Question 1

Bar One has a Young's modulus that is bigger than that of Bar Two.This indicates Bar One
A)is longer than Bar Two.
B)has a greater cross-sectional area than Bar Two.
C)has a greater elastic limit than Bar Two.
D)is made of material that is different from Bar Two.

Accepted Answer

Young's modulus is a material property that measures the stiffness of a solid material. If Bar One has a Young's modulus that is bigger than that of Bar Two, it indicates that the material of Bar One is different from that of Bar Two, as Young's modulus is independent of the shape and size of the material.

Question 2

The bulk modulus of a material,as a meaningful physical property,is applicable to which of the following?
A)only solids
B)only liquids
C)only gases
D)solids,liquids and gases

Accepted Answer

The bulk modulus is a measure of a material's resistance to compressibility. This property is applicable to all three states of matter - solids, liquids, and gases. Therefore, option D is the correct choice.

Question 3

Which of the following characterizes the net force on a particle falling through a fluid at its terminal speed?
A)It is at a maximum.
B)It is upwards.
C)It is downwards.
D)It is zero.

Accepted Answer

When a particle is falling through a fluid at its terminal speed, the drag force acting on the particle is equal in magnitude and opposite in direction to the gravitational force acting on it. As a result, the net force on the particle becomes zero, and the particle continues to fall at a constant speed.

Question 4

A small sphere is allowed to fall through air,and when the sphere has a speed of 4.8 × 10^-4 m/s,the viscous force on the sphere is 3.0 × 10^-15 N.If the viscosity of air is 1.4 × 10^-5 N·s/m²,what is the radius of the drop? A)2.4E-8 m B)8.4E-6 m C)2.3E-7 m D)8.5E-7 m

Accepted Answer

The viscous force on a sphere falling through a fluid is given by the Stokes' law:$$F_v=6\pi\eta rv$$where:* $F_v$ is the viscous force* $\eta$ is the viscosity of the fluid* $r$ is the radius of the sphere* $v$ is the speed of the sphereWe can rearrange this equation to solve for the radius of the sphere:$$r=\frac{F_v}{6\pi\eta v}$$Plugging in the given values, we get:$$r=\frac{3.0	imes10^{-15}	ext{ N}}{6\pi(1.4	imes10^{-5}	ext{ N}\cdot	ext{s/m}^2)(4.8	imes10^{-4}	ext{ m/s})}$$$$r=2.4	imes10^{-8}	ext{ m}$$Therefore, the radius of the sphere is 2.4E-8 m.

Question 5

A uniform pressure of 5.7 × 10⁵ N/m² is applied to all six sides of a copper cube.What is the percentage change in volume of the cube? (for copper,B = 14 × 10¹⁰ N/m²) A)0.00070% B)0.00040% C)0.0000020% D)0.00041%

Accepted Answer

The percentage change in volume of the cube can be calculated using the formula for bulk modulus, $B = -\frac{\Delta P}{\Delta V/V}$, where $B$ is the bulk modulus, $\Delta P$ is the change in pressure, and $\Delta V/V$ is the fractional change in volume. Rearranging the formula gives $\Delta V/V = -\frac{\Delta P}{B}$. Given $\Delta P = 5.7 \times 10^5$ N/m$^2$ and $B = 14 \times 10^{10}$ N/m$^2$, the fractional change in volume is $-\frac{5.7 \times 10^5}{14 \times 10^{10}}$. Converting this fraction to a percentage gives approximately 0.00041%.

Question 6

The quantity "stress" expressed in terms of the fundamental quantities (mass,length,time)is equivalent to A)MLT−¹. B)ML−¹T−². C)M²L−¹T−³. D)a dimensionless quantity.

Accepted Answer

Stress is defined as force per unit area. The dimension of force is MLT^-2 and area is L^2, so stress has the dimension ML^-1T^-2.

Question 7

What is the minimum diameter of a steel wire if it is to support a mass of 80 kg.The elastic limit of steel is 5.0 × 10⁸ Pa. A)1.4 mm B)2.0 mm. C)1.0 mm D)2.0 mm

Accepted Answer

The minimum diameter can be calculated using the formula for stress: Stress = Force/Area. The force is the weight of the mass (80 kg * 9.8 m/s²), and the area is π(d/2)². Solving for d using the elastic limit as the maximum stress gives approximately 1.4 mm.

Question 8

A substance is allowed to diffuse along a 10-cm length of tubing filled with water.The cross section of the tube is 5.3 cm².If the diffusion coefficient is 5.0 × 10¯¹⁰ m²/s,and 6.5 × 10¯¹⁴ kg is transported along the tube in 16 s,what is the difference in the concentration levels of the substance at the two ends of the tube? A)3.9E-1 kg/m³ B)4.3E-2 kg/m³ C)1.5E-3 kg/m³ D)8.1E-4 kg/m³

Accepted Answer

First, we need to find the cross-sectional area of the tubing: 
Area = π(r^2) = π(5.3cm/2)^2 = 22.1 cm^2 = 0.00221 m^2 
Next, we can use the formula for the amount of substance transported by diffusion: 
Amount = (diffusion coefficient)(area)(concentration gradient)(time) 
We can rearrange this formula to solve for the concentration gradient: 
Concentration gradient = (Amount)/(diffusion coefficient)(area)(time) 
Plugging in the given values: 
Concentration gradient = (6.5 × 10¯^14 kg)/(5.0 × 10¯^11 m^2/s)(0.00221 m^2)(16 s) 
Concentration gradient = 0.0015 kg/m 
However, the question asks for the difference in concentration levels at the two ends of the tube, so we need to divide this by the length of the tube: 
Difference in concentration levels = (0.0015 kg/m)/(0.1 m) = 0.015 kg/m = 1.5E-3 kg/m

Therefore, the best choice is C.

Question 9

How large a force is necessary to stretch a 1.1-mm-diameter steel wire (Y = 2.0 × 10¹¹ N/m²)by 2.0%? A)3.8E+6 N B)3.8E+3 N C)3.8E+6 N D)7.6E+7 N E)3.8E+3 N

Accepted Answer

The force can be calculated using the formula F = Y * A * (ΔL/L), where Y is Young's modulus, A is the cross-sectional area, and ΔL/L is the strain. The cross-sectional area A = π * (d/2)^2, where d is the diameter. Substituting the given values, the force is approximately 3.8E+3 N.

Question 10

A machinist needs to punch a 5.0-cm-radius hole in a steel plate which is 0.45 cm thick.If the ultimate shear strength of steel is 2.50 × 10⁸ Pa,what is the force required to accomplish this task? A)8.8E+5 N B)3.5E+5 N C)5.6E+6 N D)1.1E+8 N

Accepted Answer

The answer of A machinist needs to punch a 5.0-cm-radius...

Question 11

In an elastic solid there is a direct proportionality between strain and
A)elastic modulus.
B)temperature.
C)cross-sectional area.
D)stress.

Accepted Answer

In an elastic solid, the strain (deformation) is directly proportional to the applied stress. This relationship is described by Hooke's Law, which states that the amount a material deforms is directly proportional to the load applied to it, as long as the material remains within its elastic limit.

Question 12

A copper wire of length 5.0 m,cross sectional area 6.9 × 10−⁶ m²,and Young's modulus 11 × 10¹⁰ N/m² has a 190-kg load hung on it.What is its increase in length? (g = 9.8 m/s²) A)5.0E-3 m B)1.8E-2 m C)7.3E-3 m D)1.2E-2 m E)2.5E-2 m

Accepted Answer

The increase in length of the copper wire can be calculated by the formula:

ΔL/L = F/(A*Y)

where ΔL is the increase in length, L is the original length, F is the force applied (weight of the load), A is the cross-sectional area, and Y is the Young's modulus.

Substituting the given values, we get:

ΔL/L = (190*9.8)/(6.9*10^-16*11*10^10)

ΔL/L = 1.2*10^-2

Therefore, the increase in length is 1.2 x 10^-2 m.

Hence, the correct answer is option D.

Question 13

The quantity "strain" expressed in terms of the fundamental quantities (mass,length,time)is equivalent to A)MLT−¹. B)ML−¹T−². C)M²L−¹T−³. D)a dimensionless quantity.

Accepted Answer

Strain is defined as the ratio of change in dimension to the original dimension, which does not have any units or dimensions, making it a dimensionless quantity.

Question 14

Consider two steel rods,A and B.B has three times the area and twice the length of A,so Young's modulus for B will be what factor times Young's modulus for A?
A)3.0
B)0.5
C)1.5
D)1.0

Accepted Answer

Young's modulus is an intrinsic property of a material and does not depend on the geometry of the sample. Therefore, despite the differences in area and length between rods A and B, their Young's modulus will be the same.

Question 15

A tire stops a car by use of friction.What modulus should we use to calculate the stress and strain on the tire?
A)Young's modulus
B)compression modulus
C)shear modulus
D)bulk modulus

Accepted Answer

Young's modulus is used to calculate stress and strain in the axial direction of a material, compression modulus is used for the material's response to compression, and bulk modulus is used to measure the material's response to changes in volume under pressure. None of these is directly applicable to the stress and strain experienced by a tire during braking, which involves forces acting in multiple directions.

The shear modulus, however, is a measure of a material's resistance to deformation by shear stress, which is precisely the kind of stress the tire experiences as it grips the road and slows down the car. Therefore, the shear modulus is the best choice for calculating stress and strain on the tire during this process.

Quiz 9: Fluids and Solids

Bar One has a Young's modulus that is bigger than that of Bar Two.This indicates Bar One

The bulk modulus of a material,as a meaningful physical property,is applicable to which of the following?

Which of the following characterizes the net force on a particle falling through a fluid at its terminal speed?

A small sphere is allowed to fall through air,and when the sphere has a speed of 4.8 × 10^-4 m/s,the viscous force on the sphere is 3.0 × 10^-15 N.If the viscosity of air is 1.4 × 10^-5 N·s/m²,what is the radius of the drop?

A uniform pressure of 5.7 × 10⁵ N/m² is applied to all six sides of a copper cube.What is the percentage change in volume of the cube? (for copper,B = 14 × 10¹⁰ N/m²)

The quantity "stress" expressed in terms of the fundamental quantities (mass,length,time) is equivalent to

What is the minimum diameter of a steel wire if it is to support a mass of 80 kg.The elastic limit of steel is 5.0 × 10⁸ Pa.

How large a force is necessary to stretch a 1.1-mm-diameter steel wire (Y = 2.0 × 10¹¹ N/m²) by 2.0%?

A machinist needs to punch a 5.0-cm-radius hole in a steel plate which is 0.45 cm thick.If the ultimate shear strength of steel is 2.50 × 10⁸ Pa,what is the force required to accomplish this task?

In an elastic solid there is a direct proportionality between strain and

A copper wire of length 5.0 m,cross sectional area 6.9 × 10−⁶ m²,and Young's modulus 11 × 10¹⁰ N/m² has a 190-kg load hung on it.What is its increase in length? (g = 9.8 m/s²)

The quantity "strain" expressed in terms of the fundamental quantities (mass,length,time) is equivalent to

Consider two steel rods,A and B.B has three times the area and twice the length of A,so Young's modulus for B will be what factor times Young's modulus for A?

A tire stops a car by use of friction.What modulus should we use to calculate the stress and strain on the tire?