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The dynamic (shear) viscosity of a fluid expresses its resistance to shearing flows, where adjacent layers move parallel to each other with different ... more
The capacitance of a two parallel plates capacitor both of area A separated by a distance d is calculated by the area of overlap of the two plates, ... more
The Townsend discharge is a gas ionization process where free electrons, accelerated by a sufficiently strong electric field, give rise to electrical ... more
Capacitance is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. A common form of ... more
A uniform electric field is produced by placing a potential difference (or voltage) across two parallel metal plates. A uniform field is one in which the ... more
Capacitance is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. Capacitance is a ... more
A capacitor is an electrical/electronic device that can store energy in the electric field between a pair of conductors. The simplest capacitor consists of ... more
The Townsend discharge is a gas ionization process where free electrons, accelerated by a sufficiently strong electric field, give rise to electrical ... more
This formula calculates the geometrical requirements for pin ended members, specifically the minimum required distances from the pin hole edge to the plate ... more
Moment of inertia is the mass property of a rigid body that determines the torque needed for a desired angular acceleration about an axis of rotation. ... more
Mass moment of inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analogue to mass. Moment ... more
In electronics, a vacuum tube, an electron tube, or colloquially a tube (North America) or valve (British usage), is a device that controls electric ... more
This formula calculates the shear resistance of a pin in a pin and plate connection.
From EN 1993-1-8 (2005) (English): Eurocode 3: Design of steel
... more
Chladni’s law, named after Ernst Chladni, relates the frequency of modes of vibration for flat circular surfaces with fixed center as a function of ... more
Due to leakage of fluid between the back surface of the impeller hub plate and the casing, or through other pump components – there is a volumetric ... more
In science, buckling is a mathematical instability that leads to a failure mode.
When a structure is subjected to compressive stress, buckling may ... more
Moment of inertia is the mass property of a rigid body that determines the torque needed for a desired angular acceleration about an axis of rotation. ... more
A Newtonian fluid is a fluid in which the viscous stresses arising from its flow, at every point, are proportional to the local strain rate — the rate of ... more
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/
Friction velocity, is a form by which a shear stress may be re-written in units of velocity. It is useful as a method in fluid mechanics to compare true ... more
A fracture is the separation of an object or material into two, or more, pieces under the action of stress.There are three ways of applying a force to ... more
In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more
A fracture is the separation of an object or material into two, or more, pieces under the action of stress.There are three ways of applying a force to ... more
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he Bagnold number (Ba) is the ratio of grain collision stresses to viscous fluid stresses in a granular flow with interstitial Newtonian fluid, first ... more
The speed of sound is the distance travelled per unit of time by a sound wave propagating through an elastic medium. Sound travels faster in liquids and ... more
The speed of sound is the distance travelled per unit of time by a sound wave propagating through an elastic medium. Sound travels faster in liquids and ... more
A type of elastic wave, the S-wave, secondary wave, or shear wave (sometimes called an elastic S-wave) is one of the two main types of elastic body waves, ... more
Viscosity is a property arising from collisions between neighboring particles in a fluid that are moving at different velocities. When the fluid is forced ... more
Lateral earth pressure is the pressure that soil exerts in the horizontal direction. Rankine’s theory, is a stress field solution that predicts active and ... more
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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?