Deck 8: Equilibrium Ad Elasticity

Question 1

Tensile stress is

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

Answer 1

D

Question 2

An object attached to a spring is pulled across a horizontal frictionless surface. If the force constant (spring constant) of the spring is 45 N/m and the spring is stretched by 0.88 m when the object is accelerating at what is the mass of the object?

A) 28 kg
B) 24 kg
C) 31 kg
D) 36 kg

Answer 2

A

Question 3

A very light ideal spring stretches by when it is used to hang a 135-N object. What is the weight of a piece of electronic equipment that would stretch the spring by if you hung the equipment using the spring?

A) 289 N
B) 63 N
C) 176 N
D) 405 N

Answer 3

A

Question 4

Which one of the following is an accurate statement?

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

Question 5

A force of stretches a very light ideal spring from equilibrium. What is the force constant (spring constant) of the spring?

A) 41 N/m
B) 22 N/m
C) 34 N/m
D) 46 N/m

Question 6

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 × 10¹¹ Pa (aluminum), 0.91 × 10¹¹ (brass), and 1.1 × 10¹¹ (copper). Which wire would stretch the least distance?

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

Question 7

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

Question 8

Tensile strain is

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

Question 9

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 10

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.

Question 11

As one stretches a metal wire, which condition is reached first?

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

Question 12

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

Question 13

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 14

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 15

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

Question 16

Which of the following are SI units of Young's modulus? (There could be more than one correct choice.)

A) N/m ∙ s²
B) kg/m²
C) kg ∙ m/s²
D) kg/m ∙ s²
E) kg ∙ m²/s²

Question 17

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

Question 18

An ornament of mass 40.0 g is attached to a vertical ideal spring with a force constant (spring constant) of 20.0 N/m. The ornament is then lowered very slowly until the spring stops stretching. How much does the spring stretch?

A) 0.00200 m
B) 0.0196 m
C) 0.0816 m
D) 0.800 m
E) 0.200 m

Question 19

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

Question 20

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

Question 21

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 θ = 51° with the floor. A man weighing 874 N climbs slowly up the ladder. When he is 78 m from the bottom of the ladder, it just starts to slip. What is the coefficient of static friction between the floor and the ladder?

Question 22

An irregularly shaped object that is 10 m long is placed with each end on a scale. If the scale on the right reads while the scale on the left reads how far from the left end is the center of gravity of this object?

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

Question 23

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) 1.5 m
C) 0.10 m
D) 9.8 m
E) 2.4 m

Question 24

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

Question 25

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 what minimum value of F is required to make the crate start to tip over?

Question 26

A very light ideal spring of spring constant (force constant) 2.5 N/cm is 15 cm long when nothing is attached to it. It is now used to pull horizontally on a 12.5-kg box on a perfectly smooth horizontal floor. You observe that the box starts from rest and moves 96 cm during the first 1.6 s of its motion with constant acceleration. How long is the spring during this motion?

Question 27

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

Question 28

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

Question 29

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) 12 cm
C) 14 cm
D) 16 cm
E) 18 cm

Question 30

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 θ = 49° with the bar. The bar is uniform and weighs 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 31

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 32

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 33

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 34

A very light ideal spring with a spring constant (force constant) of 2.5 N/cm pulls horizontally on an 18-kg box that is resting on a horizontal floor. The coefficient of static friction between the box and the floor is 0.65, and the coefficient of kinetic friction is 0.45.
(a) How long is the spring just as the box is ready to move?
(b) If the spring pulls the box along with a constant forward velocity of 1.75 m/s, how long is the spring?
(c) How long is the spring if it pulls the box forward at a constant 2.75 m/s?

Question 35

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

Question 36

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) 40 N ∙ m
B) 10 N ∙ m
C) 5.0 N ∙ m
D) 20 N ∙ m
E) 30 N ∙ m

Question 37

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

Question 38

A very light ideal spring having a spring constant (force constant) of 8.2 N/cm is used to lift a 2.2-kg tool with an upward acceleration of 3.25 m/s². If the spring has negligible length when it us not stretched, how long is it while it is pulling the tool upward?

Question 39

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

Question 40

A 3.0-kg brick rests on a perfectly smooth ramp inclined at 34° above the horizontal. The brick is kept from sliding down the plane by an ideal spring that is aligned with the surface and attached to a wall above the brick. The spring has a spring constant (force constant) of 120 N/m. By how much does the spring stretch with the brick attached?

A) 360 cm
B) 240 cm
C) 14 cm
D) 24 cm
E) 36 cm

Question 41

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) 0.068 N ∙ m
B) 0.61 N ∙ m
C) 0.079 N ∙ m
D) 0.063 N ∙ m
E) 0.00070 N ∙ m

Question 42

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 43

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 m₁, m₂, and m₃ to maintain balance?

Question 44

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 x 10¹¹ Pa.

Question 45

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 ladder, just at the wall. What is the magnitude of the force that the ladder exerts on the wall?

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

Question 46

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° 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) 8400 N
C) 8100 N
D) 7500 N
E) 6900 N

Question 47

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) 230 N
C) 120 N
D) 200 N
E) 300 N

Question 48

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

Question 49

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 _M in the figure) in the upper arm exert on the lower arm?

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

Question 50

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

Question 51

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 ladder will not slip?

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

Question 52

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 × 10¹¹ N/m².
(a) By what distance does the wire stretch?
(b) If the wire diameter were doubled, what would be the stretch?

Question 53

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 54

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 × 10¹¹ Pa and for steel it is 2.0 × 10¹¹ Pa.

Question 55

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

Question 56

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 long, 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) 140 N
B) 240 N
C) 280 N
D) 360 N
E) 560 N

Question 57

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 × 10¹¹ Pa. The mass of the load is closest to

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

Question 58

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

Question 59

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) 130 N
C) 28.3 N
D) 102 N
E) 150 N

Question 60

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 magnitude of the net force that the bolt exerts on the sign?

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

Question 61

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 m². What is the change in thickness of the pad caused by the air conditioner? Young's modulus for concrete is 2.3 × 10¹⁰ N/m².

A) 1.4 × 10^-9 m
B) 2.8 × 10^-9 m
C) 1.4 × 10^-8 m
D) 1.4 × 10^-7 m
E) 2.8 × 10^-8 m

Question 62

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 × 10¹⁰ N/m².

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

Question 63

A 1200-kg car is being raised with a constant acceleration of 2.53 m/s² 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 × 10¹¹ N/m². What is the change in length of the cable caused by lifting the car?

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

Question 64

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 × 10¹⁰ N/m².

A) 3.1 × 10⁷ N/m²
B) 6.2 × 10⁷ N/m²
C) 9.3 × 10⁷ N/m²
D) 1.2 × 10⁸ N/m²

Question 65

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 × 10¹⁰ Pa
B) 1.0 × 10¹¹ Pa
C) 2.5 × 10¹² Pa
D) 1.0 ×10¹² Pa

Question 66

A cable is 100-m long and has a cross-sectional area of 1.0 mm². A 1000-N force is applied to stretch the cable. Young's modulus for the cable is 1.0 × 10¹¹ N/m². How far does the cable stretch?

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

Question 67

A bridge piling has a cross-sectional area of 1.250 m² and supports a load of 1875 N. What is the stress on the column?

A) 1875 N
B) 1875 N/m²
C) 1500 N/m²
D) 2344 N/m²

Question 68

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 × 10¹¹ Pa.

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

Question 69

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 × 10¹¹ N/m².

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

Question 70

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 × 10¹¹ Pa. What is the change in length of the cable caused by the car?

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

Question 71

A vertical 30-cm steel rod, 1.0 cm in diameter, supports a 300-kg mass. What is the change in length of the rod caused by this mass? Young's modulus for steel is 2.0 × 10¹¹ N/m².

A) 5.6 × 10^-5 m
B) 6.5 × 10^-5 m
C) 5.6 × 10^-6 m
D) 6.5 × 10^-6 m
E) 6.5 × 10^-4 m

Question 72

A solid steel column is 4.0 m long and 0.20 m in diameter. Young's modulus for this steel is 2.0 × 10¹¹ N/m². By what distance does the column shrink when a 5000-kg truck is supported by it?

A) 8.0 × 10^-7 m
B) 3.2 × 10^-6 m
C) 7.8 × 10^-6 m
D) 3.1 × 10^-5 m

Question 73

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?