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In corporate finance, Hamada’s equation, is used to separate the financial risk of a levered firm from its business risk. Hamada’s equation relates the ... more
The weighted average cost of capital is the rate that a company is expected to pay on average to all its security holders to finance its assets. It is the ... more
Tier 2 capital, or supplementary capital, include a number of important and legitimate constituents of a bank’s capital base. (Undisclosed Reserves ... more
Discounting is a financial mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a ... more
Capital Adequacy Ratio (CAR), also known as Capital to Risk (Weighted) Assets Ratio (CRAR), is the ... more
A time value of money calculation is one which solves for one of several variables in a financial problem. In a typical case, the variables might be: a ... more
The Langmuir equation (also known as the Langmuir isotherm, Langmuir adsorption equation or Hill-Langmuir equation) relates the coverage or adsorption of ... more
An amortization schedule is a table detailing each periodic payment on an amortizing loan (typically a mortgage), as generated by an amortization ... more
The cost of capital is a term used in the field of financial investment to refer to the cost of a company’s funds (both debt and equity). Equity is ... more
Purchasing power (sometimes retroactively called adjusted for inflation) is the number of goods or services that can be purchased with a unit of currency. ... more
Many government agencies and industries (such as aerospace) require the use of a margin of safety (MoS or M.S.) to describe the ratio of the strength of ... more
Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a system during operation. ... more
Many government agencies and industries (such as aerospace) require the use of a margin of safety (MoS or M.S.) to describe the ratio of the strength of ... more
In queueing theory, a discipline within the mathematical theory of probability, Little’s result, theorem, lemma, law, or formula is a theorem by John ... more
Metcalfe’s law states that the value of a telecommunications network is proportional to the square of the number of connected users of the system ... more
The ASME Boiler and Pressure Vessel Code (BPVC) is an American Society of Mechanical Engineers (... more
he ASME Boiler and Pressure Vessel Code (BPVC) is an American Society of Mechanical Engineers (... more
A graveyard orbit, also called a junk orbit or disposal orbit, is a supersynchronous orbit that lies significantly above synchronous orbit, where ... more
In finance, leverage is a general term for any technique to multiply gains and losses. Financial leverage tries to estimate the percentage change in net ... more
a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth its height.
b) Only a fraction of the workers lifted blocks; most were involved in support services such as building ramps, bringing food and water, and hauling blocks to the site. Calculate the efficiency of the workers who did the lifting, assuming there were 1000 of them and they consumed food energy at the rate of 300 Kcal/hour.
first we calculate the number of hours worked per year.
then we calculate the number of hours worked in the 20 years.
Then we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.
The efficiency is the resulting potential energy divided by the consumed energy.
In finance, leverage is a general term for any technique to multiply gains and losses. Most often it involves buying more of an asset by using borrowed ... more
In financial accounting, an asset is an economic resource. Anything tangible or intangible that is capable of being owned or controlled to produce value ... more
Earnings per share is the monetary value of earnings per each outstanding share of a company’s common stock. In business, net income – also ... more
Variable-mass systems, (like a rocket burning fuel and ejecting spent gases), are not closed and cannot be directly treated by making mass a function of ... more
Dividend payout ratio is the fraction of net income a firm pays to its stockholders in dividends. The part of the earnings not paid to investors is left ... more
Dividend cover is the ratio of company’s earnings (net income) over the dividend paid to shareholders, calculated as earnings per share divided by ... more
A typical small rescue helicopter, like the one in the Figure below, has four blades, each is 4.00 m long and has a mass of 50.0 kg. The blades can be approximated as thin rods that rotate about one end of an axis perpendicular to their length. The helicopter has a total loaded mass of 1000 kg. (a) Calculate the rotational kinetic energy in the blades when they rotate at 300 rpm. (b) Calculate the translational kinetic energy of the helicopter when it flies at 20.0 m/s, and compare it with the rotational energy in the blades. (c) To what height could the helicopter be raised if all of the rotational kinetic energy could be used to lift it?
The first image shows how helicopters store large amounts of rotational kinetic energy in their blades. This energy must be put into the blades before takeoff and maintained until the end of the flight. The engines do not have enough power to simultaneously provide lift and put significant rotational energy into the blades.
The second image shows a helicopter from the Auckland Westpac Rescue Helicopter Service. Over 50,000 lives have been saved since its operations beginning in 1973. Here, a water rescue operation is shown. (credit: 111 Emergency, Flickr)
Strategy
Rotational and translational kinetic energies can be calculated from their definitions. The last part of the problem relates to the idea that energy can change form, in this case from rotational kinetic energy to gravitational potential energy.
Solution for (a)
We must convert the angular velocity to radians per second and calculate the moment of inertia before we can find Er . The angular velocity ω for 1 r.p.m is
and for 300 r.p.m
The moment of inertia of one blade will be that of a thin rod rotated about its end.
The total I is four times this moment of inertia, because there are four blades. Thus,
and so The rotational kinetic energy is
Solution for (b)
Translational kinetic energy is defined as
To compare kinetic energies, we take the ratio of translational kinetic energy to rotational kinetic energy. This ratio is
Solution for (c)
At the maximum height, all rotational kinetic energy will have been converted to gravitational energy. To find this height, we equate those two energies:
Discussion
The ratio of translational energy to rotational kinetic energy is only 0.380. This ratio tells us that most of the kinetic energy of the helicopter is in its spinning blades—something you probably would not suspect. The 53.7 m height to which the helicopter could be raised with the rotational kinetic energy is also impressive, again emphasizing the amount of rotational kinetic energy in the blades.
Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/
In accounting and finance, earnings before interest and taxes (EBIT), is a measure of a firm’s profit that includes all ... more
In finance, leverage is a general term for any technique to multiply gains and losses. Operating leverage is an attempt to estimate the percentage change ... more
Earnings per share is the monetary value of earnings per each outstanding share of a company’s common stock. Shares outstanding are all the shares of a ... more
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The awe‐inspiring Great Pyramid of Cheops was built more than 4500 years ago. Its square base, originally 230 m on a side, covered 13.1 acres, and it was 146 m high (H), with a mass of about 7×10^9 kg. (The pyramid’s dimensions are slightly different today due to quarrying and some sagging). Historians estimate that 20,000 workers spent 20 years to construct it, working 12-hour days, 330 days per year.
