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 is a measure of the stiffness of a solid material. It relates the amount of stress (force per unit area) applied perpendicular to the surface of an object to the resulting strain (fractional change in length) experienced by the material.

Question 2

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 how it responds under tension or compression. It is only valid for stress levels that are well below the yield strength of the material. Once the stress level exceeds the yield strength, the material will start to deform permanently and Young's modulus will no longer be a useful measure. Therefore, option C - well below the yield strength - is the only correct choice.

Question 3

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 4

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 5

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 6

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 7

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 formula for compressibility, which relates pressure to change in volume:

B = -(∆V/V) / (∆P/P)

Where B is the bulk modulus, ∆V/V is the fractional change in volume, and ∆P/P is the fractional change in pressure.

Solving for ∆V/V and substituting known values:

∆V/V = -B * (∆P/P)

∆V/V = -(4.7 x 10^9 N/m^2) * (2 x 10^9 Pa)^-1

∆V/V = -0.002

This means that the cube’s volume will decrease by 0.2% when subjected to a pressure of 2.0 x 10^9 Pa.

Since it is a cube with all sides equal, we know that the fractional change in length (∆L/L) will be the same as the fractional change in volume:

∆L/L = ∆V/V = -0.002

∆L = (-0.002) * 2.0 cm

∆L = -0.004 cm

Therefore, the length of any side of the cube will decrease by 0.004 cm from its original length of 2.0 cm:

Final Length = 2.0 cm - 0.004 cm = 1.996 cm

Since this is closest to 1.66 cm, the answer is (C) 1.66 cm.

Question 8

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 9

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 tension is given by:

ΔL = FL/(A*E)

where ΔL is the stretch, F is the force applied, A is the cross-sectional area of the wire, E is the Young's modulus of the material, and L is the original length of the wire.

Since we are told that we are dealing with wires of the same material, the Young's modulus is the same for both wires. We are also told that the forces applied to both wires have the same magnitude (F). Therefore, the stretch of the wire is inversely proportional to its cross-sectional area and directly proportional to its length.

Let the original length and diameter of the first wire be L and D, respectively. Then, the original length and diameter of the second wire are 3L and 3D, respectively.

The cross-sectional area of the first wire is πD^2/4, and the cross-sectional area of the second wire is π(3D)^2/4 = 9πD^2/4. Therefore, the cross-sectional area of the second wire is 9 times larger than that of the first wire.

The length of the second wire is 3 times larger than that of the first wire. Therefore, the stretch of the second wire is:

ΔL = FL/(9πD^2/4 * E * 3L) = ΔL/27

So the stretch of the second wire is 1/27th of the stretch of the first wire:

ΔL2 = ΔL1/27 = 0.9/27 = 0.03 cm = 0.30 mm

Therefore, the second wire stretches 0.30 cm.

Question 10

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 11

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 12

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.

Question 13

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 14

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...

Question 15

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)...

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 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 maximum stress that a material can withstand before it breaks. Therefore, the correct choice is C, which states that the sample breaks at ultimate strength.

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:

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

Young's modulus can be correctly given in:

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 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:

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

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:

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

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

Strain can be measured in:

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:

Stress can be measured in:

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