A ball of unknown mass m is tossed straight up with initial speed v. At the moment it is released, the ball is a height h above a spring-mounted platform, as shown in the figure below. The ball rises, peaks, and falls back toward the platform, ultimately compressing the spring a maximum distance d from its relaxed position. Assume that the spring is perfectly ideal with spring constant k, and that the mass of the spring and platform is negligible.

What is the mass m, assuming that there is no friction or air resistance? Using g to represent the acceleration due to gravity, enter an expression for m in terms of g, h, d, k, and v.

Using g to represent the acceleration due to gravity, enter the expression for m in terms of g, h, d, k, and v.

5. Equations of the form y’ = P(x)*y^2 + Q(x)*y + R(x) are called Riccati equations.

i) If we know a solution y = φ(x) of this equation, then any other solution

can be written in the form y(x) = φ(x)+ 1/v(x), where v(x) is an unknown

function which satisfies a certain linear equation. Using the fact that

φ and y both solve the above Riccati equation, find the differential

equation that v satisfies.

ii) Consider the equation 3y’ + y^2 +2/(x^2) = 0. Find one solution of this equation by inspection.

iii) Use the method of part(i) to find the general solution of the equation

in (ii).

A student wishes to determine the chloride ion concentration in a water sample at 25 °C using a galvanic cell constructed with a graphite electrode and a half-cell of AgCl(s) + e⁻ → Ag(s) + Cl⁻(aq) E°red = 0.2223 V And a copper electrode with 0.500 M Cu²⁺ as the second half cell Cu²⁺(aq) + 2 e⁻ → Cu(s) E°red= 0.337 V The measured cell potential when the water sample was placed into the silver side of the cell was 0.0657 V.

What is the standard potential of the cell?

What is the value of standard free energy (in kJ) for this reaction?

What is the balanced equation for the overall reaction in acidic solution?

The measured cell potential is 0.0657, what is the concentration of chloride ions in the solution?

A three phase engine has an usable power of 90 kW and an efficiency of 91%. The rating plate indicates the following values:
- 90 kW
- Power factor: 0.89 (i)
- Voltage (volts): 230 delta - 400 wye
Taking as a reference of line voltages V1=V∠90º; direct sequence and a phase oltage of the supply network of 230 V, find:
a) The phasors of the line and phase voltages of the supply network
b) The true, reactive and apparent power
c) The phasors of the line and phase currents
When the engine is connected to a supply network of 400 V and direct sequence, find:
d) The phasors of the line and phase voltages of the supply network
e) The true, reactive and apparent powers
f) The phasors of the line and phase currents

A parallel plate capacitor with plate separation d is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V. (C is the capacitance and U is the stored energy.) Answer the following questions regarding the capacitor charged by a battery. For each statement below, select True or False.

After being disconnected from the battery, inserting a dielectric with κ will increase U.
With the capacitor connected to the battery, decreasing d increases U.
With the capacitor connected to the battery, inserting a dielectric with κ will increase C.
With the capacitor connected to the battery, increasing d increases C.
After being disconnected from the battery, increasing d decreases V.
After being disconnected from the battery, inserting a dielectric with κ will decrease V.

Consider a modification to the DFS procedure such that it returns for an undirected graph
G, the connected components of G. To do this, you will modify the DFS procedure to
• maintain a counter i, initially set in 1, that counts how many connected components we found so
far; and
• on each vertex v ∈ G.V maintain an attribute component indicating to which connected component
number v belong to. That is, when DFS terminates, v.component indicates the component number
1, 2, . . . i that v belongs to.
Answer the following questions:
(a) Write the pseudocode for this slightly modified version of the DFS algorithm
(b) Explain why your algorithm is correct and its running time. You do not need to provide a formal
argument for correctness, but be sure to explain in clear terms.

Three single-phase transformers are used in a Y-Y configuration to supply a load rated 4000 V, and drawing 80 kW at a power factor of 0.72 (lagging), independently of the voltage. Each transformer, rated 14500/2300 V, 40 kVA, has the following parameters in pu: series elements: 0.01 (resistive), 0.06 (inductive); magnetizing branch: 70 (resistive), 20 (inductive).

(a) Assume the transformer is ideal and the phase voltage at the primary is 13000 V. Draw the per phase equivalent circuit of the transformer and load. Give the phase voltage and current. Indicate if the transformer is overloaded. Compute the real and reactive power drawn from the feeder. Draw the per-phase V-I diagram and power diagram seen from the primary side.

(b) Draw the per phase equivalent circuit of the transformer, indicating parameters in pu and Ohm referred to the primary. Draw the equivalent circuit used under no-load and full load conditions seen from the primary side in pu and Ohm. For operation under load, draw the series impedance diagram and compute the impedance in Ohm and angle. Estimate the per phase transformer losses at rated voltage and current in pu and in kW. Find the efficiency for the given load. Indicate the impact on losses and efficiency of using a transformer with a 0.02 pu series reactance and a 100 pu core resistance.

(c) For rated voltage on the primary side and a short circuit across the load with an impedance of 0.10 pu resistive, compute the current in A as seen from the primary side. Draw the V-I diagram. Compute the current if the fault impedance is 0 and compare the 2 values. Indicate, for a 0.10 resistive short, the impact on the fault current of using a transformer with a 0.02 pu series reactance and a 100 pu core resistance. Compare the fault impedance and V-I diagrams.

1.

A parent company be prosecuted because of failures within a subsidiary company

True

False

2.

When an employee is killed while driving on work-related business, the employer organisation could be prosecuted for corporate manslaughter.

True

False

3.

The Corporate Manslaughter and Corporate Homicide Act 2007, is not retrospective and therefore can apply to deaths before its implementation date.

True

False

4.

When deciding what constitutes gross negligence it can be said that negligence turns into gross negligence if the breach of duty falls considerably below what would reasonably be expected of the organisation in the circumstances. Whether the negligence is gross negligence depends upon considerations such as: (tick all that apply)

Any health and safety guidance relating to the breach

The cost of installing safety systems and taking precautions

The attitudes, policies and accepted practices of the organisation which led to the failure

That there were no mitigating factors

Whether other people involved in the incident suffered serious injuries

How serious the failure was

How real the risk of death was

The number of people who died

5.

Historically in larger companies, it was often difficult to prove that the actions of one director or manager controlled the whole company. In the case of large companies, the prosecution often tried to secure a conviction for breach of the Health and Safety at Work Act 1974 which is easier to prove. Which of the cases listed below (which occurred before the CMCHA 2007 )resulted in convictions for corporate manslaughter? (Tick all that apply)

R v Kite, Stoddard and OLL Ltd [1994]

R v Cotswold Geotechnical (Holdings) Ltd [2011]

Tesco Supermarkets Ltd. v Nattrass [1971]

R. v P & O European Ferries (Dover) Ltd. (1990)

Williams v Farne Salmon and Trout Ltd 1988

R v Princes Sporting Club Limited (2013)

Profit maximization does not adequately describe the goal of the firm because

1. Which of the following goals of the firm are synonymous (equivalent) to the maximization of shareholder wealth?
         

   I. profit maximization
   II. risk minimization
   III. maximization of the total market value of the firm's common stock

   IV maximization of market price per share

   
         

   	I.	I and II only
   	II.	II and III only
   	III.	III and IV only
   	IV.	I and III only
   	V.	I and IV only

1. The true owners of the corporation are the

   	I.	holders of debt issues of the firm
   	II.	none of the above
   	III.	common stockholders
   	IV.	board of directors
   	V.	preferred stockholders

Ms Tamika, a financial manager of a corporation, is considering numerous different operating strategies for the coming year.  From a financial management standpoint, which of the following would be her optimal strategy?

Which of the following categories of owners enjoy limited liability?

Which of the following Mechanisms is used by shareholders to motivate management?

1-) Answer the followings;

a-) whenever they live together rather than apart there's more similarity in IQ scores between identical twins, siblings, biological parents and children, and even unrelated individuals. These findings suggest that _______________________ contributes to intelligence.

b-) The _____________ effect refers to the tendency for absolute intelligence to increase over successive generations.

c-) All psychological tests, including intelligence tests, must meet three criteria. Those include ___________, ______________ and __________.

d-) A physchologist administer an intelligence test to a representative group of 500 adults to determine the average performance and develop a set of norms for the test. This will help establish the test criterion of _________________________.

e-) A psychologist administers a personality test to group of college students in September and then has the students take the same test again in November. She then correlates the September scores with the November scores and observes a strong positive correlation between the two set of scores. In terms of the three test criteria, this personality test is ______________________________.

f-) When teachers expect that particular students will excel academicaly, the teacher may unintentionally treat these students in ways that will eilicit high academic performance. Similarly, when teacher expect that particular students will perform poorly in class, the teachers may unintentionally treat these students in ways that will elicit poor academic perofrmance. The process by which these epxectations become reality is called a ________________

g-) In attempting to explain group differences in intellgence scores, Steele had male and female students take a test composed of difficult math questions. When the students were infromed that the questions were an accurate test of mathmetical abilities and limitations, women performed worse than men. However, when the students were told that the questions were simply part of a psychology experiment, men and women performed equally well. These results illustrate a phenomenon known as _______________________________.