Question 1

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

Accepted Answer

Young's modulus relates the force per unit area applied perpendicularly at the surface of an object to the fractional change in length of that object.

Question 2

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

Accepted Answer

The stretch of a wire under a force is given by the formula $ \Delta L = \frac{1}{Y} \cdot \frac{F}{A} \cdot L $, where $ \Delta L $ is the change in length, $ Y $ is Young's modulus (a property of the material), $ F $ is the force applied, $ A $ is the cross-sectional area, and $ L $ is the original length of the wire. When the diameter is tripled, the area ($ A = \pi r^2 $) becomes 9 times larger because the radius is doubled (area is proportional to the square of the radius). When the length is tripled, the effect of the increased length is to triple the stretch. However, because the area is 9 times larger, the stretch due to the force is reduced by a factor of 9. Therefore, the overall effect is to reduce the stretch by a factor of 3 (triple the length but divide the stretch by 9 due to the increased area), making the stretch $ \frac{0.90 \, \text{cm}}{3} = 0.30 \, \text{cm} $.

Question 3

Strain can be measured in: A)N/m² B)N.m² C)N/m D)N.m E)none of these (it is dimensionless)

Accepted Answer

Strain is a dimensionless quantity as it is defined as the ratio of change in length to the original length, and thus does not have units.

Question 4

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.

Accepted Answer

The answer of If you sit on an ordinary 4-legged...

Question 5

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

Accepted Answer

The bulk modulus relates the pressure acting on an object to the fractional change in volume. The other options are related to different types of moduli.

Question 6

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

Accepted Answer

The answer of Two supports, made of the same material...

Question 7

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

Accepted Answer

The ultimate strength is the highest stress that a material can withstand before it breaks or fails. Therefore, the correct answer is C, which states that the sample breaks.

Question 8

Stress can be measured in: A)N/m² B)N.m² C)N/m D)N.m E)none of these (it is dimensionless)

Accepted Answer

The answer of Stress can be measured in: A)N/m² B)N.m² C)N/m D)N.m E)none of these...

Question 9

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

Accepted Answer

The answer of A 4.0 m steel beam with a...

Question 10

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

Accepted Answer

To shear a cube-shaped object, forces should be applied to opposite faces and in a direction parallel to those faces. This causes the layers of the object to slide over each other, resulting in a shear deformation.

Question 11

Young's modulus can be correctly given in: A)N.m B)N/m² C)N.m/s D)N/m E)joules

Accepted Answer

The answer of Young's modulus can be correctly given in: A)N.m B)N/m² C)N.m/s D)N/m E)joules...

Question 12

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

Accepted Answer

Young's modulus is only applicable for stresses below the yield strength. Once the yield strength is exceeded, the material will undergo permanent deformation and its behavior will be no longer elastic. Similarly, stresses close to or above the ultimate strength imply that the material is about to break or fracture, so the relationship between stress and strain is no longer valid.

Question 13

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

Accepted Answer

The answer of A force of 5000 N is applied...

Question 14

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

Accepted Answer

We can use the equation for bulk modulus to solve this problem:

Bulk modulus = (pressure change)/(fractional volume change)

Since the cube is subjected to a pressure of 2.0x10^10 Pa, the pressure change is also 2.0x10^10 Pa.

The fractional volume change can be determined from the fact that the cube is isotropic, meaning that it has the same properties in all directions. When a cube is squeezed, all of its sides decrease by the same amount. Therefore, the fractional volume change is equal to the fractional length change.

Using the equation for fractional length change due to pressure,

ΔL/L = -V/E

where ΔL is the change in length, L is the original length, V is the change in volume, and E is the Young's modulus (which is equal to three times the bulk modulus for isotropic materials).

Since the cube is isotropic and its sides are all equal, we can choose any side to represent L.

If each side has a length of 2.0 cm, the original volume of the cube is (2.0 cm)^3 = 8.0 cm^3.

If the pressure causes a fractional volume change of ΔV/V, then the new volume is (1 + ΔV/V) times the original volume. The new side length is then the cube root of the new volume divided by the original surface area (which is 6 times the original side length squared).

Thus,

(1 + ΔV/V) * 8.0 cm^3 = (2.0 cm)^3

ΔV/V = -0.375

Using the equation for fractional length change, we get

ΔL/L = -V/E = -(-0.375)/(3*4.7x10^10 N/m^2) = 2.128x10^-12

The change in length is therefore

ΔL = (2.0 cm)(2.128x10^-12) = 4.256x10^-12 cm

The final length of any side is the original length plus the change in length, so

Final length = 2.0 cm + 4.256x10^-12 cm = 2.00000000213 cm

This is closest to choice (C), 1.66 cm.

Question 15

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 *10¹⁰N/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

Accepted Answer

The shear strain (𝛾) can be calculated using the formula:

𝛾 = (F/A)/G

where F is the applied shearing force, A is the cross-sectional area, and G is the shear modulus of the material.

Plugging in the given values:

𝛾 = (50 N / 1.0 × 10^-4 m^2) / 2.5 × 10^10 N/m^2

𝛾 = 2.0 × 10^-3

This is the shear strain.

The distance through which the rod is sheared (𝛿x) can be calculated using the formula:

𝛿x = 𝛾 × L

where L is the length of the rod.

Plugging in the given values:

𝛿x = 2.0 × 10^-3 × 10 m

𝛿x = 2.0 × 10^-2 m

𝛿x = 2.0 mm

Therefore, the correct choice is B.

Question 16

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

Accepted Answer

The answer of A cube with edges exactly 2 cm...

Question 17

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

Accepted Answer

The answer of The uniform rod shown below is held...

Quiz 12: Equilibrium and Elasticity

Young's modulus is a proportionality constant that relates the force per unit area applied perpendicularly at the surface of an object to:

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:

Strain can be measured in:

If you sit on an ordinary 4-legged chair, which of the following is true?

The bulk modulus is a proportionality constant that relates the pressure acting on an object to:

The ultimate strength of a sample is the stress at which the sample:

Stress can be measured in:

To shear a cube-shaped object, forces of equal magnitude and opposite directions might be applied:

Young's modulus can be correctly given in:

Young's modulus can be used to calculate the strain for a stress that is:

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 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 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 10¹⁰N/m².As a result the rod is sheared through a distance of:

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:

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: