake where the pressure is 21 times what it is at the surface of the lake. Which statement best describes what happens to the volume of that piece of iron?

A) Its volume increases slightly.
B) Its volume decreases slightly.
C) Its volume becomes 1/21 what it was at the surface.
D) Its volume becomes 21 times greater than at the surface.
E) There has been no change in the volume of the iron.

Question 17

Choose the one alternative that best completes the statement or answers the question.
A large 75-kg lighting fixture can be hung from wires of identical size and shape made of aluminum, brass, or copper. The values of Young's modulus for these metals are $0.70 \times 10 ^ { 11 } \mathrm {~Pa}$ (aluminum), $0.91 \times 10 ^ { 11 } \text { (brass), and } 1.1 \times 10 ^ { 11 } \text { (copper) }$
Which wire would stretch the least distance?

A) copper
B) aluminum
C) brass
D) They will all stretch the same distance.

Question 18

Choose the one alternative that best completes the statement or answers the question.
If an object remains at rest, then the sum of both the external torques and the external forces on the
object must be zero.

Question 19

Choose the one alternative that best completes the statement or answers the question.
A piece of iron sinks to the bottom of a lake where the pressure is 21 times what it is at the surface. Which statement best describes what happens to the density of that piece of iron?

A) There has been no change in the density of the iron.
B) Its density becomes 1/21 what it was at the surface.
C) Its density decreases slightly.
D) Its density increases slightly.
E) Its density becomes 21 times greater than what it was at the surface.

Question 20

Choose the one alternative that best completes the statement or answers the question.
If the sum of both the external torques and the external forces on an object is zero, then the object
must be at rest.

Question 21

Choose the one alternative that best completes the statement or answers the question.
As one stretches a metal wire, which condition is reached first?

A) the elastic limit
B) the proportional limit
C) the breaking point

Question 22

Choose the one alternative that best completes the statement or answers the question.
An irregularly shaped object that is 10 m long is placed with each end on a scale. If the scale on the right reads 96 N while the scale on the left reads 71 N, how far from the left end is the center of
Gravity of this object?

A) 4.3 m
B) 5.7 m
C) 7.4 m
D) 14 m

Question 23

Write the word or phrase that best completes each statement or answers the question.
A light board that is 10 m long is supported by two sawhorses, one at one end of the board
and a second at the midpoint. A 40-N object is placed between the two sawhorses, 3.0 m
from the end and 2.0 m from the center. A second object, with a weight of 15 N, is placed
on the supported end. What magnitude forces do the sawhorses exert on the board?

Question 24

Write the word or phrase that best completes each statement or answers the question.
A 10-m uniform beam weighing 100 N is supported by two vertical ropes at its ends. If a
400-N person sits at a point 2.0 m from the left end of the beam, what is the tension in
each rope?

Question 25

Choose the one alternative that best completes the statement or answers the question.
A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the magnitude of the minimum force, applied 0.30 m on the other side of the pivot, that is needed to make the
Child lift off the ground?

A) 66 N
B) 75 N
C) 740 N
D) 44 N
E) 23 N

Question 26

Choose the one alternative that best completes the statement or answers the question.
A uniform rod weighs 40 N and is 1.0 m long. It is hinged to a wall at the left end, and held in a horizontal position at the right end by a vertical string of negligible weight, as shown in the figure. What is the magnitude of the torque due to the string about a horizontal axis that passes through the hinge and is perpendicular to the rod? The hinge is very small with negligible friction.

A) $5.0 \mathrm {~N} \cdot \mathrm { m }$
B) $20 \mathrm {~N} \cdot \mathrm { m }$
C) $40 \mathrm {~N} \cdot \mathrm { m }$
D) $30 \mathrm {~N} \cdot \mathrm { m }$
E) $10 \mathrm {~N} \cdot \mathrm { m }$

Question 27

Write the word or phrase that best completes each statement or answers the question.
As shown in the figure, a 10.0 m long bar is attached by a frictionless hinge to a wall and held horizontal by a light rope that makes an angle $\theta = 49 ^ { \circ }$ with the bar. The bar is uniform and weighs 66.5 N. What distance x from the hinge should a 10.0 kg mass be suspended for the tension in the rope to be 177 N?

Question 28

Write the word or phrase that best completes each statement or answers the question.
A uniform ladder 12 meters long rests against a vertical frictionless wall, as shown in the figure. The ladder weighs 400 N and makes an angle $\theta = 51 ^ { \circ }$ with the floor. A man weighing 874 N climbs slowly up the ladder. When he is 78 m from the bottom of the Iadder, it just starts to slip. What is the coefficient of static friction between the floor and the ladder?

Question 29

Choose the one alternative that best completes the statement or answers the question.
A child is trying to stack two uniform bricks, each 24 cm long, so they will protrude as far as possible over the edge of a table without tipping over, as shown in the figure. What is the maximum possible overhang distance d?

A) 10 cm
B) 16 cm
C) 12 cm
D) 18 cm
E) 14 cm

Question 30

Choose the one alternative that best completes the statement or answers the question.
A 120-kg refrigerator that is 2.0 m tall and 85 cm wide has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is 0.30 .
Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it will not tip before it begins to slide?

A) 1.0 m
B) 1.6 m
C) 1.2 m
D) 1.4 m
E) 0.71 m

Question 31

Write the word or phrase that best completes each statement or answers the question.
An 82-kg diver stands at the edge of a light 5.0-m diving board, which is supported by
two vertical pillars that are 1.6 m apart, as shown in the figure. Find the magnitude and
direction of the force exerted by each pillar.

Question 32

Write the word or phrase that best completes each statement or answers the question.
A light board that is 10 m long is supported by two sawhorses, one at one end of the board
and a second at the midpoint. A 40-N weight is placed between the two sawhorses, 3.0 m
from the end and 2.0 m from the center. What magnitude forces do the sawhorses exert on
the board?

Question 33

Choose the one alternative that best completes the statement or answers the question.
A uniform 40-N board supports two children weighing 500 N and 350 N. If the support is at the center of the board and the 500-N child is 1.5 m from its center, how far is the 350-N child from the center?

A) 2.1 m
B) 1.1 m
C) 2.7 m
D) 1.5 m

Question 34

Write the word or phrase that best completes each statement or answers the question.
The mobile shown in the figure is perfectly balanced, and the horizontal supports have insignificant masses. What must be the masses of the suspended objects $m _ { 1 } , m _ { 2 } , \text { and } m _ { 3 }$
to maintain balance?

Question 35

Choose the one alternative that best completes the statement or answers the question.
A uniform 1200-N piece of medical apparatus that is 3.5 m long is suspended horizontally by two vertical wires at its ends. A small but dense 550-N weight is placed on the apparatus 2.0 m from one end, as shown in the figure. What are the tensions, A and B , in the two wires?

A) A=910 N, B=840 N
B) A=880 N, B=880 N
C) A=9000 N, B=8200 N
D) A=840 N, B=910 N
E) A=8200 N, B=9000 N

Question 36

Choose the one alternative that best completes the statement or answers the question.
To determine the location of the center of mass (or center of gravity) of a car, the car is driven over a scale on a horizontal floor. When the front wheels are over the scale, the weight recorded by the scale is 5800 N, and when the rear wheels are over the scale, the scale reads 6500 N. The distance between the front and rear wheels is measured to be 3.20 m. How far behind the front wheels is the center of mass located?

A) 1.72 m
B) 1.50 m
C) 0.845 m
D) 1.69 m
E) 1.59 m

Question 37

Choose the one alternative that best completes the statement or answers the question.
A meter stick balances at the 50.0-cm mark. If a mass of 50.0 g is placed at the 90.0-cm mark, the stick balances at the 61.3-cm mark. What is the mass of the meter stick?

A) 178 g
B) 89.7 g
C) 73.4 g
D) 127 g
E) 32.6 g

Question 38

Write the word or phrase that best completes each statement or answers the question.
An 82-kg painter stands on a long horizontal board 1.55 m from one end. This 27-kg
board is uniform, 5.5 m long, and supported at each end by vertical posts.
(a) What is the magnitude of the total force provided by both posts?
(b) With what force does the post that is closest to the painter push upward on the board?

Question 39

Choose the one alternative that best completes the statement or answers the question.
A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the minimum distance, on the other side of the pivot, such that a 220-N force will make the child lift off the
Ground?

A) 1.0 m
B) 0.10 m
C) 1.5 m
D) 2.4 m
E) 9.8 m

Question 40

Write the word or phrase that best completes each statement or answers the question.
As shown in the figure, a uniform rectangular crate 0.40 m wide and 1.0 m tall sits on a horizontal surface. The crate weighs 460 N, and its center of gravity is at its geometric center. A horizontal force of magnitude F is applied at a distance h above the floor. Friction at the floor is great enough to prevent the crate from sliding. If h=0.69 m, what minimum value of F is required to make the crate start to tip over?

Question 41

Choose the one alternative that best completes the statement or answers the question.
When a 125-kg piece of equipment is hung from a steel wire of length 75 cm, it stretches the wire by 4.00 mm . If instead the wire had a length of 150 cm, but all else were the same, by what distance would the same equipment stretch the wire?

A) 8.00 mm
B) 2.00 mm
C) 16.0 mm
D) 4.00 mm
E) 1.00 mm

Question 42

Choose the one alternative that best completes the statement or answers the question.
In the figure, a uniform ladder of weight 200 N and length 10 m leans against a perfectly smooth wall. A firefighter of weight 600 N climbs a distance x up the ladder. The coefficient of static friction between the ladder and the floor is 0.50 . What is the maximum value of x for which the Iadder will not slip?

A) 8.4 m
B) 3.9 m
C) 6.3 m
D) 6.0 m
E) 5.0 m

Question 43

Write the word or phrase that best completes each statement or answers the question.
An aluminum wire and a steel wire, each of length 2.0 m, are hung from the ceiling. A 5.0-kg mass is suspended from the lower end of each wire. The aluminum wire has a diameter of 2.2 mm. What must be the diameter of the steel wire if it is to stretch the same distance as the aluminum wire, so that the two wires maintain equal lengths after the masses are attached? Young's modulus for aluminum is $0.70 \times 10 ^ { 11 } \mathrm {~Pa}$ and for steel it is 2.0 x 10¹¹ Pa

Question 44

Write the word or phrase that best completes each statement or answers the question.
A 50-kg bucket of concrete is suspended from a steel wire that is 1.0 mm in diameter 1.0 mm and 11.2 m long. What distance will the wire stretch? Young's modulus for steel is $2.0$ $\times 10 ^ { 11 } \mathrm {~Pa}$

Question 45

Choose the one alternative that best completes the statement or answers the question.
A store's sign has a mass of 20 kg and is 3.0 m long. It is uniform, so its center of gravity is at the center of the sign. It is supported horizontally by a small loose bolt attached to the wall at one end and by a wire at the other end, as shown in the figure. What is the tension in the wire?

A) 460 N
B) 200 N
C) 120 N
D) 230 N
E) 300 N

Question 46

Choose the one alternative that best completes the statement or answers the question.
A 100-kg nonuniform boom that is 6.0 m long is loosely pinned at the pivot at P. A 600-kg concrete block is suspended from the end of the boom at A , as shown in the figure. The boom forms a $30 ^ { \circ }$ angle above the horizontal, and is supported by a 4.0 -m cable between points D and B . Point B is 4.0 m from P , and point D is 4.0 m above P . The center of mass of the boom is at point C , which is 2.0 m from P. Assume that all the quantities shown in the figure are accurate to two significant figures. What is the tension in the cable connected between points B and D?

A) 9300 N
B) 6900 N
C) 7500 N
D) 8100 N
E) 8400 N

Question 47

Choose the one alternative that best completes the statement or answers the question.
A mobile is shown in the figure. The horizontal supports have negligible mass. Assume that all the numbers given in the figure are accurate to two significant figures. What mass M is required to balance the mobile?

A) 36 g
B) 30 g
C) 90 g
D) 18 g
E) 60 g

Question 48

Choose the one alternative that best completes the statement or answers the question.
When a 125-kg piece of equipment is hung from a steel wire of diameter 6.00 mm, it stretches the wire by 4.00 mm. If instead the wire had a diameter of 3.00 mm, but all else were the same, by what distance would the same equipment stretch the wire?

A) 4.00 mm
B) 2.00 mm
C) 1.00 mm
D) 16.0 mm
E) 8.00 mm

Question 49

Choose the one alternative that best completes the statement or answers the question.
A 320-g ball and a 400-g ball are attached to the two ends of a string that goes over a pulley with a radius of 8.7 cm. Because of friction in its axle, the pulley does not begin to rotate. What is the magnitude of the frictional torque at the axle of the pulley if the system remains at rest when the balls are released?

A) $0.00070 \mathrm {~N} \cdot \mathrm { m }$
B) $0.61 \mathrm {~N} \cdot \mathrm { m }$
C) $0.068 \mathrm {~N} \cdot \mathrm { m }$
D) $0.063 \mathrm {~N} \cdot \mathrm { m }$
E) $0.079 \mathrm {~N} \cdot \mathrm { m }$

Question 50

Choose the one alternative that best completes the statement or answers the question.
A steel wire, 3.2 m long, has a diameter of 1.2 mm. The wire stretches 1.6 mm when it bears a load. Young's modulus for steel is $2.0 \times 10 ^ { 11 } \mathrm {~Pa}$
The mass of the load is closest to

A) 24 kg
B) 20 kg
C) 12 kg
D) 28 kg
E) 16 kg

Question 51

Choose the one alternative that best completes the statement or answers the question.
A 5.00-m-long uniform ladder, weighing 200 N, rests against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1.20 m away from the wall. The coefficient of static
Friction between the ladder and the floor is 0.200. How far up the ladder, measured along the
Ladder, can a 600-N person climb before the ladder begins to slip?

A) 4.56 m
B) 3.95 m
C) 1.26 m
D) 1.05 m
E) 1.50 m

Question 52

Choose the one alternative that best completes the statement or answers the question.
A solid steel column is 4.0 m long and 0.20 m in diameter. Young's modulus for this steel is $2.0 \times$ $10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
By what distance does the column shrink when a 5000-\mathrm{kg} truck is supported by it?

A) $3.2 \times 10 ^ { - 6 } \mathrm {~m}$
B) $7.8 \times 10 ^ { - 6 } \mathrm {~m}$
C) $3.1 \times 10 ^ { - 5 } \mathrm {~m}$
D) $8.0 \times 10 ^ { - 7 } \mathrm {~m}$

Question 53

Choose the one alternative that best completes the statement or answers the question.
A cable is 100-m long and has a cross-sectional area of $1.0 \mathrm {~mm} ^ { 2 }$
stretch the cable. Young's modulus for the cable is $1.0 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$ stretch?

A) 0.10 m
B) 1.0 m
C) 10 m
D) 0.010 m

Question 54

Choose the one alternative that best completes the statement or answers the question.
A stepladder consists of two halves that are hinged at the top and connected by a tie rod which keeps the two halves from spreading apart. In this particular instance, the two halves are 2.5 m Iong, the tie rod is connected to the center of each half and is 70 cm long. An 800-N person stands 3/5 of the way up the stepladder, as shown in the figure. The ladder is light enough that we can neglect its weight, and it rests on an extremely smooth floor. What is the tension in the tie rod? (Note: To solve this problem, it is helpful to imagine cutting the ladder in half vertically and consider the forces and torques acting on each half of the ladder.)

A) 560 N
B) 240 N
C) 140 N
D) 280 N
E) 360 N

Question 55

Choose the one alternative that best completes the statement or answers the question.
A 40-kg uniform ladder that is 5.0 m long is placed against a smooth wall at a height of h=4.0 m, as shown in the figure. The base of the ladder rests on a rough horizontal surface whose coefficient of static friction with the ladder is 0.40 . An 80-kg bucket is suspended from the top rung of the Iadder, just at the wall. What is the magnitude of the force that the ladder exerts on the wall?

A) 1300 N
B) 900 N
C) 980 N
D) 1100 N
E) 740 N

Question 56

Write the word or phrase that best completes each statement or answers the question.
A 7.0-kg pipe is hung from a steel wire that is 2.5 m long and has a diameter of 0.75 mm.
Young's modulus for steel is $2.0 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
(a) By what distance does the wire stretch?
(b) If the wire diameter were doubled, what would be the stretch?

Question 57

Choose the one alternative that best completes the statement or answers the question.
An athlete holds a 7.5-kg shot put in his hand with his lower arm horizontal, as shown in the figure. His lower arm has a mass of 2.8 kg and its center of gravity (or center of mass) is 12 cm from the elbow-joint pivot. How much force must the extensor muscle (which is $\overrightarrow { \mathrm { F } } _ { \mathrm { M } }$ in the figure) in the upper arm exert on the lower arm?

A) 100 N
B) 500 N
C) 1500 N
D) 1000 N

Question 58

Choose the one alternative that best completes the statement or answers the question.
A store's sign has a mass of 20 kg and is 3.0 m long. It is uniform, so its center of gravity is at the center of the sign. It is supported horizontally by a small loose bolt attached to the wall at one er and by a wire at the other end, as shown in the figure. What is the magnitude of the net force th the bolt exerts on the sign?

A) 230 N
B) 120 N
C) 200 N
D) 300 N
E) 460 N

Question 59

Choose the one alternative that best completes the statement or answers the question.
A wire of diameter 0.20 mm stretches by 0.20 % when a 6.28-N force is applied to it. What is Young's modulus for this wire?

A) $2.5 \times 10 ^ { 10 } \mathrm {~Pa}$
B) $2.5 \times 10 ^ { 12 } \mathrm {~Pa}$
C) $1.0 \times 10 ^ { 11 } \mathrm {~Pa}$
D) $1.0 \times 10 ^ { 12 } \mathrm {~Pa}$

Question 60

Choose the one alternative that best completes the statement or answers the question.
A 3.00-m-long ladder, weighing 200 N, leans against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1.00 m away from the wall. The ladder is not completely
Uniform, so its center of gravity is 1.20 m from its base. What force of friction must the floor exert
On the base of the ladder to prevent the ladder from sliding down?

A) 93.3 N
B) 150 N
C) 28.3 N
D) 130 N
E) 102 N

Question 61

Choose the one alternative that best completes the statement or answers the question.
A 50-kg air conditioner is placed on top of a concrete pad that is 20 cm thick and has a cross-sectional area of $3.0 \mathrm {~m} ^ { 2 }$ What is the change in thickness of the pad caused by the air conditioner? Young's modulus for concrete is $2.3 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$

A) $1.4 \times 10 ^ { - 9 } \mathrm {~m}$
B) $2.8 \times 10 ^ { - 9 } \mathrm {~m}$
C) $1.4 \times 10 ^ { - 7 } \mathrm {~m}$
D) $2.8 \times 10 ^ { - 8 } \mathrm {~m}$
E) $1.4 \times 10 ^ { - 8 } \mathrm {~m}$

Question 62

Choose the one alternative that best completes the statement or answers the question.
A copper sphere that is 10 cm in diameter at an atmospheric pressure of $1.01 \times 10 ^ { 5 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
is put into a chamber where the pressure is $1.0 \times 10 ^ { 6 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
What is the change in the diameter of the sphere caused by this change in pressure? The bulk modulus for copper is $1.4 \times 10 ^ { 11 } \mathrm {~Pa}$

A) $- 7.1 \times 10 ^ { - 4 } \mathrm {~cm}$
B) $- 2.1 \times 10 ^ { - 5 } \mathrm {~cm}$
C) $- 7.1 \times 10 ^ { - 5 } \mathrm {~cm}$
D) $- 7.1 \times 10 ^ { - 6 } \mathrm {~cm}$
E) $- 2.1 \times 10 ^ { - 4 } \mathrm {~cm}$

Question 63

Choose the one alternative that best completes the statement or answers the question.
A 50-kg load is suspended from a steel wire of diameter 1.0 mm and length 11.2 m. By what distance will the wire stretch? Young's modulus for steel is $2.0 \times 10 ^ { 11 } \mathrm {~Pa}$

A) 2.5 cm
B) 3.5 cm
C) 1.5 cm
D) 4.5 cm

Question 64

Choose the one alternative that best completes the statement or answers the question.
A 12-L volume of oil is subjected to pressure which produces a volume strain of $- 3.0 \times 10 ^ { - 4 }$ bulk modulus of the oil is $6.0 \times 10 ^ { 9 } \mathrm {~Pa}$ and is independent of the pressure. The change in the The pressure of the oil in megapascals is closest to

A) $\text { 1.2 MPa. }$
B) $\text { 1.4 MPa. }$
C) $2.0 \mathrm { MPa }$
D) $1.8 \mathrm { MPa }$
E) $1.6 \mathrm { MPa }$

Question 65

Choose the one alternative that best completes the statement or answers the question.
A piano wire has a radius of 0.50 mm . One end is fixed and the other is wrapped around a tuning peg, which has a diameter of 3.5 mm and is 80 cm away. After the wire just becomes taut, the peg is given three full turns. What is the tension in the wire? Young's modulus for steel is $2.0 \times 10 ^ { 11 }$ $\mathrm { N } / \mathrm { m } ^ { 2 }$

A) 4.3 kN
B) 8.7 kN
C) 3.8 kN
D) 9.8 kN
E) 6.5 kN

Question 66

Choose the one alternative that best completes the statement or answers the question.
A 12-L volume of oil is subjected to pressure which produces a volume strain of $- 3.0 \times 10 ^ { - 4 }$ The bulk modulus of the oil is $6.0 \times 10 ^ { 9 } \mathrm {~Pa}$ and is independent of the pressure. The reduction in the volume of the oil in milliliters is closest to

A) 3.2 mL
B) 2.8 mL
C) 2.0 mL
D) 2.4 mL
E) 3.6 mL

Question 67

Choose the one alternative that best completes the statement or answers the question.
At a depth of 1030 m in Lake Baikal (a fresh water lake in Siberia), the pressure has increased by 100 atmospheres $\text { (to about } 10 ^ { 7 } \mathrm {~N} / \mathrm { m } ^ { 2 } \text { ). }$
By what volume has $1.0 \mathrm {~m} ^ { 3 }$ of water from the surface of the lake been compressed if it is forced down to this depth? The bulk modulus of water is $2.3 \times 10 ^ { 9 }$ $\text { Pa. }$

A) $2.3 \times 10 ^ { - 3 } \mathrm {~m} ^ { 3 }$
B) $3.3 \times 10 ^ { - 3 } \mathrm {~m} ^ { 3 }$
C) $5.3 \times 10 ^ { - 3 } \mathrm {~m} ^ { 3 }$
D) $4.3 \times 10 ^ { - 3 } \mathrm {~m} ^ { 3 }$

Question 68

Write the word or phrase that best completes each statement or answers the question.
When the pressure applied to an unknown liquid is increased from $1.0 \times 10 ^ { 7 } \mathrm {~Pa}$
to $5.5 \times$ $10 ^ { 7 } \mathrm {~Pa}$ the volume of the liquid decreases by 0.70 % . Calculate the bulk modulus of the liquid.

Question 69

Choose the one alternative that best completes the statement or answers the question.
The base of a metal block, which is fixed in place, measures 90 cm by 90 cm, and the height of the
block is 60 cm. A force, applied to the upper face and parallel to it, produces a shear strain of
0.0060 . The shear modulus of this metal is $3.0 \times 10 ^ { 10 } \mathrm {~Pa}$
megapascals is closest to The shear stress on the block in

A) 360 MPa
B) 720 MPa
C) 600 MPa
D) 900 MPa
E) 180 MPa

Question 70

Choose the one alternative that best completes the statement or answers the question.
A 5000-N force compresses a steel block by 0.0025 cm. How much force, applied over the same area, would be needed to compress the block by 0.0125 cm?

A) 5,000 N
B) 25,000 N
C) 1,000 N
D) 2,500 N

Question 71

Write the word or phrase that best completes each statement or answers the question.
A wire that is 1.0 mm in diameter and 3.5 m long stretches 3.5 mm when an 8.0-kg tool is
hung from it.
(a) What is Young's modulus for the material from this wire is made?
(b) What is the effective spring constant for the stretching wire?

Question 72

Choose the one alternative that best completes the statement or answers the question.
A 1200-kg car is being raised with a constant acceleration of $2.53 \mathrm {~m} / \mathrm { s } ^ { 2 }$
Iong steel cable that is 1.5 cm in diameter. Young's modulus for steel is $2.0 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$
the change in length of the cable caused by lifting the car?

A) 8.4 cm
B) 8.4 mm
C) 4.9 mm
D) 4.9 cm
E) 4.9 m

Question 73

Choose the one alternative that best completes the statement or answers the question.
A brass wire 2.0 m long and 2.0 mm in diameter supports a 10.0-kg fixture. By what distance did this fixture stretch the wire? Young's modulus for brass is $10 \times 1010 \mathrm {~N} / \mathrm { m } _ { 2 }$

A) 0.62 mm
B) 0.11 mm
C) 0.33 mm
D) 0.22 mm

Question 74

Choose the one alternative that best completes the statement or answers the question.
A 1200-kg car is being raised at a constant speed if 25 cm/s by a crane, using a 20-m long steel cable that is 1.5 cm in diameter. Young's modulus for steel is $2.0 \times 10 ^ { 11 } \mathrm {~Pa}$ Iength of the cable caused by the car?
What is the change in length of the cable caused by the car?

A) 3.3 mm
B) 6.7 mm
C) 3.3 cm
D) 3.3 m
E) 6.7 cm

Question 75

Choose the one alternative that best completes the statement or answers the question.
The base of a metal block, which is fixed in place, measures 90 cm by 90 cm, and the height of the block is 60 cm. A force, applied to the upper face and parallel to it, produces a shear strain of 0.0060 . The shear modulus of this metal is $3.0 \times 10 ^ { 10 } \mathrm {~Pa}$ The displacement of the upper face, in the direction of the applied force is closest to

A) 5.4 mm
B) 4.8 mm
C) 3.0 mm
D) 4.2 mm
E) 3.6 mm

Question 76

Choose the one alternative that best completes the statement or answers the question.
An aluminum wire 2.0 m long and 2.0 mm in diameter supports a 10.0-kg fixture. What is the stress in the wire? Young's modulus for aluminum is $7.0 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$

A) $6.2 \times 107 \mathrm {~N} / \mathrm { m } _ { 2 }$
B) $1.2 \times 108 \mathrm {~N} / \mathrm { m } 2$
C) $9.3 \times 107 \mathrm {~N} / \mathrm { m } ^ { 2 }$
D) $3.1 \times 107 \mathrm {~N} / \mathrm { m } ^ { 2 }$

Question 77

Choose the one alternative that best completes the statement or answers the question.
A bridge piling has a cross-sectional area of $1.250 \mathrm {~m} ^ { 2 }$ and supports a load of 1875 N. What is the stress on the column?

A) 1875 N
B) $2344 \mathrm {~N} / \mathrm { m } ^ { 2 }$
C) $1500 \mathrm {~N} / \mathrm { m } ^ { 2 }$
D) $1875 \mathrm {~N} / \mathrm { m } ^ { 2 }$

Question 78

Choose the one alternative that best completes the statement or answers the question.
Opposing shearing forces of 3000 N are applied to the 3.00-cm x 4.00-cm faces of a metal block measuring 3.00 cm x 4.00 cm x 5.00 cm. By what distance does the block become slanted? The shear modulus for this metal is $8.10 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$

A) $9.88 \times 10 ^ { - 7 } \mathrm {~m}$
B) $6.98 \times 10 ^ { - 6 } \mathrm {~m}$
C) $1.54 \times 10 ^ { - 6 } \mathrm {~m}$
D) $5.56 \times 10 ^ { - 7 } \mathrm {~m}$
E) $3.08 \times 10 ^ { - 6 } \mathrm {~m}$

Question 79

Choose the one alternative that best completes the statement or answers the question.
A vertical 30-cm steel rod, 1.0 cm in diameter, supports a 300-kg mass. What is the change in Iength of the rod caused by this mass? Young's modulus for steel is $2.0 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$

A) $6.5 \times 10 ^ { - 5 } \mathrm {~m}$
B) $6.5 \times 10 ^ { - 6 } \mathrm {~m}$
C) $6.5 \times 10 ^ { - 4 } \mathrm {~m}$
D) $5.6 \times 10 ^ { - 6 } \mathrm {~m}$
E) $5.6 \times 10 ^ { - 5 } \mathrm {~m}$

Question 80

Choose the one alternative that best completes the statement or answers the question.
A shear force of 400 N is applied to one face of an aluminum cube having sides of 30 cm each. What is the resulting displacement of this face of the cube if the opposite face is held fixed? The shear modulus for aluminum is $2.5 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$

A) $4.4 \times 10 ^ { - 8 } \mathrm {~m}$
B) $5.3 \times 10 ^ { - 8 } \mathrm {~m}$
C) $1.9 \times 10 ^ { - 8 } \mathrm {~m}$
D) $8.2 \times 10 ^ { - 8 } \mathrm {~m}$