Deck 12: Equilibrium and Elasticity

Question 1

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

Answer 1

the sum of the torques about any point must equal zero

Question 2

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

Answer 2

94 N

Question 3

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

Answer 3

greatest in III

Question 4

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

Question 5

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 $\theta$
B) T sin $\theta$
C) T cos $\theta$
D) 2T sin $\theta$
E) 2T cos $\theta$

Question 6

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 not be directed opposite to and have magnitude
D) must not be in the same direction as and have magnitude
E) must be directed opposite to and have magnitude

Question 7

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 cm

Question 8

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

Question 9

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

Question 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

Question 11

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

Question 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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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 not be in the same direction as and have magnitude
E) must not be directed opposite to and have magnitude

Question 18

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

Question 19

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

Question 20

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

Question 21

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 $\degree$ to the ground but remains in place when the angle is greater than 75 $\degree$ . 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

Question 22

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

Question 23

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

Question 24

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 $\degree$ 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

Question 25

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

Question 26

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 N

Question 27

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

Question 28

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 $\degree$ 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

Question 29

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

Question 30

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 N

Question 31

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

Question 32

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

Question 33

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

Question 34

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

Question 35

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

Question 36

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

Question 37

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

Question 38

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 $\degree$ 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

Question 39

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 N.m
B) 60 N.m
C) 120 N.m
D) 160 N.m
E) 240 N.m

Question 40

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

Question 41

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

Question 42

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

Question 43

Young's modulus can be correctly given in:

A) N.m
B) N.m²
C) N.m/s
D) N/m
E) joules

Question 44

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 *10¹⁰ N/m². 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 m

Question 45

A 4.0 m steel beam with a cross sectional area of 1.0 * 10^-2 m² and a Young's modulus of 2.0 * 10¹¹ N/m² 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 kg

Question 46

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* 10⁸ N/m². 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 mm

Question 47

A cube with 2.0-cm sides is made of material with a bulk modulus of 4.7* 10⁵ N/m². When it is subjected to a pressure of 2.0 * 10⁵ 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 these

Question 48

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.

Question 49

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

Question 50

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

Question 51

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

Question 52

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

Question 53

Strain can be measured in:

A) N/m²
B) N.m²
C) N/m
D) N.m
E) none of these (it is dimensionless)

Question 54

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

Question 55

Stress can be measured in:

A) N/m²
B) N.m²
C) N/m
D) N.m
E) none of these (it is dimensionless)

Question 56

A cube with edges exactly 2 cm long is made of material with a bulk modulus of 3.5 * 10⁹ N/m². When it is subjected to a pressure of 3.0*10⁵ Pa its volume is:

A) 7.31 cm³
B) 7.99931 cm³
C) 8.00069 cm³
D) 8.69 cm³
E) none of these

Question 57

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 $\degree$
E) does none of these