Question 1

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 2

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 3

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 is defined as the ratio of the change in pressure to the fractional change in volume of a material.

Question 4

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 a measure of the stiffness of a material and is only valid when the material is behaving elastically. Once the material reaches its yield point, it begins to deform plastically and Young's modulus is no longer applicable. Therefore, it can only be used to calculate the strain for stresses that are well below the yield strength.

Question 5

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/m^2.As a result the rod is sheared through a distance of: A) zero B) 1.9 mm C) 1.9 cm D) 19 cm E) 1.9 m

Accepted Answer

The shear strain is calculated using the formula: shear strain = shear force / (shear modulus × area). Substituting the given values, the shear strain is 50 N / (2.5 × 10^10 N/m² × 10^-5 m²) = 2 × 10^-4. The sheared distance is then shear strain × length = 2 × 10^-4 × 10 m = 0.002 m = 2 mm, which is approximately 1.9 mm.

Question 6

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 or perpendicular to the faces
E) to a single face, in any direction

Accepted Answer

Shearing involves applying forces parallel to the faces of an object, causing layers to slide over each other.

Question 7

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)...

Question 8

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 0.70, the maximum mass (including its own) it can bear without slipping is: A) 0 B) 3.6 kg C) 36 kg D) 71 kg E) 710 kg

Accepted Answer

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

Question 9

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 is defined as the ratio of the stress (force per unit area) applied perpendicular to the surface of an object to the strain (fractional change in length) of the object. Therefore, the correct answer is C.

Question 10

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 11

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 of a sample is the stress at which it breaks.

Question 12

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. The mass of the block is:
A) zero
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 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 cm and a Young's modulus of 125 * 10⁸ N/m². The elongation of the rod is: A) 0.0020 mm B) 0.0040 mm C) 0.14 mm D) 0.55 mm E) 1.42 mm

Accepted Answer

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

Quiz 12: Equilibrium and Elasticity

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

Young's modulus can be used to calculate the strain for a stress that 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/m^2.As a result the rod is sheared through a distance of:

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 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:

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

A force of 5000 N is applied outwardly to each end of a 5.0-m long rod with a radius of 34.0 cm and a Young's modulus of 125 * 10⁸ N/m². The elongation of the rod is: