# Quiz 12: Equilibrium and Elasticity

Physics & Astronomy

Q 1Q 1

A net torque applied to a rigid object always tends to produce:
A)linear acceleration
B)rotational equilibrium
C)angular acceleration
D)rotational inertia
E)none of these

Free

Multiple Choice

C

Q 2Q 2

Which of the following is NOT in equilibrium?
A)a rock resting on the ground
B)a rock sliding at constant velocity across a frictionless surface
C)a rock rotating in place on a frictionless surface
D)a rock rotating at a constant rate as it slides at constant velocity across a frictionless surface
E)a rock falling off a cliff

Free

Multiple Choice

E

Q 3Q 3

Which of the following is in static equilibrium?
A)a rock resting on the ground
B)a rock sliding at constant velocity across a frictionless surface
C)a rock rotating in place on a frictionless surface
D)a rock rotating at a constant rate as it slides at constant velocity across a frictionless surface
E)a rock falling off a cliff

Free

Multiple Choice

A

Q 4Q 4

The conditions that the sum of forces and the sum of the torques both vanish:
A)hold for every solid body in equilibrium
B)hold only for elastic solid bodies in equilibrium
C)hold for every solid body
D)are always sufficient to calculate the forces on a solid object in equilibrium
E)are sufficient to calculate the forces on a solid object in equilibrium only if the object is elastic

Free

Multiple Choice

Q 5Q 5

For an object in equilibrium the sum of the torques acting on it vanishes only if each torque is calculated about:
A)the center of mass
B)the center of gravity
C)the geometrical center
D)the point of application of the force
E)the same point

Free

Multiple Choice

Q 6Q 6

For a body to be equilibrium under the combined action of several forces:
A)all the forces must be applied at the same point
B)all of the forces are composed of pairs of equal and opposite forces
C)the sum of the components of all the forces in any direction must equal zero
D)any two of these forces must be balanced by a third force
E)the lines of action of all the forces must pass through the center of gravity of the body

Free

Multiple Choice

Q 7Q 7

For a body to be equilibrium under the combined action of several forces:
A)all the forces must be applied at the same point
B)all of the forces are composed of pairs of equal and opposite forces
C)any two of these forces must be balanced by a third force
D)the sum of the torques about any point must equal zero
E)the lines of action of all the forces must pass through the center of gravity of the body

Free

Multiple Choice

Q 8Q 8

To determine if a rigid body is in equilibrium the vector sum of the gravitational forces acting on the particles of the body can be replaced by a single force acting at:
A)the center of mass
B)the geometrical center
C)the center of gravity
D)a point on the boundary
E)none of the above

Free

Multiple Choice

Q 9Q 9

The center of gravity coincides with the center of mass:
A)always
B)never
C)if the center of mass is at the geometrical center of the body
D)if the acceleration due to gravity is uniform over the body
E)if the body has a uniform distribution of mass

Free

Multiple Choice

Q 10Q 10

The location of which of the following points within an object might depend on the orientation of the object?
A)Its center of mass
B)Its center of gravity
C)Its geometrical center
D)Its center of momentum
E)None of the above

Free

Multiple Choice

Q 11Q 11

A cylinder placed so it can roll on a horizontal table top, with its center of gravity above its geometrical center, is:
A)in stable equilibrium
B)in unstable equilibrium
C)in neutral equilibrium
D)not in equilibrium
E)none of the above

Free

Multiple Choice

Q 12Q 12

A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its geometrical center, is:
A)in stable equilibrium
B)in unstable equilibrium
C)in neutral equilibrium
D)not in equilibrium
E)none of the above

Free

Multiple Choice

Q 13Q 13

A cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in ________ equilibrium with respect to rotation about the edge and in ________ equilibrium with respect to rotation about a horizontal axis that is perpendicular to the edge.
A)stable, stable
B)stable, unstable
C)unstable, stable
D)unstable, unstable
E)unstable, neutral

Free

Multiple Choice

Q 14Q 14

A 5.1-kg mass is located at the origin, and a 2.3-kg mass is located at x = 4.9 cm.Assuming g is constant, what is the location of the center of mass x

_{com}, and the location of the center of gravity x_{cog}, of the two masses? A)x_{com}= 1.5 cm, x_{cog}= 3.4 cm B)x_{com}= 3.4 cm, x_{cog}= 1.5 cm C)x_{com}= 1.5 cm, x_{cog}= 1.5 cm D)x_{com}= 3.4 cm, x_{cog}= 3.4 cm E)x_{com}= 1.5 cm, x_{cog}= 0 cmFree

Multiple Choice

Q 15Q 15

A massless meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark.A force is applied perpendicularly to the end of the stick at 0 cm, as shown.A second force (not shown)is applied perpendicularly to the stick at the 100-cm end of the stick.The forces are in the plane of the table top.If the stick does not move, the force exerted by the pivot on the stick:
A)must be zero
B)must be in the same direction as and have magnitude
C)must be directed opposite to and have magnitude
D)must be in the same direction as and have magnitude
E)must be directed opposite to and have magnitude

Free

Multiple Choice

Q 16Q 16

A massless meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark.A force is applied perpendicularly to the end of the stick at 0 cm, as shown.A second force (not shown)is applied perpendicularly at the 60-cm mark.The forces are in the plane of the table top.If the stick does not move, the force exerted by the pivot on the stick:
A)must be zero
B)must be in the same direction as and have magnitude
C)must be directed opposite to and have magnitude
D)must be in the same direction as and have magnitude
E)must be directed opposite to and have magnitude

Free

Multiple Choice

Q 17Q 17

Three identical uniform rods are each acted on by two or more forces, all perpendicular to the rods.Which of the rods could be in static equilibrium if an additional force is applied at the center of mass of the rod?
A)Only 1
B)Only 2
C)Only 3
D)Only 1 and 2
E)All three

Free

Multiple Choice

Q 18Q 18

A 160-N child sits on a light swing and is pulled back and held with a horizontal force of 100 N.The magnitude of the tension force of each of the two supporting ropes is:
A)60 N
B)94 N
C)120 N
D)190 N
E)260 N

Free

Multiple Choice

Q 19Q 19

A picture P of weight W is hung by two strings as shown.The magnitude of the tension force of each string is T.The total upward pull of the strings on the picture is:
A)2W cos
B)T sin
C)T cos
D)2T sin
E)2T cos

Free

Multiple Choice

Q 20Q 20

A picture can be hung on a wall in three different ways, as shown.The tension in the string is:
A)least in I
B)greatest in I
C)greatest in II
D)least in III
E)greatest in III

Free

Multiple Choice

Q 21Q 21

A uniform plank XY is supported by two equal 120-N forces at X and Y, as shown.The support at X is then moved to Z (half-way to the plank center).The supporting forces at Y and Z are then:
A)F

_{Y}_{ }= 240 N, F_{Z}= 120 N B)F_{Y}_{ }= 200 N, F_{Z}= 40 N C)F_{Y}_{ }= 40 N, F_{Z}= 200 N D)F_{Y}_{ }= 80 N, F_{Z}= 160 N E)F_{Y}_{ }= 160 N, F_{Z}= 80 NFree

Multiple Choice

Q 22Q 22

A uniform rod AB is 1.2 m long and weighs 16 N.It is suspended by strings AC and BD as shown.A block P weighing 96 N is attached at E, 0.30 m from A.The magnitude of the tension force in the string BD is:
A)8.0 N
B)24 N
C)32 N
D)48 N
E)80 N

Free

Multiple Choice

Q 23Q 23

A 5.0 m weightless strut, hinged to a wall, is used to support an 800-N block as shown.The horizontal and vertical components of the force of the hinge on the strut are:
A)F

_{H}_{ }= 800 N, F_{Y}= 800 N B)F_{H}_{ }= 600 N, F_{Y}= 800 N C)F_{H}_{ }= 800 N, F_{Y}= 600 N D)F_{H}_{ }= 1200 N, F_{Y}= 800 N E)F_{H}_{ }= 0 N, F_{Y}= 800 NFree

Multiple Choice

Q 24Q 24

A uniform plank is 6.0 m long and weighs 80 N.It is balanced on a sawhorse at its center.An additional 160 N weight is now placed on the left end of the plank.To keep the plank balanced, it must be moved what distance to the right?
A)6.0 m
B)2.0 m
C)1.5 m
D)1.0 m
E)0.50 m

Free

Multiple Choice

Q 25Q 25

A uniform 240-g meter stick can be balanced by a 240-g weight placed at the 100-cm mark if the fulcrum is placed at the point marked:
A)75 cm
B)60 cm
C)50 cm
D)40 cm
E)80 cm

Free

Multiple Choice

Q 26Q 26

A ladder leans against a wall.If the ladder is not to slip, which one of the following must be true?
A)The coefficient of friction between the ladder and the wall must not be zero
B)The coefficient of friction between the ladder and the floor must not be zero
C)Both A and B
D)Either A or B
E)Neither A nor B

Free

Multiple Choice

Q 27Q 27

An 80-N uniform plank leans against a frictionless wall as shown.The torque (about point P)applied to the plank by the wall is:
A)40 Nm
B)60 Nm
C)120 Nm
D)160 Nm
E)240 Nm

Free

Multiple Choice

Q 28Q 28

An 800-N man stands halfway up a 5.0 m ladder of negligible weight.The base of the ladder is 3.0 m from the wall as shown.Assuming that the wall-ladder contact is frictionless, the wall pushes against the ladder with a force of:
A)150 N
B)300 N
C)400 N
D)600 N
E)800 N

Free

Multiple Choice

Q 29Q 29

A uniform ladder is 10 m long and weighs 400 N.It rests with its upper end against a frictionless vertical wall.Its lower end rests on the ground and is prevented from slipping by a peg driven into the ground.The ladder makes a 30 angle with the horizontal.The force exerted on the wall by the ladder is:
A)47 N
B)74 N
C)120 N
D)350 N
E)460 N

Free

Multiple Choice

Q 30Q 30

A window washer attempts to lean a ladder against a frictionless wall.He finds that the ladder slips on the ground when it is placed at an angle of less than 75 to the ground but remains in place when the angle is greater than 75.The coefficient of static friction between the ladder and the ground:
A)is 0.13
B)is 0.27
C)is 1.3
D)depends on the mass of the ladder
E)depends on the length of the ladder

Free

Multiple Choice

Q 31Q 31

The 600-N ball shown is suspended on a string AB and rests against the frictionless vertical wall.The string makes an angle of 30 with the wall.The line AB goes through the center of the ball, and the contact point with the wall is at the same vertical height as the center of the ball.The magnitude of the tension in the string is:
A)300 N
B)520 N
C)690 N
D)1200 N
E)none of these

Free

Multiple Choice

Q 32Q 32

The 600-N ball shown is suspended on a string AB and rests against the frictionless vertical wall.The string makes an angle of 30 with the wall.The line AB goes through the center of the ball, and the contact point with the wall is at the same vertical height as the center of the ball.The ball presses against the wall with a force of magnitude:
A)300 N
B)350 N
C)520 N
D)600 N
E)690 N

Free

Multiple Choice

Q 33Q 33

A 240-N weight is hung from two ropes as shown.The tension in the horizontal rope has magnitude:
A)0 N
B)660 N
C)480 N
D)420 N
E)140 N

Free

Multiple Choice

Q 34Q 34

A 960-N block is suspended as shown.The beam AB is weightless and is hinged to the wall at A.The tension force of the cable BC has magnitude:
A)720 N
B)1200 N
C)1280 N
D)1600 N
E)none of these

Free

Multiple Choice

Q 35Q 35

A horizontal beam of weight W is supported by a hinge and cable as shown.The force exerted on the beam by the hinge has a vertical component that must be:
A)nonzero and up
B)nonzero and down
C)nonzero but not enough information given to know whether up or down
D)zero
E)equal to W

Free

Multiple Choice

Q 36Q 36

A 400-N uniform vertical boom is attached to the ceiling by a hinge, as shown.An 800-N weight W and a horizontal guy wire are attached to the lower end of the boom as indicated.The pulley is massless and frictionless.The tension force T of the horizontal guy wire has magnitude:
A)350 N
B)400 N
C)690 N
D)800 N
E)1200 N

Free

Multiple Choice

Q 37Q 37

A picture is to be hung from the ceiling by means of two wires.Order the following arrangements of the wires according to the tension in wire B, from least to greatest.
A)I, II, III
B)III, I, II
C)I and II tie, then III
D)II, I, III
E)all tie

Free

Multiple Choice

Q 38Q 38

The pull P is just sufficient to keep the 14-N block and the weightless pulleys in equilibrium as shown.The tension T in the upper cable is:
A)14 N
B)28 N
C)16 N
D)9.3 N
E)19 N

Free

Multiple Choice

Q 39Q 39

The ideal mechanical advantage (i.e.the ratio of the weight W to the pull P for equilibrium)of the combination of pulleys shown is:
A)1
B)2
C)3
D)4
E)5

Free

Multiple Choice

Q 40Q 40

The diagram shows a stationary 5-kg uniform rod (AC), 1 m long, held against a wall by a rope (AE)and friction between the rod and the wall.To use a single equation to find the force exerted on the rod by the rope at which point should you place the reference point for computing torque?
A)A
B)B
C)C
D)D
E)E

Free

Multiple Choice

Q 41Q 41

The uniform rod shown below is held in place by the rope and wall.Suppose you know the weight of the rod and all dimensions.Then you can solve a single equation for the force exerted by the rope, provided you write expressions for the torques about the point:
A)1
B)2
C)3
D)4
E)1, 2, or 3

Free

Multiple Choice

Q 42Q 42

Stress can be measured in:
A)N/m

^{2}B)Nm^{2}C)N/m D)Nm E)none of these (it is dimensionless)Free

Multiple Choice

Q 43Q 43

Strain can be measured in:
A)N/m

^{2}B)Nm^{2}C)N/m D)Nm E)none of these (it is dimensionless)Free

Multiple Choice

Free

Multiple Choice

Q 45Q 45

To shear a cube-shaped object, forces of equal magnitude and opposite directions might be applied:
A)to opposite faces, perpendicular to the faces
B)to opposite faces, parallel to the faces
C)to adjacent faces, perpendicular to the faces
D)to adjacent faces, neither parallel nor perpendicular to the faces
E)to a single face, in any direction

Free

Multiple Choice

Q 46Q 46

If you sit on an ordinary 4-legged chair, which of the following is true?
A)As long as you know your weight and the point at which it acts on the chair, you can calculate the forces exerted by all four chair legs on the floor.
B)As long as you know your weight and the point at which it acts on the chair, you can calculate the forces exerted by all four chair legs on the floor, but only if your own feet are not also on the floor.
C)This is an indeterminate situation, and the forces of the chair legs on the floor cannot be uniquely calculated.
D)This is an indeterminate situation, and the forces of the chair legs on the floor cannot be uniquely calculated without knowing how your weight is distributed on the chair.
E)This is an indeterminate situation, and the forces of the chair legs on the floor cannot be uniquely calculated without knowing how the chair deforms due to your weight.

Free

Multiple Choice

Q 47Q 47

Young's modulus is a proportionality constant that relates the force per unit area applied perpendicularly at the surface of an object to:
A)the shear
B)the fractional change in volume
C)the fractional change in length
D)the pressure
E)the spring constant

Free

Multiple Choice

Q 48Q 48

A certain wire stretches 0.90 cm when outward forces with magnitude F are applied to each end.The same forces are applied to a wire of the same material but with three times the diameter and three times the length.The second wire stretches:
A)0.10 cm
B)0.30 cm
C)0.90 cm
D)2.7 cm
E)8.1 cm

Free

Multiple Choice

Q 49Q 49

A force of 5000 N is applied outwardly to each end of a 5.0-m long rod with a radius of 34.0 mm and a Young's modulus of 125 10

^{8}N/m^{2}.The elongation of the rod is: A)0.022 mm B)0.0040 mm C)0.11 mm D)0.55 mm E)1.42 mmFree

Multiple Choice

Q 50Q 50

A 4.0 m steel beam with a cross sectional area of 1.0 10

^{-2}m^{2}and a Young's modulus of 2.0 10^{11}N/m^{2}is wedged horizontally between two vertical walls.In order to wedge the beam, it is compressed by 0.020 mm.If the coefficient of static friction between the beam and the walls is 0.35, the maximum mass (including its own)it can bear without slipping is: A)0 kg B)36 kg C)70 kg D)360 kg E)700 kgFree

Multiple Choice

Q 51Q 51

Two supports, made of the same material and initially of equal length, are 2.0 m apart.A stiff board with a length of 4.0 m and a mass of 10 kg is placed on the supports, with one support at the left end and the other at the midpoint.A block is placed on the board a distance of 0.50 m from left end.As a result the board is horizontal (that is, the downward force on each support is the same).The mass of the block is:
A)0 kg
B)2.3 kg
C)6.6 kg
D)10 kg
E)20 kg

Free

Multiple Choice

Q 52Q 52

Young's modulus can be used to calculate the strain for a stress that is:
A)just below the ultimate strength
B)just above the ultimate strength
C)well below the yield strength
D)well above the yield strength
E)none of the above

Free

Multiple Choice

Q 53Q 53

The ultimate strength of a sample is the stress at which the sample:
A)returns to its original shape when the stress is removed
B)remains underwater
C)breaks
D)bends 180
E)does none of these

Free

Multiple Choice

Q 54Q 54

A shearing force of 50 N is applied to an aluminum rod with a length of 10 m, a cross-sectional area of 1.0 10

^{}^{5}m, and shear modulus of 2.5 10^{10 }N/m^{2}.^{ }As a result the rod is sheared through a distance of: A)zero B)2.0 mm C)2.0 cm D)20 cm E)2.0 mFree

Multiple Choice

Q 55Q 55

The bulk modulus is a proportionality constant that relates the pressure acting on an object to:
A)the shear
B)the fractional change in volume
C)the fractional change in length
D)Young's modulus
E)the spring constant

Free

Multiple Choice

Q 56Q 56

A cube with edges exactly 2 cm long is made of material with a bulk modulus of 3.5 10

^{9}N/m^{2}.When it is subjected to a pressure of 3.0 10^{5}Pa its volume is: A)7.31 cm^{3}B)7.99931 cm^{3}C)8.00069 cm^{3}D)8.69 cm^{3}E)none of theseFree

Multiple Choice

Q 57Q 57

A cube with 2.0-cm sides is made of material with a bulk modulus of 4.7 10

^{5}N/m^{2}.When it is subjected to a pressure of 2.0 10^{5}Pa the length in cm of its any of its any of its sides is: A)0.85 cm B)1.15 cm C)1.66 cm D)2.0 cm E)none of theseFree

Multiple Choice