# ME-B41 Lab 1: Hydrostatics. Experimental Procedures

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 ME-B41 Lab 1: Hydrostatics In this lab you will do four brief experiments related to the following topics: manometry, buoyancy, forces on submerged planes, and hydraulics (a hydraulic jack). Each experiment should take less than 15 minutes and the write-up should take 1 hour or less for each. Manometry: Experimental Procedures WHAT YOU ARE GOING TO DO: You will find the density of the fluid in one manometer by measuring the pressure applied to that manometer using a second manometer with a fluid of known density. WHAT YOU SHOULD LEARN: You should learn how a manometer works and how the elevation in a manometer depends on the density of the fluid in the manometer. DETAILS: In this experiment there are two U-tube manometers. One leg of each manometer is connected by a flexible tube to a hand pump. The purple fluid in one manometer has a known density of ρ=1 gm/cm 3. The flexible tube connecting the manometers is filled with air. The red fluid in the second manometer has an unknown density. You are to find the density of the red fluid. Procedure: p1. Sketch the set-up on the back of the attached data sheet. (This is for your reference when you write the lab report). p2. Apply a vacuum to the tubes between the manometers using the hand pump. Be careful: a short gentle stroke on the pump is very effective. Do not overflow the manometer. p3. Measure the difference in height between the two legs of each U-tube (both purple and red) and record on the data sheet. Release the vacuum using the red lever on the hand pump nozzle. p4. Repeat steps p2 and p3 three more times, each time with a different applied vacuum, to obtain a total of four readings. Calculations: c1. Use the equation for hydrostatic pressure of a constant density fluid to write an expression for the difference between air pressure in the tube between manometers and atmospheric pressure using the difference in height between the two legs of U-tube for the purple fluid; repeat for red fluid. c2. Set the equations in c1 equal. c3. Use equation in c2 to find density of the red fluid for the first applied vacuum; repeat for all readings. c4. Calculate the average density of the red fluid found from the four measurements. Write-Up: Include the following in your write-up: 1. Derivation of equations in steps c1 and c2; Sample of calculation (step c3). 2. Table of red fluid density for each applied pressure. Also include the average density in the table. 3. Discuss briefly (a few sentences per topic) Why can the effect of the air in the tube between the two manometers be neglected? Sources of error. 4. Manometry Data Sheet

2 MANOMETRY DATA SHEET Run #1 Run #2 Run #3 Run #4 h Purple liquid (ρ = g/cm 3 ) in. in. in. in. h Red liquid in. in. in. in. h signifies height difference Note any apparant sources of error in your measurements:

3 Buoyancy: WHAT YOU ARE GOING TO DO: You will find the density (mass/volume) of two different solid bodies in two different ways: 1) measure the volume of the body directly; 2) measure the volume using buoyancy relations. WHAT YOU SHOULD LEARN: You should learn how to get an accurate measure of a solid's volume using buoyancy. DETAILS: In this experiment, you are to find the density two different cylindrical bodies--one solid metal and one hollow plastic. Procedure: p1. You may ignore the weight of the cord, rod, hook, etc. in this experiment. p2. Sketch the metal body (body a) and measure its dimensions to the nearest 0.1 cm. p3. Screw the small hook all of the way into the rod at the bottom of the scale until the hook bottoms out. Zero the scale using the thumbwheel below the display. Weigh the body by hanging it from the scale, so that it is not submerged in the water. Be careful not to drop the weight in the water or torque the shaft connected to the scale. Record the weight. p4. Use the cord between the body and the scale so that the body is fully immersed in the water. Record the weight of the body when it is fully immersed (convert to N). This is equivalent to the tension force in the cord. p5. Sketch the experimental setup on the back of your data sheet. (This is for your reference when you write the lab report). p6. Repeat steps p2 through p5 for the plastic hollow body (body b), except here you must use the a rigid rod between the body and the scale to keep the body fully immersed in the water in step p4. The rigid rod is needed because the body floats, and you need to record the net upward force of the body on the scale when the body is submerged. To do this, screw the threaded rod into the plastic hollow body. Remove the hook from the rod attached to the scale and slide the narrow end of the rod attached to the plastic body into the rod attached to the scale. (Use caution so that the rod does not bend.) Calculations: c1. Using the dimensions that you measured in 1 above, calculate the volume of the body a in cm 3. c2. Calculate the density of the body using the weight of the body and the volume from step c1, in gm/cm 3. c3. Draw a free body diagram of the body when it is fully submerged in the fluid. Include the weight force, buoyancy force, and tension for in the string to the scale. c4. Using the principles of buoyancy and a force balance on the body, calculate the volume of the body in cm 3. c5. Calculate the density of the body using the volume from step c4, in gm/cm 3. c6. Repeat calculations for body b. Write-Up: Include the following in your write-up: 1. Calculations of volume and density (c1 and c2) based on dimensions for each body. 2. Free Body Diagram of each body and calculations of volume and density (c3, c4, and c5) for each body. 3. Discuss briefly (a few sentences per topic) Which method for calculating density is more accurate? Why? Sources of error. 4. Buoyancy Data Sheet Note: 1 lbf = N = 444,820 gm-cm/s 2

4 BUOYANCY DATA SHEET d a = cm (diameter of body a) h a = cm (height of body a) W a air = lbf = N (weight of body a in air) W a liquid = lbf = N (weight of body a in liquid) d b = cm (diameter of body b) h b = cm (height of body b) W b air = lbf = N (weight of body b in air) W b liquid = lbf = N (weight of body b in liquid) Note any apparant sources of error in your measurements:

6 Force on a Submerged Plane Data Sheet t = in (door thickness) h = in (door height) w = in (door width) d = in (vertical distance from point of rotation to liquid/air interface) l = in (vertical distance from point of rotation to attachment site of resisting cable) T = lbf (tension in resisting cable) Note any apparant sources of error in your measurements:

7 Practical Application--Hydraulic Jack: WHAT YOU ARE GOING TO DO: You will take apart a hydraulic jack and determine the work done by the jack in lifting a weight. WHAT YOU SHOULD LEARN: You should learn how a hydraulic jack is used to obtain leverage. DETAILS: The workings of common instruments are not always intuitive. For instance, a hydraulic jack lifts very heavy objects without requiring a lot of human effort to operate it. This is because a jack incorporates leverage, as do similar tools such as a block and tackle, a winch, and a prybar. In leveraging effort, the application of a small force through a long distance has the same effect as a greater force applied through a shorter distance. There are three identical hydraulic jacks on display for this lab: 1) jack with no fluid so that you can take it apart to see how it works; 2) jack with parts of it cut away to expose its inner workings; 3) jack that works and is used to make measurements. Below is a schematic of the pump. In the schematic, valve body contains one check valve which opens on pump upstroke and one which opens on pump downstroke. Pump Piston W Ram Piston Air Vent Pump Volume Valve Body Ram Volume Reservoir Release Valve Note the following: * Assume all three jacks in this lab are identical in every respect, so that you can make measurements on one jack and apply them to another jack. * Remember that energy is conserved (it is not created or destroyed, although it can be transformed from one type to another). * Work = W = F ds, where F is the vector force and s is the vector displacement. Note that for a constant force parallel to the displacement we can use the magnitudes and W = F ds = Fs. * Assume that the fluid used in the jack is incompressible and isothermal (remains at the same temperature) throughout the exercise. In other words, assume that all of your effort applied to the jack handle goes into raising the weight and doesn't go into raising the temperature of the fluid via compression or friction. * The jack's "leverage" is determined by the relative sizes of the ram (large) cylinder diameter and the pump (small) cylinder diameter. These will determine the distance each piston travels in the ram and pump cylinders.

8 Procedure: p1. Take apart the fluid-less model and measure: The distance from the mark on the handle to the pivot point. (Measure the distance parallel to the pump handle.) The distance from the pump piston connection point to the pivot point. The inside diameters of both the ram cylinder and the pump cylinder (not the piston diameter). Pump Handle Mark Pump Piston Connection Pivot Point Pump Piston Pump Piston and Handle Assembly p2. Figure out how the hydraulic jack works. Note the function of the valves. p3. Lift the weight by pumping the handle several times. Make sure that the weight is high enough so that it does not interfere with a complete stroke of the handle. Record the weight including the weight of the platform and bar (11.1 lbf). p4. Measure the distance traveled by the pump piston in one stroke of the handle by standing a ruler up next to the pump and noting how far the wire marker moves during a pump stroke. p5. Measure the distance traveled by the ram piston (ram plunger) in three pumps of the handle by standing a ruler up next to the pump and noting how far the wire marker moves during the pump strokes. Calculations: c1. Sketch a free body diagram of the ram piston. c2. Calculate the pressure in the hydraulic fluid in the chamber between the pump piston and the ram piston using the free body diagram of the ram piston. c3. Sketch a free body diagram of the pump piston and handle assembly (including the pivot point and the pump piston connection). c4. Calculate the minimum force that needs to be applied to the mark on the handle for the given weight based on the free body diagram in c3 by summing the moments about the pivot point. c5. Calculate the work done by the pump piston in one stroke of the handle. c6. Calculate the work done by the ram piston in one stroke of the handle. (You measured the travel for three strokes of the handle so you need to divide this measurement by 3 before calculating the work). Write-Up: Include the following in your write-up: 1. Calculation of the pressure in the hydraulic fluid (c1 and c2). 2. Calculation of the minimum force applied at the mark on the handle to lift the weight (c3 and c4). 3. Calculation of the work done by the pump piston and the ram piston (c5 and c6). 4. Discuss briefly (a few sentences per topic) Describe how the hydraulic jack works. What is the function of each of the three valves? Why is the work done by both pistons the same? In an analysis of the hydraulic jack we neglected friction due to o-rings, hinges, etc. Why can we do this?

9 5. Hydraulic Jack Data Sheet

10 HYDRAULIC JACK DATA SHEET rh= in. rp= in. dr= in. dp= in. W= lbf. dist pump = in. dist ram = in. distance from mark on handle to pivot pt. distance from pump piston connection to pivot pt. diameter of ram cylinder (not the piston) diameter of pump cylinder (not the piston) weight including weight platform and bar distance traveled by pump(1 stroke of pump) distance traveled by ram(3 strokes of pump) Note any apparant sources of error in your measurements:

11 Appendix: Fluid Statics When a fluid has no motion at all, the pressure gradient in the fluid balances the body forces in the fluid. This can be expressed mathematically as p = ρ f (1), where is the vector gradient operator, p is the pressure, ρ is the fluid density, and f is the vector body force. The most common body force is gravity. If z is positive upward from the surface of the earth, then the body force f is the acceleration of gravity, g, in the negative z direction. The body force is zero in the x and y direction. Equation (1) becomes dp dz = - ρ g (2). The minus sign on the right hand side results from the acceleration of gravity in the negative z direction. If the density and acceleration of gravity are independent of z (which they usually are in a laboratory situation), equation (2) can be integrated to p2-p1= - ρ g (z2-z1) (3). Manometry: From equation (3) it is apparent that the height of a static fluid column can be used to measure a pressure difference, if the density of the fluid is known. This is the basis of a device known as a manometer. In a manometer, the difference in height of fluid in the legs of a U-tube indicate the difference in pressure applied to each of the two legs. Consider the example shown below. p = p 2 atm p 1 g z 1 z 2 z=0 The left leg of the manometer is exposed to an unknown pressure p1. The pressure in the right leg is atmospheric, so p2=patm. The coordinates z1 and z2 are measured from an arbitrary reference plane. Substituting into equation (3) results in p1= ρ g (z2 - z1) +patm Multiple fluids in a manometer are handled similarly by careful and consistent application of equation (3). Buoyancy:

12 Two principles, developed by Archimedes in about 300 B.C., describe buoyancy forces on submerged or partially submerged bodies. These two principles are: 1) The buoyant force acting on a body, Fb, equals the weight of the fluid displaced by a body. This can be written as Fb = ρ g Vdisplaced (4), where Vdisplaced is the volume of fluid displaced by the body. 2) A floating body displaces its own weight in fluid. This is written as W = ρ g Vdisplaced (5), where W is the weight of the body. Forces on submerged plane surfaces: The fluid static pressure will exert a resultant force on a submerged surface that is given by F = p da A (6), where A is the "wetted" area over which the pressure acts. Consider the submerged plane surface shown below. Free Surface p = p =0 atm h θ point O y=0 da g h c Resultant force F y c y p Plane with surface area A y Here the coordinate y is parallel to the plane at angle θ with respect to the fluid surface. The depth to an incremental area, da, is h. Assuming that the reference plane is at the surface, we substitute z1=0, p1=patm=0, and z2=-h=(y sin θ) into equation (3) to obtain the pressure, p, acting on da at any arbitrary z2 on the surface as p = ρ g y sin θ (7).

13 Substituting (7) into (6) yields F = ρ g sin θ y da A (8). But the integral is simply the centroid of the surface times the area of the surface, yc A. The quantity in brackets is the depth of the centroid of the surface, hc, times the area of the surface, since hca = (ycent sin θ) A. Now (8) can be rewritten as F = ρ g hc A (9). Thus, all that is needed to calculate the force on the submerged plane surface is the area of the surface that is in contact with the fluid, A, and the distance from the fluid surface to the centroid of the surface, hc. Now the question that remains is where does the resultant force, F, act on the submerged surface? This can be answered by considering the moment balance about point O, where yp is the distance parallel to the surface to the center of pressure where F acts. The moment balance is y p F = y df A (10). Noting that df = p da and using (7) and (9), equation (10) can be rewritten as Simplifying results in y p (ρ g h c A) = y (ρ g y sin θ) da A (11). y p h c A = sin θ y 2 da A (12). But the integral is simply the moment of inertia about the horizontal axis, Ix, where x is perpendicular to the plane of the paper through point O. Noting that Ix = Ixc + yc 2 A, where Ixc is the moment of inertia about the centroidal horizontal axis, (12) can be rewritten as yp hc A = sin θ Ixc + sin θ yc 2 A (13). But hc = sin θ yc so we can finally write y p - y c = I xc y c A (14). Equation (14) gives the position of the position where a single force, F, equivalent to the distributed hydrostatic force would be applied.

### Hydrostatic. Pressure distribution in a static fluid and its effects on solid surfaces and on floating and submerged bodies.

Hydrostatic Pressure distribution in a static fluid and its effects on solid surfaces and on floating and submerged bodies. M. Bahrami ENSC 283 Spring 2009 1 Fluid at rest hydrostatic condition: when a

### Static Forces on Surfaces-Buoyancy. Fluid Mechanics. There are two cases: Case I: if the fluid is above the curved surface:

Force on a Curved Surface due to Hydrostatic Pressure If the surface is curved, the forces on each element of the surface will not be parallel (normal to the surface at each point) and must be combined

### 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

### 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

### 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;

### Upthrust and Archimedes Principle

1 Upthrust and Archimedes Principle Objects immersed in fluids, experience a force which tends to push them towards the surface of the liquid. This force is called upthrust and it depends on the density

### 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

### P = ρ{ g a } + µ 2 V II. FLUID STATICS

II. FLUID STATICS From a force analysis on a triangular fluid element at rest, the following three concepts are easily developed: For a continuous, hydrostatic, shear free fluid: 1. Pressure is constant

### 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

### 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

### SCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER 1 EXAMINATIONS 2012/2013 XE121. ENGINEERING CONCEPTS (Test)

s SCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER EXAMINATIONS 202/203 XE2 ENGINEERING CONCEPTS (Test) Time allowed: TWO hours Answer: Attempt FOUR questions only, a maximum of TWO questions

### 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

### VALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR DEPARTMENT OF MECHANICAL ENGINEERING

VALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR 603203 DEPARTMENT OF MECHANICAL ENGINEERING BRANCH: MECHANICAL YEAR / SEMESTER: I / II UNIT 1 PART- A 1. State Newton's three laws of motion? 2.

### Physics 6A Lab Experiment 6

Biceps Muscle Model Physics 6A Lab Experiment 6 APPARATUS Biceps model Large mass hanger with four 1-kg masses Small mass hanger for hand end of forearm bar with five 100-g masses Meter stick Centimeter

### FORCE & MOTION Instructional Module 6

FORCE & MOTION Instructional Module 6 Dr. Alok K. Verma Lean Institute - ODU 1 Description of Module Study of different types of forces like Friction force, Weight force, Tension force and Gravity. This

### Newton s Second Law Physics Lab V

Newton s Second Law Physics Lab V Objective The Newton s Second Law experiment provides the student a hands on demonstration of forces in motion. A formulated analysis of forces acting on a dynamics cart

### 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

### Fluid Mechanics. Chapter 12. PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman

Chapter 12 Fluid Mechanics PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 12 To study the concept of density

### Demonstrating Archimedes Principle

Demonstrating Archimedes Principle Archimedes Principle states that a floating body will displace its own weight of liquid. In this first exercise we will test this idea by comparing the masses of different

### 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

### THE SCREW GAUGE. AIM: To learn to use a Screw Gauge and hence use it to find the dimensions of various regular materials given.

EXPERIMENT NO: DATE: / / 0 THE SCREW GAUGE AIM: To learn to use a Screw Gauge and hence use it to find the dimensions of various regular materials given. APPARUTUS: Given a Screw Gauge, cylindrical glass

### 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

### MARIA REGINA COLLEGE

MARIA REGINA COLLEGE PHYSICS Creative, Innovative, Professional HALF YEARLY EXAMINATION 2017 YEAR: 9 TRACK / LEVEL: 3 TIME: 1 hr 30 mins NAME: CLASS: Answer ALL questions in the spaces provided on the

### Aerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved)

Flow with no friction (inviscid) Aerodynamics Basic Aerodynamics Continuity equation (mass conserved) Flow with friction (viscous) Momentum equation (F = ma) 1. Euler s equation 2. Bernoulli s equation

### DIMENSIONS AND UNITS

DIMENSIONS AND UNITS A dimension is the measure by which a physical variable is expressed quantitatively. A unit is a particular way of attaching a number to the quantitative dimension. Primary Dimension

### Physics 201 Lab 9: Torque and the Center of Mass Dr. Timothy C. Black

Theoretical Discussion Physics 201 Lab 9: Torque and the Center of Mass Dr. Timothy C. Black For each of the linear kinematic variables; displacement r, velocity v and acceleration a; there is a corresponding

### CHIEF ENGINEER REG III/2 APPLIED MECHANICS

CHIEF ENGINEER REG III/2 APPLIED MECHANICS LIST OF TOPICS A B C D E F G H I J Vector Representation Statics Friction Kinematics Dynamics Machines Strength of Materials Hydrostatics Hydrodynamics Control

### SECOND ENGINEER REG. III/2 APPLIED MECHANICS

SECOND ENGINEER REG. III/2 APPLIED MECHANICS LIST OF TOPICS Static s Friction Kinematics Dynamics Machines Strength of Materials Hydrostatics Hydrodynamics A STATICS 1 Solves problems involving forces

### 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

### FORCE TABLE INTRODUCTION

FORCE TABLE INTRODUCTION All measurable quantities can be classified as either a scalar 1 or a vector 2. A scalar has only magnitude while a vector has both magnitude and direction. Examples of scalar

### PHY 221 Lab 5 Diverse Forces, Springs and Friction

Name: Partner: Partner: PHY 221 Lab 5 Diverse Forces, Springs and Friction Goals: To explore the nature of forces and the variety of ways in which they can be produced. Characterize the nature of springs

### EQUILIBRIUM OBJECTIVES PRE-LECTURE

27 FE3 EQUILIBRIUM Aims OBJECTIVES In this chapter you will learn the concepts and principles needed to understand mechanical equilibrium. You should be able to demonstrate your understanding by analysing

### 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 (

### Physics 1020 Experiment 6. Equilibrium of a Rigid Body

1 2 Introduction Static equilibrium is defined as a state where an object is not moving in any way. The two conditions for the equilibrium of a rigid body (such as a meter stick) are 1. the vector sum

### Chapter 10: Friction A gem cannot be polished without friction, nor an individual perfected without

Chapter 10: Friction 10-1 Chapter 10 Friction A gem cannot be polished without friction, nor an individual perfected without trials. Lucius Annaeus Seneca (4 BC - 65 AD) 10.1 Overview When two bodies are

### 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,

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) You are standing in a moving bus, facing forward, and you suddenly fall forward as the

### Static Equilibrium and Torque

10.3 Static Equilibrium and Torque SECTION OUTCOMES Use vector analysis in two dimensions for systems involving static equilibrium and torques. Apply static torques to structures such as seesaws and bridges.

### Projectile Motion (Photogates)

Projectile Motion (Photogates) Name Section Theory Projectile motion is the combination of different motions in the x and y direction. In the x direction, which is taken as parallel to the surface of the

### TutorBreeze.com 7. ROTATIONAL MOTION. 3. If the angular velocity of a spinning body points out of the page, then describe how is the body spinning?

1. rpm is about rad/s. 7. ROTATIONAL MOTION 2. A wheel rotates with constant angular acceleration of π rad/s 2. During the time interval from t 1 to t 2, its angular displacement is π rad. At time t 2

### Lab 4: Gauss Gun Conservation of Energy

Lab 4: Gauss Gun Conservation of Energy Before coming to Lab Read the lab handout Complete the pre-lab assignment and hand in at the beginning of your lab section. The pre-lab is written into this weeks

### PORTMORE COMMUNITY COLLEGE

PORTMORE COMMUNITY COLLEGE ASSOCIATE DEGREE IN ENGINEERING TECHNOLOGY RESIT EXAMINATIONS SEMESTER 2 July 2012 COURSE NAME: Mechanical Engineering Science CODE: GROUP: ADET 1 DATE: July 3, 2012 TIME: DURATION:

### THERMODYNAMICS, FLUID AND PLANT PROCESSES. The tutorials are drawn from other subjects so the solutions are identified by the appropriate tutorial.

THERMOYNAMICS, FLUI AN PLANT PROCESSES The tutorials are drawn from other subjects so the solutions are identified by the appropriate tutorial. SELF ASSESSMENT EXERCISE No.1 FLUI MECHANICS HYROSTATIC FORCES

### Copyright 2008, University of Chicago, Department of Physics. Experiment I. RATIO OF SPECIFIC HEATS OF GASES; γ C p

Experiment I RATIO OF SPECIFIC HEATS OF GASES; γ C p / C v 1. Recommended Reading M. W. Zemansky, Heat and Thermodynamics, Fifth Edition, McGraw Hill, 1968, p. 122-132, 161-2. 2. Introduction You have

### Physics 2210 Homework 18 Spring 2015

Physics 2210 Homework 18 Spring 2015 Charles Jui April 12, 2015 IE Sphere Incline Wording A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle

### 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

### 150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces

Fluid Statics Pressure acts in all directions, normal to the surrounding surfaces or Whenever a pressure difference is the driving force, use gauge pressure o Bernoulli equation o Momentum balance with

### AP Physics C: Rotation II. (Torque and Rotational Dynamics, Rolling Motion) Problems

AP Physics C: Rotation II (Torque and Rotational Dynamics, Rolling Motion) Problems 1980M3. A billiard ball has mass M, radius R, and moment of inertia about the center of mass I c = 2 MR²/5 The ball is

### 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

### PART 1B EXPERIMENTAL ENGINEERING. SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) BOUNDARY LAYERS AND DRAG

1 PART 1B EXPERIMENTAL ENGINEERING SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) EXPERIMENT T3 (LONG) BOUNDARY LAYERS AND DRAG OBJECTIVES a) To measure the velocity

### Torques and Static Equilibrium

Torques and Static Equilibrium INTRODUCTION Archimedes, Greek mathematician, physicist, engineer, inventor and astronomer, was widely regarded as the leading scientist of the ancient world. He made a study

### 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

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

### Dynamics; Newton s Laws of Motion

Dynamics; Newton s Laws of Motion Force A force is any kind of push or pull on an object. An object at rest needs a force to get it moving; a moving object needs a force to change its velocity. The magnitude

### Fluids, Continuity, and Bernouli

Fluids, Continuity, and Bernouli Announcements: Exam Tomorrow at 7:30pm in same rooms as before. Web page: http://www.colorado.edu/physics/phys1110/phys1110_sp12/ Clicker question 1 A satellite, mass m,

### Exam 3 Practice Solutions

Exam 3 Practice Solutions Multiple Choice 1. A thin hoop, a solid disk, and a solid sphere, each with the same mass and radius, are at rest at the top of an inclined plane. If all three are released at

### Rotational Inertia (approximately 2 hr) (11/23/15)

Inertia (approximately 2 hr) (11/23/15) Introduction In the case of linear motion, a non-zero net force will result in linear acceleration in accordance with Newton s 2 nd Law, F=ma. The moving object

### Equilibrium. For an object to remain in equilibrium, two conditions must be met. The object must have no net force: and no net torque:

Equilibrium For an object to remain in equilibrium, two conditions must be met. The object must have no net force: F v = 0 and no net torque: v τ = 0 Worksheet A uniform rod with a length L and a mass

### CENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer

CENG 501 Examination Problem: Estimation of Viscosity with a Falling - Cylinder Viscometer You are assigned to design a fallingcylinder viscometer to measure the viscosity of Newtonian liquids. A schematic

### 1301W.600 Lecture 16. November 6, 2017

1301W.600 Lecture 16 November 6, 2017 You are Cordially Invited to the Physics Open House Friday, November 17 th, 2017 4:30-8:00 PM Tate Hall, Room B20 Time to apply for a major? Consider Physics!! Program

### CHAPTER 3: SURFACE AND INTERFACIAL TENSION. To measure surface tension using both, the DuNouy ring and the capillary tube methods.

CHAPTER 3: SURFACE AND INTERFACIAL TENSION Objective To measure surface tension using both, the DuNouy ring and the capillary tube methods. Introduction In a fluid system, the presence of two or more phases

### Fluid Mechanics. Chapter 14. Modified by P. Lam 6_7_2012

Chapter 14 Fluid Mechanics PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 6_7_2012 Goals for Chapter 14 To study

### CHAPTER 2 Pressure and Head

FLUID MECHANICS Gaza, Sep. 2012 CHAPTER 2 Pressure and Head Dr. Khalil Mahmoud ALASTAL Objectives of this Chapter: Introduce the concept of pressure. Prove it has a unique value at any particular elevation.

### 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

### 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)

### 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.

### [1] (b) State why the equation F = ma cannot be applied to particles travelling at speeds very close to the speed of light

1 (a) Define the newton... [1] (b) State why the equation F = ma cannot be applied to particles travelling at speeds very close to the speed of light... [1] (c) Fig. 3.1 shows the horizontal forces acting

### Models and Anthropometry

Learning Objectives Models and Anthropometry Readings: some of Chapter 8 [in text] some of Chapter 11 [in text] By the end of this lecture, you should be able to: Describe common anthropometric measurements

### Types of Forces. Pressure Buoyant Force Friction Normal Force

Types of Forces Pressure Buoyant Force Friction Normal Force Pressure Ratio of Force Per Unit Area p = F A P = N/m 2 = 1 pascal (very small) P= lbs/in 2 = psi = pounds per square inch Example: Snow Shoes

### Experiment 2 Vectors. using the equations: F x = F cos θ F y = F sin θ. Composing a Vector

Experiment 2 Vectors Preparation Study for this week's quiz by reviewing the last experiment, reading this week's experiment carefully and by looking up force and vectors in your textbook. Principles A

### End-of-Chapter Exercises

End-of-Chapter Exercises Exercises 1 12 are conceptual questions that are designed to see if you have understood the main concepts of the chapter. 1. When a spring is compressed 10 cm, compared to its

### Forces I. Newtons Laws

Forces I Newtons Laws Kinematics The study of how objects move Dynamics The study of why objects move Newton s Laws and Forces What is force? What are they? Force A push or a pull Symbol is F Unit is N

### = o + t = ot + ½ t 2 = o + 2

Chapters 8-9 Rotational Kinematics and Dynamics Rotational motion Rotational motion refers to the motion of an object or system that spins about an axis. The axis of rotation is the line about which the

### A Physical Introduction to Fluid Mechanics. Study Guide and Practice Problems Spring 2017

A Physical Introduction to Fluid Mechanics Study Guide and Practice Problems Spring 2017 A Physical Introduction to Fluid Mechanics Study Guide and Practice Problems Spring 2017 by Alexander J. Smits

### Physics, Chapter 3: The Equilibrium of a Particle

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1958 Physics, Chapter 3: The Equilibrium of a Particle

### PLANNING EXPERIMENT (SECTION B)

SIMPLE PENDULUM OF Period depends on length of pendulum Length increase, period increase To investigate the relationship between period and length of pendulum MV : length of pendulum RV : period FV : angle

### Ph1a: Solution to the Final Exam Alejandro Jenkins, Fall 2004

Ph1a: Solution to the Final Exam Alejandro Jenkins, Fall 2004 Problem 1 (10 points) - The Delivery A crate of mass M, which contains an expensive piece of scientific equipment, is being delivered to Caltech.

### Physics 207 Lecture 25. Lecture 25. HW11, Due Tuesday, May 6 th For Thursday, read through all of Chapter 18. Angular Momentum Exercise

Lecture 5 Today Review: Exam covers Chapters 14-17 17 plus angular momentum, rolling motion & torque Assignment HW11, Due Tuesday, May 6 th For Thursday, read through all of Chapter 18 Physics 07: Lecture

### Acid-Base Titration. Evaluation copy

Acid-Base Titration Computer 7 A titration is a process used to determine the volume of a solution that is needed to react with a given amount of another substance. In this experiment, your goal is to

### UNIT D: MECHANICAL SYSTEMS

1 UNIT D: MECHANICAL SYSTEMS Science 8 2 Section 2.0 AN UNDERSTANDING OF MECHANICAL ADVANTAGE AND WORK HELPS IN DETERMINING THE EFFICIENCY OF MACHINES. 1 3 MACHINES MAKE WORK EASIER Topic 2.1 4 WHAT WOULD

### 13-Nov-2015 PHYS Rotational Inertia

Objective Rotational Inertia To determine the rotational inertia of rigid bodies and to investigate its dependence on the distance to the rotation axis. Introduction Rotational Inertia, also known as Moment

### Empirical Gas Laws (Parts 1 and 2) Pressure-volume and pressure-temperature relationships in gases

Empirical Gas Laws (Parts 1 and 2) Pressure-volume and pressure-temperature relationships in gases Some of the earliest experiments in chemistry and physics involved the study of gases. The invention of

### Hint 1. The direction of acceleration can be determined from Newton's second law

Chapter 5 [ Edit ] Overview Summary View Diagnostics View Print View with Answers Chapter 5 Due: 11:59pm on Sunday, October 2, 2016 To understand how points are awarded, read the Grading Policy for this

### Name Period. What force did your partner s exert on yours? Write your answer in the blank below:

Nae Period Lesson 7: Newton s Third Law and Passive Forces 7.1 Experient: Newton s 3 rd Law Forces of Interaction (a) Tea up with a partner to hook two spring scales together to perfor the next experient:

### Chapter 10. Rotation

Chapter 10 Rotation Rotation Rotational Kinematics: Angular velocity and Angular Acceleration Rotational Kinetic Energy Moment of Inertia Newton s nd Law for Rotation Applications MFMcGraw-PHY 45 Chap_10Ha-Rotation-Revised

### Solution The light plates are at the same heights. In balance, the pressure at both plates has to be the same. m g A A A F A = F B.

43. A piece of metal rests in a toy wood boat floating in water in a bathtub. If the metal is removed from the boat, and kept out of the water, what happens to the water level in the tub? A) It does not

### Rotational Motion. 1 Purpose. 2 Theory 2.1 Equation of Motion for a Rotating Rigid Body

Rotational Motion Equipment: Capstone, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME-9472), string with loop at one end and small white bead at the other end (125 cm bead

### Chapter 4: Newton s Second Law F = m a. F = m a (4.2)

Lecture 7: Newton s Laws and Their Applications 1 Chapter 4: Newton s Second Law F = m a First Law: The Law of Inertia An object at rest will remain at rest unless, until acted upon by an external force.

### 2.1 Forces and Free-Body Diagrams

2.1 Forces and Free-Body Diagrams A is a push or a pull. Forces act on objects, and can result in the acceleration, compression, stretching, or twisting of objects. Forces can also act to stabilize an

### 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

### ELASTIC STRINGS & SPRINGS

ELASTIC STRINGS & SPRINGS Question 1 (**) A particle of mass m is attached to one end of a light elastic string of natural length l and modulus of elasticity 25 8 mg. The other end of the string is attached

### 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

### Q1. A) 46 m/s B) 21 m/s C) 17 m/s D) 52 m/s E) 82 m/s. Ans: v = ( ( 9 8) ( 98)

Coordinator: Dr. Kunwar S. Wednesday, May 24, 207 Page: Q. A hot-air balloon is ascending (going up) at the rate of 4 m/s and when the balloon is 98 m above the ground a package is dropped from it, vertically

### Topic: Fluids PHYSICS 231

Topic: Fluids PHYSICS 231 Key Concepts Density, Volume, Mass density as material property Pressure units, how to measure, direction Hydrostatic pressure in liquid on earth Buoyancy and Archimedes Principle

### Fluid Mechanics. Spring Course Outline

Fluid Mechanics (Fluidmekanik) Course Code: 1TV024 5 hp Fluid Mechanics Spring 2011 Instruct: Chris Hieronymus Office: Geocentrum Dk255 Phone: 471 2383 email: christoph.hieronymus@geo.uu.se Literature:

### Name Date: Course number: MAKE SURE TA & TI STAMPS EVERY PAGE BEFORE YOU START. Laboratory Section: Partners Names: Last Revised on December 15, 2014

Laboratory Section: Partners Names: Last Revised on December 15, 2014 Grade: EXPERIMENT 7 Absolute Volt & Electrostatic Potential 0. Pre-Lab Homework [2 pts] 1. In the first part of this lab you will be

### 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

### 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

### Written Homework problems. Spring (taken from Giancoli, 4 th edition)

Written Homework problems. Spring 014. (taken from Giancoli, 4 th edition) HW1. Ch1. 19, 47 19. Determine the conversion factor between (a) km / h and mi / h, (b) m / s and ft / s, and (c) km / h and m