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Hamada's equation

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

Weighted average cost of capital

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

Tier 2 capital, or supplementary capital, include a number of important and legitimate constituents of a bank’s capital base. (Undisclosed Reserves ... more

Capital Adequacy Ratio

Capital Adequacy Ratio (CAR), also known as Capital to Risk (Weighted) Assets Ratio (CRAR), is the ... more

Total Leverage

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

Langmuir equation

The Langmuir equation (also known as the Langmuir isotherm, Langmuir adsorption equation or Hill-Langmuir equation) relates the coverage or adsorption of ... more

Discounting

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

Asset turnover ratio

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

Financial leverage

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

Margin of safety (measure of structural capacity)

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

Margin of safety for a failure load (measure of structural capacity)

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

Earnings per share (net income formula)

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

Future value of a present sum

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

Dividend payout ratio

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

Operating Leverage

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 before interest and taxes

In accounting and finance, earnings before interest and taxes (EBIT), is a measure of a firm’s profit that includes all ... more

Dividend cover ratio

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

Rule of 70 ( estimating the time for money's buying power to halve)

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

Mean Time Between Failures - MTBF

Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a system during operation. ... more

Newton's second law (variable-mass system)

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

Cost of equity

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

Amortization schedule

An amortization schedule is a table detailing each periodic payment on an amortizing loan (typically a mortgage), as generated by an amortization ... more

Earnings per share (continuing operations formula)

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

Net present value

In finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present ... more

Graveyard Orbit - Minimum Perigee Altitude

A graveyard orbit, also called a junk orbit or disposal orbit, is a supersynchronous orbit that lies significantly above synchronous orbit, where ... more

Worksheet 333

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

Angular velocity

and for 300 r.p.m

Multiplication

The moment of inertia of one blade will be that of a thin rod rotated about its end.

Moment of Inertia - Rod end

The total I is four times this moment of inertia, because there are four blades. Thus,

Multiplication

and so The rotational kinetic energy is

Rotational energy

Solution for (b)

Translational kinetic energy is defined as

Kinetic energy ( related to the object 's velocity )

To compare kinetic energies, we take the ratio of translational kinetic energy to rotational kinetic energy. This ratio is

Division

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:

Potential energy

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/

Worksheet 341

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.

a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth its height.

Division
Potential energy

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.

Multiplication

then we calculate the number of hours worked in the 20 years.

Multiplication

Then we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.

Multiplication
Multiplication

The efficiency is the resulting potential energy divided by the consumed energy.

Division
Net Profit Margin

Profit margin, net margin, net profit margin or net profit ratio all refer to a measure of profitability. It is calculated by finding the net profit as a ... more

Degree of Combined Leverage

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

Degree of Operating Leverage

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

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