HERIOT-WATT UNIVERSITY SCHOOL OF ENGINEERING AND PHYSICAL SCIENCES (MECHANICAL ENGINEERING) MECHANICAL ENGINEERING SCIENCE 3 (B58EC1) DYNAMICS LABORATORY : WHEEL AND AXLE ACCELERATION

Objective: To predict the time taken for a wheel to roll on its axle, down a slope using energy methods Theory: Energy Method Release Ød or radius r After descent h v m/sec m kg I kg.m2 ØD or radius R

Figure 1. Energy in a rolling wheel Referring to Figure 1 when the wheel is released from rest and subsequently rolls down the slope, it accelerates and hence gains energy. Now for a rolling wheel the kinetic energy has two components, translational due to the bodily movement of the mass centre down the slope and rotational due to the wheel spin. Now the source of this energy is the loss in potential energy as the wheel moves down the slope. If it is reasonable to assume that friction effects are insignificant then no energy is lost. Thus the loss in potential energy becomes a gain in kinetic energy. Hence, Loss in potential energy = mgh, is equal to the Gain in kinetic energy = 0.5mv2 + 0.5Iω 2 where v = velocity of the mass centre down slope (m/sec) ω = angular velocity of wheel (rad/sec) = v/r, r is the axle radius when rolling I = Polar moment of inertia = mR2/2 (1) (2)

Applying conservation of energy, equate equations 1 and 2 to derive an expression for the velocity v at the bottom of the slope. Using the linear equations of motion, find the expression for time t. Show these derivations in your report.

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Experiment: Using the measured distances (100mm to 500mm, intervals of 100mm) travelled by the wheel and the expressions i.e. (1) velocity at bottom of slope and (2) acceleration down the slope, calculate the time taken for the wheel to roll down the slope. Compare the calculated values with the experimental data Discussions: Plot a graph of time t2 vs distance s for calculated and experimental data. Explain the discrepancies between calculated values and...

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Wheel/axle assembly report
Contents
1. Terms of reference
This report is completed as requirement for the outcome two Relationship between Linear and Angular Motion.
A rotating wheel travelling along a surface has both angular motion and linear motion. Hence it will possess kinetic energy due to its linear velocity called kinetic energy of translation, and kinetic energy due to its angular velocity called kinetic energy of rotation. The aim of this report is to define differences between measured and theoretical distance travelled by the wheel used during an experiment.
2. Procedure
2.1. Apparatus
Electric motor
Voltmeter/ammeter
Optical tachometer
Wooden ramp
Axle assembly
Stopwatch
Measure tape
2 pen Y/T recorder
2.2. Method
In order to carry out experiment electric motor was connected to axle assembly and optical tachometer was used to record rpm of the axle in the same time value of V and A were recorded by 2 pen Y/T recorder. Time taken by the axle assembly to travel up the ramp was recorded by one of the students using a stopwatch. Stopwatch was started when axle assembly touched the ramp and stopped when wheels travelling up the slope. Then place in which...

...Semester (s)1 and 2 |
Laboratory TitleWheel and Axle Acceleration |
Objective: To predict the time taken for a wheel to roll on its axle, down a slope using the energy method.
Theory:
Release
Energy Method
Ød or radius r
After descent
m kg
I kg.m2
h
v m/sec
ØD or radius R
Figure 1. Energy in a rolling wheel
Referring to Figure 1 when the wheel is released from rest and subsequently rolls down the slope, it accelerates and hence gains energy. Now for a rolling wheel the kinetic energy has two components, translational due to the bodily movement of the mass centre down the slope and rotational due to the wheel spin. Now the source of this energy is the loss in potential energy as the wheel moves down the slope. If it is reasonable to assume that friction effects are insignificant then no energy is lost. Thus the loss in potential energy becomes a gain in kinetic energy.
Hence,
Loss in potential energy = mgh, is equal to the (1)
Gain in kinetic energy = 0.5mv2 + 0.5I 2 (2)
where v = velocity of the mass centre down slope (m/sec)
= angular velocity of wheel (rad/sec)
= v/r, r is the axle radius when rolling
I = Polar moment of inertia = mR2/2
Applying conservation of energy, equate equations 1 and 2 to derive an expression for the velocity v at the bottom of the slope....

...Table of Contents
Abstract……………………………………………………………………………………………2
Introduction………………………………………………………………………………………..2
Background………………………………………………………………………………..2
Objectives…………………………………………………………………………………2
Scope………………………………………………………………………………………3
Theory review……………………………………………………………………………………..3
Design of report…………………………………………………………………………………...5
Procedures…………………………………………………………………………………………5
Results……………………………………………………………………………………………..6
Discussion…………………………………………………………………………………………6
Conclusion………………………………………………………………………………………...7
Reference……………………………………………………………………………………….....7
Appendix…………………………………………………………………………………………..7
ABSTRACT
This experiment introduces the use of dimensionless analysis and conventionally analytical method to survey the performance of centrifugal pump. The end of this experiment points out the benefit of using the “new” method to the conventional in most practical problem, especially in the survey of turbo-machine. Also, through this experiment, students know some basic indexes to assess the efficiency of pumps used. We will that for the specific fan conducting this experiment, the best efficiency point occurs at CQ = 0.2, the specific speed NS ~1.23.
INTRODUCTION
Background
A fan is a turbo-machine in which work is done to increase the total pressure of the fluid leaving the device. This is achieved by a rotor or impeller, which is driven by an external source of power to move a row of blades so as to...

...Daphny Maldonado
Bio Lab 2107
Kiah Britton
W 10-12:30
Is H20 Bad for You?
Abstract:
In the village of Gopher Hollow there’s a cluster of Blue Baby Syndrome. There were
four infants affected by this cluster. The families from the infants would collect their
water from wells. We have to determine what’s the source of the high levels of nitrites in
the water. The four sources that could be the point of contamination are a new
subdivision, textile plant, an organic farm, and a mountain lake. We had to ﬁnd the
concentration of each known standard and unknown standard. We did this by using a
spectrophotometer. The results were the following, the organic farm with a herd of 50
cows and a 10 acre ﬁeld of zucchini had the highest levels of nitrites.
Introduction:
Blue Baby Syndrome is a condition that affects many infants. This condition makes
the baby’s skin turn blue because of the lack of oxygen. This condition can exhibit
lethargy, vomiting and not being able to breathe. It can even lead to death in rare cases.
This condition is caused by the excess amount of nitrate that is then converted into
nitrite by the digestive system. The hemoglobin then reacts with the nitrites to form
Methemoglobin. Methemoglobin is not a problem in adults since they have an enzyme
that converts methemoglobin back to hemoglobin. Infants don’t have many of the
enzyme to convert methemoglobin to hemoglobin, resulting in Blue Baby Syndrome. For
example in Gopher...

...
Objective: the purpose of this lab is to investigate the law of conservation of energy. This can be achieved by measuring both potential and kinetic energy through the experiment conducted.
Back ground:
Kinetic energy is said to be the energy of motion. Kinetic energy can be defined through this equation:
KE=12mv2 (equation 1)
Where m is the mass of the object in motion, and v is the velocity of the moving object.
Potential energy is the energy associated with the forces that depend on the position of the object. However, there are specific types of potential energy and in this lab we will consider gravitational potential energy. Gravitational potential energy is the energy possessed by the objected due to earth's gravity. This can be specifically defined by the equation:
PEgrav=mgy (equation 2)
Where m is the mass of the object, g is the acceleration due to gravity and y is the height of the object.
With these energies defined, total energy of the system is the sum of its kinetic energy and potential energy at any point in time.
Total energy= kinetic energy+ potential energy=constant
Therefore the law of conservation of energy is defined as: the total energy is neither increased nor decreased in any process. Energy can be transformed from one to another, and transferred from one object to another, but the total amount remained constant, therefore conserve.
Procedure:
the procedure of this...

...Experiment Title: Torsion Vibration.
Introduction : Torsion is the twisting of a metallic rod shaped object, when a torque is applied on two sides’ perpendicular to the radius of a uniform cross-sectional bar.
Objective : Determining the natural frequency of a system undergoing tortional vibration.
Theory : Using Newton’s second law of tortional system.
( [pic] …………………. ( Equation 1 )
where Io = mass moment of inertia of the disk
Hence, [pic] ……..……... ( Equation 2 )
where k = torsional stiffness of the shaft
Rearrange Equation 2
( [pic] .………..……... ( Equation 3 )
where natural frequency of the system,
[pic] …..…….…..……... ( Equation 4 )
From Simple Theory of Torsion, [pic]
where T = Applied torque J = Polar second moment of area
[pic] = Shear stress R = Radius of shaft
G = Shear modulus [pic] = Angle of twist
L = Length of shaft
As torsional stiffness [pic], it can be determined through [pic] ………….. ( Equation 5 )
Apparatus :
• One solid circular disk with mass = 4.536kg, diameter = 150mm and thickness = 30mm.
• One annular circular disk with mass 1.89kg, outer diameter 150mm, inner diameter = 110mm and thickness = 30mm.
• Two chucks; one steel rod; one stopwatch....

...INTRODUCTION
In hydroelectric power plant, turbine been used to generate power from reservoir of water. Turbine been selected by their characteristic curves based on the potential energy available in the water and the amount of power to be generated. Turbine is a type that develops torque by reacting to the pressure or weight of a fluid. The operation of reaction turbine can be describes by the Newton’s third law of motion that is for every action, there is an equal and opposite reaction. In this experiment, the main objectives are to study the characteristic curves of a reaction turbine.
Reaction turbine can be defined as a turbine with blades arranged to develop torque form gradual decrease of steam pressure from inlet to exhaust. When the velocity of a fluid is changed, the reaction forces are exerted like a simple nozzle when the fluid accelerated due to the changes in the cross sectional area. The kinetic energy of the fluid increases and since energy is conserved, the pressure of the fluid drops. This is meant that the pressure behind the fluid forces it through the nozzle causing it to speed up. The accelerated fluid in the direction of acceleration is required by force. Every force has an equal and opposite reaction so an equal and opposite force is exerted on the nozzle. There are three types of reaction turbine, in this experiment the radial flow reaction turbine been use. The radial flow reaction turbine has the liquid mainly in a plane perpendicular to the...

...solution with small amounts of H30+ and A- because only a small amount of base has been added therefore a small amount of ionization has occurred. As we added more base, more HA is ionized and more salt formation occurs meaning the concentration of HA will decrease while the concentration of A- will increase. The pH rises above the equivalence point because we are adding base to a solution with a relatively large volume. At the end of the titration the ratio of [A-]/[HA] goes from low to high. This means that all of the HA will be neutralized, causing the pH to change. Because of the rapid pH change around the equivalence point, the titrant has to be added in lesser and lesser amounts as we approach the equivalence point.
Procedure:
CHM 113 Lab Manual, 2014, Determination of : Titration of a Weak Acid, pgs.89-96
Equations/Experimental Equipment and Apparatus:
LoggerPro, LabPro, pH probe, drop counter, 60 mL reagent reservoir, stir station
=p
Data and Observations:
Data:
Original pH=3.23
Equivalence volume = 50.51 mL at pH of 8.58
Drop rate: 1 drop every 2 seconds
Observations:
In the beginning of the titration the solution was made up of mostly acetic acid with a small amount of and because ionization was starting to occur. As the titration progressed, we watched the graph on the computer and saw the pH increase and then rise very slowly. This slow rise continued for a long period of time. After this portion of the graph, the pH increased...