# cos(θ)sin(θ) Alternative Exercise Correct Correct θ = 0 skiladæmi 10 Part A Part B Part C Due: 11:59pm on Wednesday, November 11, 2015

Save this PDF as:

Size: px
Start display at page:

Download "cos(θ)sin(θ) Alternative Exercise Correct Correct θ = 0 skiladæmi 10 Part A Part B Part C Due: 11:59pm on Wednesday, November 11, 2015"

## Transcription

1 skiladæmi 10 Due: 11:59pm on Wednesday, November 11, 015 You will receive no credit for items you complete after the assignment is due Grading Policy Alternative Exercise 1115 A bar with cross sectional area A is subjected to equal and opposite tensile forces F at its ends Consider a plane through the bar making an angle θ with a plane at right angles to the bar (the figure ) Part A What is the tensile (normal) stress at this plane in terms of F, A, and θ? F cos (θ) A Part B What is the shear (tangential) stress at the plane in terms of F, A, and θ? F cos(θ)sin(θ) A Part C For what value of θ is the tensile stress a maximum? θ = 0

2 Part D For what value of θ is the shear stress a maximum? θ = 45 Alternative Exercise A moonshiner produces pure ethanol (ethyl alcohol) late at night and stores it in a stainless steel tank in the form of a cylinder 0310 m in diameter with a tight fitting piston at the top The total volume of the tank is 60 L In an attempt to squeeze a little more into the tank, the moonshiner piles lead breaks of total mass 1430 on top of the piston kg Part A What additional volume of ethanol can the moonshiner squeeze into the tank? (Assume that the wall of the tank is perfectly rigid) V = L ± A Wire under Stress A steel wire of length 01 with circular cross section must stretch no more than 000 when a tensile (stretching) force of 380 is applied to each end of the wire N m cm Part A What minimum diameter dmin is required for the wire? Express your answer in millimeters Take Young's modulus for steel to be Y = Pa Hint 1 How to approach the problem Recall that Young's modulus is defined as Y = tensile stress tensile strain Compute the strain in terms of quantities given in the problem introduction, and write the stress in terms of given quantities and the unknown wire diameter Use these along with the given value of Young's modulus for steel to solve for the diameter of the wire Hint Calculate the tensile strain

3 Calculate the tensile strain on the wire Hint 1 Definition of tensile strain Tensile strain is defined as the ratio of the elongation ΔL to the original length L0 of a material that is under stress: tensile strain= ΔL L0 tensile strain = Hint 3 Definition of tensile stress Tensile stress is defined as the force perpendicular to the surface of a material divided by the cross sectional area of the surface: tensile stress = F A Hint 4 Relation between the area and the diameter The relation between the area A and the diameter d of a circle is A = π d 4 dmin = 156 mm Note that you were asked for the minimum diameter Where does this figure? The extension is directly proportional to the stress, ie, the force per unit area One way to decrease the stress is to increase the surface area over which the stretching force is applied So any diameter (and so area) greater than the one you calculated would serve to keep the extension within the tolerance specified (ie, the maximum allowable extension) ± Young's Modulus Learning Goal: To understand the meaning of Young's modulus, to perform some real life calculations related to stretching steel, a common construction material, and to introduce the concept of breaking stress Hooke's law states that for springs and other "elastic" objects F = kδx, where F is the magnitude of the stretching force, Δx is the corresponding elongation of the spring from equilibrium, and k is a constant that depends on the geometry and the material of the spring If the deformations are small enough, most materials, in fact, behave like springs: Their deformation is directly proportional to the external force Therefore, it may be useful to operate with an expression that is similar to Hooke's law but describes the properties of various materials, as

4 opposed to objects such as springs Such an expression does exist Consider, for instance, a bar of initial length L and cross sectional area A stressed by a force of magnitude F As a result, the bar stretches by ΔL Let us define two new terms: Tensile stress is the ratio of the stretching force to the cross sectional area: stress= F A Tensile strain is the ratio of the elongation of the rod to the initial length of the bar: strain= ΔL L It turns out that the ratio of the tensile stress to the tensile strain is a constant as long as the tensile stress is not too large That constant, which is an inherent property of a material, is called Young's modulus and is given by F/A Y = ΔL/L Part A What is the SI unit of Young's modulus? Hint 1 Look at the dimensions If you look at the dimensions of Young's modulus, you will see that they are equivalent to the dimension of pressure Use the SI unit of pressure Pa Part B Consider a metal bar of initial length L and cross sectional area A The Young's modulus of the material of the bar is Y Find the "spring constant" k of such a bar for low values of tensile strain Express your answer in terms of Y, L, and A Hint 1 Use the definition of Young's modulus Consider the equation defining Y Then isolate F and compare the result with Hooke's law: F = kδx k = Y A L Part C

5 Ten identical steel wires have equal lengths L and equal "spring constants" k The wires are connected end to end, so that the resultant wire has length What is the "spring constant" of the resulting wire? 10L Hint 1 The spring constant Use the expression for the spring constant determined in Part B From the expression derived in the Part B, you can determine what happens to the spring constant when the length of the spring increases 01k k 10k 100k Part D Ten identical steel wires have equal lengths L and equal "spring constants" k The wires are slightly twisted together, so that the resultant wire has length L and its cross sectional area is ten times that of the individual wire What is the "spring constant" of the resulting wire? Hint 1 The spring constant Use the expression for the spring constant determined in Part B From the expression derived in Part B, you can determine what happens to the spring constant when the area of the spring increases 01k k 10k 100k Part E Ten identical steel wires have equal lengths L and equal "spring constants" k The Young's modulus of each wire is Y The wires are connected end to end, so that the resultant wire has length 10L What is the Young's modulus of the resulting wire? 01Y Y 10Y 100Y

6 Part F Ten identical steel wires have equal lengths L and equal "spring constants" k The Young's modulus of each wire is Y The wires are slightly twisted together, so that the resultant wire has length L and is ten times as thick as the individual wire What is the Young's modulus of the resulting wire? 01Y Y 10Y 100Y By rearranging the wires, we create a new object with new mechanical properties However, Young's modulus depends on the material, which remains unchanged To change the Young's modulus, one would have to change the properties of the material itself, for instance by heating or cooling it Part G L = 100 A = 0500 Consider a steel guitar string of initial length meter and cross sectional area square millimeters The Young's modulus of the steel is Y = pascals How far ( ΔL) would such a string stretch under a tension of 1500 newtons? Use two significant figures in your answer Express your answer in millimeters ΔL = 15 mm Steel is a very strong material For these numeric values, you may assume that Hooke's law holds However, for greater values of tensile strain, the material no longer behaves elastically If the strain and stress are large enough, the material deteriorates The final part of this problem illustrates this point and gives you a sense of the "stretching limit" of steel Part H Although human beings have been able to fly hundreds of thousands of miles into outer space, getting inside the earth has proven much more difficult The deepest mines ever drilled are only about 10 miles deep To illustrate the difficulties associated with such drilling, consider the following: The density of steel is about 7900 kilograms per cubic meter, and its breaking stress, defined as the maximum stress the material can bear without deteriorating, is about pascals What is the maximum length of a steel cable that can be lowered into a mine? Assume that the magnitude of the acceleration due to gravity remains constant at 98 meters per second per second Use two significant figures in your answer, expressed in kilometers Hint 1 Why does the cable break? The cable breaks because of the stress exerted on it by its own weight At the moment that the breaking stress is reached, the stress at the top of the cable reaches its maximum, and the material begins to deteriorate

7 Introduce an arbitrary cross sectional area of the cable (which will cancel out of the final answer) The mass of the cable below the top point can be found as the product of its volume and its density Use this to find the force at the top that will lead to the breaking stress Hint Find the stress in the cable Assume that the cable has cross sectional area A and length L The density is ρ The maximum stress in the cable is at the very top, where it has to support its own weight What is this maximum stress? Express your answer in terms of ρ, L, and g, the magnitude of the acceleration due to gravity Recall that the stress is the force per unit area, so the area will not appear in your expression maximum stress = ρlg 6 km This is only about 16 miles, and we have assumed that no extra load is attached By the way, this length is small enough to justify the assumption of virtually constant acceleration due to gravity When making such assumptions, one should always check their validity after obtaining a result Problem 1176 N Two identical, uniform beams weighing 60 each are connected at one end by a frictionless hinge A light horizontal crossbar attached at the midpoints of the beams maintains an angle of 530 between the beams The beams are suspended from the ceiling by vertical wires such that they form a " ", as shown in the figure V Part A What force does the crossbar exert on each beam? F = 130 N

8 Part B Is the crossbar under tension or compression? tension compression Part C What is the magnitude of the force that the hinge at point A exerts on each beam? F = 130 N Part D What is the direction of the force that the hinge at point A exerts on the right hand beam? ϕ = 180 with the direction to the right Part E What is the direction of the force that the hinge at point A exerts on the left hand beam? ϕ = 0 with the direction to the right Understanding Bernoulli's Equation Bernoulli's equation is a simple relation that can give useful insight into the balance among fluid pressure, flow speed, and elevation It applies exclusively to ideal fluids with steady flow, that is, fluids with a constant density and no internal friction

9 forces, whose flow patterns do not change with time Despite its limitations, however, Bernoulli's equation is an essential tool in understanding the behavior of fluids in many practical applications, from plumbing systems to the flight of airplanes For a fluid element of density ρ that flows along a streamline, Bernoulli's equation states that p 1 +ρg + ρ = +ρg + ρ h1 1 v 1 p h where p is the pressure, v is the flow speed, h is the height, g is the acceleration due to gravity, and subscripts 1 and refer to any two points along the streamline The physical interpretation of Bernoulli's equation becomes clearer if we rearrange the terms of the equation as follows: The term p 1 p on the left hand side represents the total work done on a unit volume of fluid by the pressure forces of the surrounding fluid to move that volume of fluid from point 1 to point The two terms on the right hand side represent, 1 respectively, the change in potential energy,, and the change in kinetic energy,, of the unit volume during its flow from point 1 to point In other words, Bernoulli's equation states that the work done on a unit volume of fluid by the surrounding fluid is equal to the sum of the change in potential and kinetic energy per unit volume that occurs during the flow This is nothing more than the statement of conservation of mechanical energy for an ideal fluid flowing along a streamline 1 v = ρg( )+ 1 ρ( ) p 1 p h h1 ρg( ) v v 1 h h1 ρ( ), v v 1 Part A Consider the portion of a flow tube shown in the figure Point 1 and point are at the same height An ideal fluid enters the flow tube at point 1 and moves steadily toward point If the cross section of the flow tube at point 1 is greater than that at point, what can you say about the pressure at point? Hint 1 How to approach the problem Apply Bernoulli's equation to point 1 and to point Since the points are both at the same height, their elevations cancel out in the equation and you are left with a relation between pressure and flow speeds Even though the problem does not give direct information on the flow speed along the flow tube, it does tell you that the cross section of the flow tube decreases as the fluid flows toward point Apply the continuity equation to points 1 and and determine whether the flow speed at point is greater than or smaller than the flow speed at point 1 With that information and Bernoulli's equation, you will be able to determine the pressure at point with respect to the pressure at point 1 Hint Apply Bernoulli's equation Apply Bernoulli's equation to point 1 and to point to complete the expression below Here p and v are the pressure and flow speed, respectively, and subscripts 1 and refer to point 1 and point Also, use h for elevation with the appropriate subscript, and use ρ for the density of the fluid Express your answer in terms of some or all of the variables p1, v1, h1, p, v, h, and ρ Hint 1 Flow along a horizontal streamline Along a horizontal streamline, the change in potential energy of the flowing fluid is zero In other words, when applying Bernoulli's equation to any two points of the streamline, h1 = h and they cancel out

10 + ρ p 1 1 v 1 = + ρv p Hint 3 Determine v with respect to v1 By applying the continuity equation, determine which of the following is true Hint 1 The continuity equation The continuity equation expresses conservation of mass for incompressible fluids flowing in a tube It says that the amount of fluid ΔV flowing through a cross section A of the tube in a time interval Δt must be the same for all cross sections, or ΔV Δt = = A1v1 Av Therefore, the flow speed must increase when the cross section of the flow tube decreases, and vice versa v v v > = < v1 v1 v1 The pressure at point is lower than the pressure at point 1 equal to the pressure at point 1 higher than the pressure at point 1 Thus, by combining the continuity equation and Bernoulli's equation, one can characterize the flow of an ideal fluidwhen the cross section of the flow tube decreases, the flow speed increases, and therefore the pressure decreases In other words, if A < A1, then v > v1 and p < p1 Part B As you found out in the previous part, Bernoulli's equation tells us that a fluid element that flows through a flow tube with decreasing cross section moves toward a region of lower pressure Physically, the pressure drop experienced by the fluid element between points 1 and acts on the fluid element as a net force that causes the fluid to Hint 1 Effects from conservation of mass Recall that, if the cross section A of the flow tube varies, the flow speed v must change to conserve mass This means that there is a nonzero net force acting on the fluid that causes the fluid to increase or decrease speed depending on whether the fluid is flowing through a portion of the tube with a smaller or larger cross section

11 decrease in speed increase in speed remain in equilibrium Part C Now assume that point is at height h with respect to point 1, as shown in the figure The ends of the flow tube have the same areas as the ends of the horizontal flow tube shown in Part A Since the cross section of the flow tube is decreasing, Bernoulli's equation tells us that a fluid element flowing toward point from point 1 moves toward a region of lower pressure In this case, what is the pressure drop experienced by the fluid element? Hint 1 How to approach the problem Apply Bernoulli's equation to point 1 and to point, as you did in Part A Note that this time you must take into account the difference in elevation between points 1 and Do you need to add this additional term to the other term representing the pressure drop between the two ends of the flow tube or do you subtract it? The pressure drop is smaller than the pressure drop occurring in a purely horizontal flow equal to the pressure drop occurring in a purely horizontal flow larger than the pressure drop occurring in a purely horizontal flow Part D From a physical point of view, how do you explain the fact that the pressure drop at the ends of the elevated flow tube from Part C is larger than the pressure drop occurring in the similar but purely horizontal flow from Part A? Hint 1 Physical meaning of the pressure drop in a tube As explained in the introduction, the difference in pressure p 1 p between the ends of a flow tube represents the total work done on a unit volume of fluid by the pressure forces of the surrounding fluid to move that volume of fluid from one end to the other end of the flow tube

12 A greater amount of work is needed to balance the increase in potential energy from the elevation change decrease in potential energy from the elevation change larger increase in kinetic energy larger decrease in kinetic energy In the case of purely horizontal flow, the difference in pressure between the two ends of the flow tube had to balance only the increase in kinetic energy resulting from the acceleration of the fluid In an elevated flow tube, the difference in pressure must also balance the increase in potential energy of the fluid; therefore a higher pressure is needed for the flow to occur Water Flowing from a Tank Water flows steadily from an open tank as shown in the figure The elevation of point 1 is 100 meters, and the elevation of points and 3 is 00 meters The cross sectional area at point is square meters; at point 3, where the water is discharged, it is square meters The cross sectional area of the tank is very large compared with the cross sectional area of the pipe Part A dv Assuming that Bernoulli's equation applies, compute the discharge rate dt Express your answer in cubic meters per second Hint 1 How to approach the problem The discharge rate is the rate at which a given volume of water flows across the exit of the pipe per unit time It is also defined as volume flow rate, and it depends on both the cross sectional area of the pipe at the exit and the fluid speed at that point Hint The volume flow rate Consider a steadily moving incompressible fluid, and let A denote the cross sectional area of a flow tube The volume ΔV of fluid flowing across the cross section of area A at speed v during a small interval of time Δt is given by AvΔt Therefore, the rate at which fluid volumes cross a portion of the flow tube is dv dt Hint 3 Find the fluid speed at the end of the pipe = Av

13 Assuming that Bernoulli's equation applies, find the speed v3 of the water at point 3 Recall that the area of the tank is very large compared to the cross sectional area of the pipe, and consequently, the velocity of water at a point on the surface of the water in the tank may be considered to be zero Express your answer in meters per second to three significant figures Hint 1 Apply Bernoulli's principle Let pa be the atmospheric pressure and ρ the density of water Consider the entire volume of water as a single flow tube and apply Bernoulli's principle to point 3 and to point 1 Complete the expression below, where v3 is the fluid speed at point 3 Express your answer in terms of p a, ρ, and g the free fall acceleration due to gravity Hint 1 Bernoulli's principle For the steady flow of an incompressible fluid with no internal friction, the pressure p and the flow speed v at depth H below the surface are linked by an important relationship, known as Bernoulli's principle In particular, at any point at depth H along a flow tube, the following relation holds: p +ρgh + 1 ρ v = constant, where ρ is the density of the fluid and g is the accereleration due to gravity Since Bernoulli's principle is valid at any point along a flow tube, it takes the form p 1 +ρg H ρ v 1 = p +ρg H + 1 ρv when applied to two distinct points along a flow tube The subscripts 1 and refer to such points p +ρg + 1 a ρv 3 = + 10ρg p a v3 = 15 m/s dv dt = 000 m 3 /s Part B What is the gauge pressure at point? Express your answer in pascals Hint 1 Definition of gauge pressure

14 Gauge pressure is defined as the excess pressure above atmospheric pressure Let p a pressure and p the total pressure of a fluid Then the gauge pressure is p p a be the atmospheric Hint How to approach the problem You can relate the fluid pressure at point with the atmospheric pressure by applying Bernoulli's principle to point and point 1, or alternatively to point and point 3 To determine the fluid speed at point you can use the continuity equation, using the fluid speed at the exit of the pipe found in Part A Hint 3 Apply Bernoulli's principle Consider the entire volume of water as a single flow tube Let p and v be respectively the pressure and the fluid speed at point Let the atmospheric pressure be p a and the density of water ρ Apply Bernoulli's principle to point 1 and point and complete the expression below Express your answer in terms of v, ρ, and g, the free fall acceleration Hint 1 Bernoulli's principle For the steady flow of an incompressible fluid with no internal friction, the pressure p and the flow speed v at depth H below the surface are linked by an important relationship, known as Bernoulli's principle In particular, at any point at depth H along a flow tube, the following relation holds: p +ρgh + 1 ρ v = constant, where ρ is the density of the fluid and g is the accereleration due to gravity Since Bernoulli's principle is valid at any point along a flow tube, it takes the form p 1 +ρg + ρ = +ρg + ρ H1 1 v 1 p H when applied to two distinct points along a flow tube The subscripts 1 and refer to such points 1 v p p a = 05ρ v + 8gρ Hint 4 Find the fluid speed at point Find v, the speed of the water at point Express your answer in meters per second to three significant figures Hint 1 The continuity equation In a steadily moving incompressible fluid, the mass of fluid flowing along a flow tube is constant In particular, consider a flow tube between two stationary cross sections with areas A1 and A Let v1 and v be the fluid speeds at these sections, respectively Then conservation of mass takes the form A1v1 which is known as the continuity equation = Av, v = 417 m/s Hint 5 Density of Water Recall that the density of water is 3

15 Recall that the density of water is 1000 kg/m Pa Score Summary: Your score on this assignment is 101% You received 707 out of a possible total of 7 points

### Equilibrium & Elasticity

PHYS 101 Previous Exam Problems CHAPTER 12 Equilibrium & Elasticity Static equilibrium Elasticity 1. A uniform steel bar of length 3.0 m and weight 20 N rests on two supports (A and B) at its ends. A block

### Statics. Phys101 Lectures 19,20. Key points: The Conditions for static equilibrium Solving statics problems Stress and strain. Ref: 9-1,2,3,4,5.

Phys101 Lectures 19,20 Statics Key points: The Conditions for static equilibrium Solving statics problems Stress and strain Ref: 9-1,2,3,4,5. Page 1 The Conditions for Static Equilibrium An object in static

### Summary PHY101 ( 2 ) T / Hanadi Al Harbi

الكمية Physical Quantity القانون Low التعريف Definition الوحدة SI Unit Linear Momentum P = mθ be equal to the mass of an object times its velocity. Kg. m/s vector quantity Stress F \ A the external force

### Mechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering

Mechanics Of Solids Suraj kr. Ray (surajjj2445@gmail.com) Department of Civil Engineering 1 Mechanics of Solids is a branch of applied mechanics that deals with the behaviour of solid bodies subjected

### UNIVERSITY PHYSICS I. Professor Meade Brooks, Collin College. Chapter 12: STATIC EQUILIBRIUM AND ELASTICITY

UNIVERSITY PHYSICS I Professor Meade Brooks, Collin College Chapter 12: STATIC EQUILIBRIUM AND ELASTICITY Two stilt walkers in standing position. All forces acting on each stilt walker balance out; neither

### Page 1. Chapters 2, 3 (linear) 9 (rotational) Final Exam: Wednesday, May 11, 10:05 am - 12:05 pm, BASCOM 272

Final Exam: Wednesday, May 11, 10:05 am - 12:05 pm, BASCOM 272 The exam will cover chapters 1 14 The exam will have about 30 multiple choice questions Consultations hours the same as before. Another review

### Chapter 13 ELASTIC PROPERTIES OF MATERIALS

Physics Including Human Applications 280 Chapter 13 ELASTIC PROPERTIES OF MATERIALS GOALS When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions

### Lecture 8 Equilibrium and Elasticity

Lecture 8 Equilibrium and Elasticity July 19 EQUILIBRIUM AND ELASTICITY CHAPTER 12 Give a sharp blow one end of a stick on the table. Find center of percussion. Baseball bat center of percussion Equilibrium

### Figure 1 Answer: = m

Q1. Figure 1 shows a solid cylindrical steel rod of length =.0 m and diameter D =.0 cm. What will be increase in its length when m = 80 kg block is attached to its bottom end? (Young's modulus of steel

### 1 Lecture 5. Linear Momentum and Collisions Elastic Properties of Solids

1 Lecture 5 Linear Momentum and Collisions Elastic Properties of Solids 2 Linear Momentum and Collisions 3 Linear Momentum Is defined to be equal to the mass of an object times its velocity. P = m θ Momentum

### PHYS 185 Practice Final Exam Fall You may answer the questions in the space provided here, or if you prefer, on your own notebook paper.

PHYS 185 Practice Final Exam Fall 2013 Name: You may answer the questions in the space provided here, or if you prefer, on your own notebook paper. Short answers 1. 2 points When an object is immersed

### Liquids CHAPTER 13 FLUIDS FLUIDS. Gases. Density! Bulk modulus! Compressibility. To begin with... some important definitions...

CHAPTER 13 FLUIDS FLUIDS Liquids Gases Density! Bulk modulus! Compressibility Pressure in a fluid! Hydraulic lift! Hydrostatic paradox Measurement of pressure! Manometers and barometers Buoyancy and Archimedes

### 22 Which of the following correctly defines the terms stress, strain and Young modulus? stress strain Young modulus

PhysicsndMathsTutor.com Which of the following correctly defines the terms stress, strain and Young modulus? 97/1/M/J/ stress strain Young modulus () x (area) (extension) x (original length) (stress) /

### Chapter 26 Elastic Properties of Materials

Chapter 26 Elastic Properties of Materials 26.1 Introduction... 1 26.2 Stress and Strain in Tension and Compression... 2 26.3 Shear Stress and Strain... 4 Example 26.1: Stretched wire... 5 26.4 Elastic

### MECHANICAL PROPERTIES OF SOLIDS

Chapter Nine MECHANICAL PROPERTIES OF SOLIDS MCQ I 9.1 Modulus of rigidity of ideal liquids is (a) infinity. (b) zero. (c) unity. (d) some finite small non-zero constant value. 9. The maximum load a wire

### Physics. Assignment-1(UNITS AND MEASUREMENT)

Assignment-1(UNITS AND MEASUREMENT) 1. Define physical quantity and write steps for measurement. 2. What are fundamental units and derived units? 3. List the seven basic and two supplementary physical

### Chapter 12. Static Equilibrium and Elasticity

Chapter 12 Static Equilibrium and Elasticity Static Equilibrium Equilibrium implies that the object moves with both constant velocity and constant angular velocity relative to an observer in an inertial

### In steady flow the velocity of the fluid particles at any point is constant as time passes.

Chapter 10 Fluids Fluids in Motion In steady flow the velocity of the fluid particles at any point is constant as time passes. Unsteady flow exists whenever the velocity of the fluid particles at a point

### Lesson 6 Review of fundamentals: Fluid flow

Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass

### Chapter 15: Fluid Mechanics Dynamics Using Pascal s Law = F 1 = F 2 2 = F 2 A 2

Lecture 24: Archimedes Principle and Bernoulli s Law 1 Chapter 15: Fluid Mechanics Dynamics Using Pascal s Law Example 15.1 The hydraulic lift A hydraulic lift consists of a small diameter piston of radius

### Strength of Material. Shear Strain. Dr. Attaullah Shah

Strength of Material Shear Strain Dr. Attaullah Shah Shear Strain TRIAXIAL DEFORMATION Poisson's Ratio Relationship Between E, G, and ν BIAXIAL DEFORMATION Bulk Modulus of Elasticity or Modulus of Volume

### PHYSICS. Chapter 5 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.

PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 5 Lecture RANDALL D. KNIGHT Chapter 5 Force and Motion IN THIS CHAPTER, you will learn about the connection between force and motion.

### Static Equilibrium; Elasticity & Fracture

Static Equilibrium; Elasticity & Fracture The Conditions for Equilibrium Statics is concerned with the calculation of the forces acting on and within structures that are in equilibrium. An object with

### Two Cars on a Curving Road

skiladæmi 4 Due: 11:59pm on Wednesday, September 30, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy Two Cars on a Curving Road A small car of mass m

### Nicholas J. Giordano. Chapter 10 Fluids

Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 10 Fluids Fluids A fluid may be either a liquid or a gas Some characteristics of a fluid Flows from one place to another Shape varies according

### Class XI Physics. Ch. 9: Mechanical Properties of solids. NCERT Solutions

Downloaded from Class XI Physics Ch. 9: Mechanical Properties of solids NCERT Solutions Page 242 Question 9.1: A steel wire of length 4.7 m and cross-sectional area 3.0 10 5 m 2 stretches by the same amount

### Translational Motion Rotational Motion Equations Sheet

PHYSICS 01 Translational Motion Rotational Motion Equations Sheet LINEAR ANGULAR Time t t Displacement x; (x = rθ) θ Velocity v = Δx/Δt; (v = rω) ω = Δθ/Δt Acceleration a = Δv/Δt; (a = rα) α = Δω/Δt (

### Chapter 14. Lecture 1 Fluid Mechanics. Dr. Armen Kocharian

Chapter 14 Lecture 1 Fluid Mechanics Dr. Armen Kocharian States of Matter Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas unconfined Has neither a definite

### Two Hanging Masses. ) by considering just the forces that act on it. Use Newton's 2nd law while

Student View Summary View Diagnostics View Print View with Answers Edit Assignment Settings per Student Exam 2 - Forces [ Print ] Due: 11:59pm on Tuesday, November 1, 2011 Note: To underst how points are

### 2008 FXA THREE FORCES IN EQUILIBRIUM 1. Candidates should be able to : TRIANGLE OF FORCES RULE

THREE ORCES IN EQUILIBRIUM 1 Candidates should be able to : TRIANGLE O ORCES RULE Draw and use a triangle of forces to represent the equilibrium of three forces acting at a point in an object. State that

### Rutgers University Department of Physics & Astronomy. 01:750:271 Honors Physics I Fall Lecture 19. Home Page. Title Page. Page 1 of 36.

Rutgers University Department of Physics & Astronomy 01:750:271 Honors Physics I Fall 2015 Lecture 19 Page 1 of 36 12. Equilibrium and Elasticity How do objects behave under applied external forces? Under

### Physics 201 Chapter 13 Lecture 1

Physics 201 Chapter 13 Lecture 1 Fluid Statics Pascal s Principle Archimedes Principle (Buoyancy) Fluid Dynamics Continuity Equation Bernoulli Equation 11/30/2009 Physics 201, UW-Madison 1 Fluids Density

### Question 9.1: Answer. Length of the steel wire, L 1 = 4.7 m. Area of cross-section of the steel wire, A 1 = m 2

Question 9.1: A steel wire of length 4.7 m and cross-sectional area 3.0 10 5 m 2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 10 5 m 2 under a given load.

### UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation.

UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The magnitude

### Fluids. Fluids in Motion or Fluid Dynamics

Fluids Fluids in Motion or Fluid Dynamics Resources: Serway - Chapter 9: 9.7-9.8 Physics B Lesson 3: Fluid Flow Continuity Physics B Lesson 4: Bernoulli's Equation MIT - 8: Hydrostatics, Archimedes' Principle,

### Lecture Outline Chapter 6. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 6 Physics, 4 th Edition James S. Walker Chapter 6 Applications of Newton s Laws Units of Chapter 6 Frictional Forces Strings and Springs Translational Equilibrium Connected Objects

### 1 (a) On the axes of Fig. 7.1, sketch a stress against strain graph for a typical ductile material. stress. strain. Fig. 7.1 [2]

1 (a) On the axes of Fig. 7.1, sketch a stress against strain graph for a typical ductile material. stress strain Fig. 7.1 [2] (b) Circle from the list below a material that is ductile. jelly c amic gl

### 1 of 6 10/21/2009 6:33 PM

1 of 6 10/21/2009 6:33 PM Chapter 10 Homework Due: 9:00am on Thursday, October 22, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment

Question 9.1: A steel wire of length 4.7 m and cross-sectional area 3.0 10 5 m 2 stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 10 5 m 2 under a given load.

### Homework 6. problems: 8.-, 8.38, 8.63

Homework 6 problems: 8.-, 8.38, 8.63 Problem A circus trapeze consists of a bar suspended by two parallel ropes, each of length l. allowing performers to swing in a vertical circular arc. Suppose a performer

### Contents. Concept Map

Contents 1. General Notes on Forces 2. Effects of Forces on Motion 3. Effects of Forces on Shape 4. The Turning Effect of Forces 5. The Centre of Gravity and Stability Concept Map April 2000 Forces - 1

### Chapter 8. Rotational Equilibrium and Rotational Dynamics. 1. Torque. 2. Torque and Equilibrium. 3. Center of Mass and Center of Gravity

Chapter 8 Rotational Equilibrium and Rotational Dynamics 1. Torque 2. Torque and Equilibrium 3. Center of Mass and Center of Gravity 4. Torque and angular acceleration 5. Rotational Kinetic energy 6. Angular

### Pressure in stationary and moving fluid. Lab-On-Chip: Lecture 2

Pressure in stationary and moving fluid Lab-On-Chip: Lecture Fluid Statics No shearing stress.no relative movement between adjacent fluid particles, i.e. static or moving as a single block Pressure at

### AP Physics Multiple Choice Practice Torque

AP Physics Multiple Choice Practice Torque 1. A uniform meterstick of mass 0.20 kg is pivoted at the 40 cm mark. Where should one hang a mass of 0.50 kg to balance the stick? (A) 16 cm (B) 36 cm (C) 44

### Physics 3 Summer 1990 Lab 7 - Hydrodynamics

Physics 3 Summer 1990 Lab 7 - Hydrodynamics Theory Consider an ideal liquid, one which is incompressible and which has no internal friction, flowing through pipe of varying cross section as shown in figure

### Physics Mechanics. Lecture 11 Newton s Laws - part 2

Physics 170 - Mechanics Lecture 11 Newton s Laws - part 2 Newton s Second Law of Motion An object may have several forces acting on it; the acceleration is due to the net force: Newton s Second Law of

### Physics 201 Chapter 13 Lecture 1

Physics 201 Chapter 13 Lecture 1 Fluid Statics Pascal s Principle Archimedes Principle (Buoyancy) Fluid Dynamics Continuity Equation Bernoulli Equation 11/30/2009 Physics 201, UW-Madison 1 Fluids Density

### PHYS 101 Previous Exam Problems. Force & Motion I

PHYS 101 Previous Exam Problems CHAPTER 5 Force & Motion I Newton s Laws Vertical motion Horizontal motion Mixed forces Contact forces Inclines General problems 1. A 5.0-kg block is lowered with a downward

### EQUILIBRIUM and ELASTICITY

PH 221-1D Spring 2013 EQUILIBRIUM and ELASTICITY Lectures 30-32 Chapter 12 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) 1 Chapter 12 Equilibrium and Elasticity In this chapter we will

### PHYSICS. Course Structure. Unit Topics Marks. Physical World and Measurement. 1 Physical World. 2 Units and Measurements.

PHYSICS Course Structure Unit Topics Marks I Physical World and Measurement 1 Physical World 2 Units and Measurements II Kinematics 3 Motion in a Straight Line 23 4 Motion in a Plane III Laws of Motion

### Physics 207 Lecture 20. Chapter 15, Fluids

Chapter 15, Fluids This is an actual photo of an iceberg, taken by a rig manager for Global Marine Drilling in St. Johns, Newfoundland. The water was calm and the sun was almost directly overhead so that

### Use the following to answer question 1:

Use the following to answer question 1: On an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. The seats begin from rest and are uniformly accelerated for 21 seconds to

### Solution Only gravity is doing work. Since gravity is a conservative force mechanical energy is conserved:

8) roller coaster starts with a speed of 8.0 m/s at a point 45 m above the bottom of a dip (see figure). Neglecting friction, what will be the speed of the roller coaster at the top of the next slope,

### SIR MICHELANGELO REFALO CENTRE FOR FURTHER STUDIES VICTORIA GOZO

SIR MICHELANGELO REFALO CENTRE FOR FURTHER STUDIES VICTORIA GOZO Half-Yearly Exam 2013 Subject: Physics Level: Advanced Time: 3hrs Name: Course: Year: 1st This paper carries 200 marks which are 80% of

### Exam 3 PREP Chapters 6, 7, 8

PHY241 - General Physics I Dr. Carlson, Fall 2013 Prep Exam 3 PREP Chapters 6, 7, 8 Name TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) Astronauts in orbiting satellites

### BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS)

BE Semester- I ( ) Question Bank (MECHANICS OF SOLIDS) All questions carry equal marks(10 marks) Q.1 (a) Write the SI units of following quantities and also mention whether it is scalar or vector: (i)

### Mass of fluid leaving per unit time

5 ENERGY EQUATION OF FLUID MOTION 5.1 Eulerian Approach & Control Volume In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics.

### Elastic Properties of Solid Materials. Notes based on those by James Irvine at

Elastic Properties of Solid Materials Notes based on those by James Irvine at www.antonine-education.co.uk Key Words Density, Elastic, Plastic, Stress, Strain, Young modulus We study how materials behave

### AER210 VECTOR CALCULUS and FLUID MECHANICS. Quiz 4 Duration: 70 minutes

AER210 VECTOR CALCULUS and FLUID MECHANICS Quiz 4 Duration: 70 minutes 26 November 2012 Closed Book, no aid sheets Non-programmable calculators allowed Instructor: Alis Ekmekci Family Name: Given Name:

### The Laws of Motion. Newton s first law Force Mass Newton s second law Gravitational Force Newton s third law Examples

The Laws of Motion Newton s first law Force Mass Newton s second law Gravitational Force Newton s third law Examples Gravitational Force Gravitational force is a vector Expressed by Newton s Law of Universal

### Chapter Four Holt Physics. Forces and the Laws of Motion

Chapter Four Holt Physics Forces and the Laws of Motion Physics Force and the study of dynamics 1.Forces - a. Force - a push or a pull. It can change the motion of an object; start or stop movement; and,

### Chapter 12. Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = -kx

Chapter 1 Lecture Notes Chapter 1 Oscillatory Motion Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = -kx When the mass is released, the spring will pull

### Pressure in stationary and moving fluid Lab- Lab On- On Chip: Lecture 2

Pressure in stationary and moving fluid Lab-On-Chip: Lecture Lecture plan what is pressure e and how it s distributed in static fluid water pressure in engineering problems buoyancy y and archimedes law;

Connected Bodies 1. Two 10 kg bodies are attached to a spring balance as shown in figure. The reading of the balance will be 10 kg 10 kg 1) 0 kg-wt ) 10 kg-wt 3) Zero 4) 5 kg-wt. In the given arrangement,

### M o d u l e B a s i c A e r o d y n a m i c s

Category A B1 B2 B3 Level 1 2 3 M o d u l e 0 8-0 1 B a s i c A e r o d y n a m i c s P h y s i c s o f t h e A t m o s p h e r e 08-01- 1 Category A B1 B2 B3 Level 1 2 3 T a b l e o f c o n t e n t s

### STATICALLY INDETERMINATE STRUCTURES

STATICALLY INDETERMINATE STRUCTURES INTRODUCTION Generally the trusses are supported on (i) a hinged support and (ii) a roller support. The reaction components of a hinged support are two (in horizontal

### Potential Energy. Serway 7.6, 7.7;

Potential Energy Conservative and non-conservative forces Gravitational and elastic potential energy Mechanical Energy Serway 7.6, 7.7; 8.1 8.2 Practice problems: Serway chapter 7, problems 41, 43 chapter

### Fluids. Fluid = Gas or Liquid. Density Pressure in a Fluid Buoyancy and Archimedes Principle Fluids in Motion

Chapter 14 Fluids Fluids Density Pressure in a Fluid Buoyancy and Archimedes Principle Fluids in Motion Fluid = Gas or Liquid MFMcGraw-PHY45 Chap_14Ha-Fluids-Revised 10/13/01 Densities MFMcGraw-PHY45 Chap_14Ha-Fluids-Revised

### Description: Using conservation of energy, find the final velocity of a "yo yo" as it unwinds under the influence of gravity.

Chapter 10 [ Edit ] Overview Summary View Diagnostics View Print View with Answers Chapter 10 Due: 11:59pm on Sunday, November 6, 2016 To understand how points are awarded, read the Grading Policy for

### Practice. Newton s 3 Laws of Motion. Recall. Forces a push or pull acting on an object; a vector quantity measured in Newtons (kg m/s²)

Practice A car starts from rest and travels upwards along a straight road inclined at an angle of 5 from the horizontal. The length of the road is 450 m and the mass of the car is 800 kg. The speed of

### Class XI Chapter 9 Mechanical Properties of Solids Physics

Book Name: NCERT Solutions Question : A steel wire of length 4.7 m and cross-sectional area 5 3.0 0 m stretches by the same 5 amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 0 m

### Objectives: After completion of this module, you should be able to:

Chapter 12 Objectives: After completion of this module, you should be able to: Demonstrate your understanding of elasticity, elastic limit, stress, strain, and ultimate strength. Write and apply formulas

### Chapter 3. Inertia. Force. Free Body Diagram. Net Force. Mass. quantity of matter composing a body represented by m. units are kg

Chapter 3 Mass quantity of matter composing a body represented by m Kinetic Concepts for Analyzing Human Motion units are kg Inertia tendency to resist change in state of motion proportional to mass has

### UNIVERSITY OF MANITOBA. All questions are of equal value. No marks are subtracted for wrong answers.

(3:30 pm 6:30 pm) PAGE NO.: 1 of 7 All questions are of equal value. No marks are subtracted for wrong answers. Record all answers on the computer score sheet provided. USE PENCIL ONLY! Black pen will

### Chapter 15B - Fluids in Motion. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 15B - Fluids in Motion A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 007 Paul E. Tippens Fluid Motion The lower falls at Yellowstone National

### **********************************************************************

Department of Civil and Environmental Engineering School of Mining and Petroleum Engineering 3-33 Markin/CNRL Natural Resources Engineering Facility www.engineering.ualberta.ca/civil Tel: 780.492.4235

### Physics 111 Lecture 4 Newton`s Laws

Physics 111 Lecture 4 Newton`s Laws Dr. Ali ÖVGÜN EMU Physics Department www.aovgun.com he Laws of Motion q Newton s first law q Force q Mass q Newton s second law q Newton s third law q Examples Isaac

### Chapter 13 Elastic Properties of Materials

Chapter 13 Elastic Properties of Materials GOALS When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions Define each of the following terms, and

### Newton s First Law and IRFs

Goals: Physics 207, Lecture 6, Sept. 22 Recognize different types of forces and know how they act on an object in a particle representation Identify forces and draw a Free Body Diagram Solve 1D and 2D

### TEST REPORT. Question file: P Copyright:

Date: February-12-16 Time: 2:00:28 PM TEST REPORT Question file: P12-2006 Copyright: Test Date: 21/10/2010 Test Name: EquilibriumPractice Test Form: 0 Test Version: 0 Test Points: 138.00 Test File: EquilibriumPractice

### 4.0 m s 2. 2 A submarine descends vertically at constant velocity. The three forces acting on the submarine are viscous drag, upthrust and weight.

1 1 wooden block of mass 0.60 kg is on a rough horizontal surface. force of 12 N is applied to the block and it accelerates at 4.0 m s 2. wooden block 4.0 m s 2 12 N hat is the magnitude of the frictional

### 1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor.

Elasticity Homework Problems 2014 Section 1. The Strain Tensor. 1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor. 2. Given a steel bar compressed with a deformation

### Rotational Kinetic Energy

Lecture 17, Chapter 10: Rotational Energy and Angular Momentum 1 Rotational Kinetic Energy Consider a rigid body rotating with an angular velocity ω about an axis. Clearly every point in the rigid body

### Figure 3: Problem 7. (a) 0.9 m (b) 1.8 m (c) 2.7 m (d) 3.6 m

1. For the manometer shown in figure 1, if the absolute pressure at point A is 1.013 10 5 Pa, the absolute pressure at point B is (ρ water =10 3 kg/m 3, ρ Hg =13.56 10 3 kg/m 3, ρ oil = 800kg/m 3 ): (a)

### Angular Speed and Angular Acceleration Relations between Angular and Linear Quantities

Angular Speed and Angular Acceleration Relations between Angular and Linear Quantities 1. The tires on a new compact car have a diameter of 2.0 ft and are warranted for 60 000 miles. (a) Determine the

### MECHANICS OF MATERIALS. Prepared by Engr. John Paul Timola

MECHANICS OF MATERIALS Prepared by Engr. John Paul Timola Mechanics of materials branch of mechanics that studies the internal effects of stress and strain in a solid body. stress is associated with the

### Dynamics Review Checklist

Dynamics Review Checklist Newton s Laws 2.1.1 Explain Newton s 1 st Law (the Law of Inertia) and the relationship between mass and inertia. Which of the following has the greatest amount of inertia? (a)

### CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS NOOR ALIZA AHMAD

CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS 1 INTRODUCTION Flow often referred as an ideal fluid. We presume that such a fluid has no viscosity. However, this is an idealized situation that does not exist.

### Static Equilibrium. University of Arizona J. H. Burge

Static Equilibrium Static Equilibrium Definition: When forces acting on an object which is at rest are balanced, then the object is in a state of static equilibrium. - No translations - No rotations In

### Determine the resultant internal loadings acting on the cross section at C of the beam shown in Fig. 1 4a.

E X M P L E 1.1 Determine the resultant internal loadings acting on the cross section at of the beam shown in Fig. 1 a. 70 N/m m 6 m Fig. 1 Support Reactions. This problem can be solved in the most direct

### Physics 231 Lecture 23

Physics 31 Lecture 3 Main points of today s lecture: Gravitation potential energy GM1M PEgrav r 1 Tensile stress and strain Δ Y ΔL L 0 Bulk stress and strain: Δ V Δ P B Δ V Pressure in fluids: P ; Pbot

### UNIVERSITY OF MANITOBA

PAGE NO.: 1 of 6 + Formula Sheet Equal marks for all questions. No marks are subtracted for wrong answers. Record all answers on the computer score sheet provided. USE PENCIL ONLY! Black pen will look

### PHYS 1303 Final Exam Example Questions

PHYS 1303 Final Exam Example Questions (In summer 2014 we have not covered questions 30-35,40,41) 1.Which quantity can be converted from the English system to the metric system by the conversion factor

### St Olave s Grammar School. AS Physics Mock Revision Checklist

St Olave s Grammar School Mock Practical skills.. a Can you design experiments, including ones to solve problems set in a practical context?.. b Can you identify the variables that must be controlled in

### FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003

FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003 NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 14 pages. Make sure none are missing 2. There is

### ! =!"#\$% exerted by a fluid (liquid or gas) !"#\$ =!"# FUNDAMENTAL AND MEASURABLE INTENSIVE PROPERTIES PRESSURE, TEMPERATURE AND SPECIFIC VOLUME

FUNDAMENTAL AND MEASURABLE INTENSIVE PROPERTIES PRESSURE, TEMPERATURE AND SPECIFIC VOLUME PRESSURE, P! =!"#\$%!"#! exerted by a fluid (liquid or gas) Thermodynamic importance of pressure One of two independent

### Physics 218: FINAL EXAM April 29 th, 2016

Physics 218: FINAL EXAM April 29 th, 2016 Please read the instructions below, Do not open the exam until told to do so. Rules of the Exam: 1. You have 120 minutes to complete the exam. 2. Formulae are

### AP Physics QUIZ Chapters 10

Name: 1. Torque is the rotational analogue of (A) Kinetic Energy (B) Linear Momentum (C) Acceleration (D) Force (E) Mass A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible