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

Is a measure that describes tthe “tailedness” of the probability distribution of a real-valued random variable. Particles logarithmic mean size ... more

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

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

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

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The weighted mean is similar to an arithmetic mean (the most common type of average), where instead of each of the data points contributing equally to the ... more

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

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

The weighted mean is similar to an arithmetic mean (the most common type of average), where instead of each of the data points contributing equally to the ... 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.

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 **E _{r}** . 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/

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 **F _{B}** 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 **F _{B}**, that of the elbow joint is

**F**, that of the weights of the forearm is

_{E}**w**, and its load is

_{a}**w**. Two of these are unknown

_{b}**F**, so that the first condition for equilibrium cannot by itself yield

_{B}**F**. But if we use the second condition and choose the pivot to be at the elbow, then the torque due to

_{B}**F**is zero, and the only unknown becomes

_{E}**F**.

_{B}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 **τ = 0**) becomes

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

which yields

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

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/

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

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

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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

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

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

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

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

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

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

Silts, sands and gravels are classified by their size, and hence they may consist of a variety of minerals. Owing to the stability of quartz compared to ... more

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

The orbital period is the time taken for a given object to make one complete orbit around another object.When mentioned without further qualification in ... more

Crest vertical curves are curves which, when viewed from the side, are convex upwards. This includes vertical curves at hill crests, but it also includes ... more

Crest vertical curves are curves which, when viewed from the side, are convex upwards. This includes vertical curves at hill crests, but it also includes ... more

For a particle size distribution, the graphic mean size can be estimated from the percentages of the particles corresponding to the 16%, 50% and 84%

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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.