'

Search results

Found 1194 matches
Geometric Kurtosis - 4th moment

Is a measure that describes the “tailedness” of the probability distribution of a real-valued random variable. Geometric mean size (1st moment) ... more

Logarithmic Standard Deviation - 2nd moment

Shows how much variation or dispersion from the average exists. Logarithmic mean size (1st moment) needs to be precalculated.

... more

Logarithmic Mean Size - 1st moment

Calculates the logarithmic mean size (moments method) of the particles’ size distribution of a soil, in phi scale

... more

Arithmetic Standard Deviation - 2nd moment

Shows how much variation or dispersion from the average exists, on the particles’ size distribution of a soil, in metric scale. Arithmetic mean size (1st ... more

Arithmetic mean size - 1st moment

Calculates the arithmetic mean size (arithmetic method of moments) of the particles’ size distribution of a soil, in metric scale. In statistics, the ... more

Pearson's moment coefficient of kurtosis (excess kurtosis)

In probability theory and statistics, kurtosis is any measure of the “tailedness” of the probability distribution of a real-valued random ... more

Variance of the sample kurtosis of a sample of size n

In statistics and quantitative research methodology, a data sample is a set of data collected and/or selected from a statistical population by a defined ... more

Weighted geometric mean

In mathematics, the geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the ... more

Relation between the standard deviation of logarithmized sample and the non-logarithmized sample values

Log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. The standard ... more

Probability density function of a log-normal distribution

In probability theory, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, ... more

Particle diameter (phi scale)

Particle size, also called grain size, refers to the diameter of individual grains of sediment, or the lithified particles in clastic rocks.
Size ... more

Generalized volatility for time T

In finance, volatility is a measure for variation of price of a financial instrument over time. An implied volatility is derived from the market price of a ... more

Annualized volatility

In finance, volatility is a measure for variation of price of a financial instrument over time. return is a profit on an investment. It comprises any ... more

Perfectly inelastic collision

A collision is an isolated event in which two or more moving bodies (colliding bodies) exert forces on each other for a relatively short time. Collision is ... more

IT Grade

IT Grade refers to the International Tolerance Grade of an industrial process defined in ISO 286. This grade identifies what ... more

Worksheet 306

Calculate the force the biceps muscle must exert to hold the forearm and its load as shown in the figure below, and compare this force with the weight of the forearm plus its load. You may take the data in the figure to be accurate to three significant figures.


(a) The figure shows the forearm of a person holding a book. The biceps exert a force FB to support the weight of the forearm and the book. The triceps are assumed to be relaxed. (b) Here, you can view an approximately equivalent mechanical system with the pivot at the elbow joint

Strategy

There are four forces acting on the forearm and its load (the system of interest). The magnitude of the force of the biceps is FB, that of the elbow joint is FE, that of the weights of the forearm is wa , and its load is wb. Two of these are unknown FB, so that the first condition for equilibrium cannot by itself yield FB . But if we use the second condition and choose the pivot to be at the elbow, then the torque due to FE is zero, and the only unknown becomes FB .

Solution

The torques created by the weights are clockwise relative to the pivot, while the torque created by the biceps is counterclockwise; thus, the second condition for equilibrium (net Ď„ = 0) becomes

Force (Newton's second law)
Torque
Force (Newton's second law)
Torque

Note that sin θ = 1 for all forces, since θ = 90º for all forces. This equation can easily be solved for FB in terms of known quantities,yielding. Entering the known values gives

Mechanical equilibrium - 3=3 Torque example

which yields

Torque
Addition

Now, the combined weight of the arm and its load is known, so that the ratio of the force exerted by the biceps to the total weight is

Division

Discussion

This means that the biceps muscle is exerting a force 7.38 times the weight supported.

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/

Standard Error

The standard error (SE) is the standard deviation of the sampling distribution of a statistic. The term may also be used to refer to an estimate of that ... more

Graphic Standard Deviation

Is an approximate measure of sorting or variation of a particle size distribution in phi scale; can be estimated from the percentages of the particles ... more

Pearson's moment coefficient of skewness

In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its ... more

Vertical Curve - Parabolic formula

Vertical Curves are the second of the two important transition elements in geometric design for highways, the first being Horizontal Curves. A vertical ... more

Standard Gravitational Parameter - Two bodies orbiting each other

In celestial mechanics, the standard gravitational parameter ÎĽ of a celestial body is the product of the gravitational constant G and the mass M of the ... more

Final Grade conversion to the German system - Bavarian Formular

A number of systems exist for the conversion of grades from other countries into German grades. One such system, used by most universities in ... 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/

Volume-based particle size

Particle size is a notion introduced for comparing dimensions of solid particles (flecks), liquid particles (droplets), or gaseous particles (bubbles).
... more

Kepler's Third Law

In astronomy, Kepler’s laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

1.The orbit of a ... more

Area-based particle size

Particle size is a notion introduced for comparing dimensions of solid particles (flecks), liquid particles (droplets), or gaseous particles (bubbles).
... more

Second moment of area - I-Beam (W-section)

An I-beam, also known as H-beam, W-beam (for “wide flange”), Universal Beam (UB), Rolled Steel Joist (RSJ), or ... more

Inclusive Graphic Standard Deviation

Is the measure of sorting or variation of a particle size distribution in phi scale; can be estimated from the percentages of the particles which ... more

Moment magnitude scale

The Moment magnitude scale is used to measure the size of earthquakes in terms of the energy released.The magnitude is based on the seismic moment of the ... more

Colpitts oscillator (frequency)

Colpitts oscillator is an oscillator that uses an LC circuit (also called a resonant circuit, tank circuit, or tuned circuit) combined with a transistor ... more

...can't find what you're looking for?

Create a new formula