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Child's Law - related to anode voltage

First proposed by Clement D. Child in 1911, Child’s law states that the space-charge limited current (SCLC) in a ... more

Capacitance of a Pair of parallel identical wires

Capacitance is the ability of a body to store an electrical charge. Any object that can be electrically charged exhibits capacitance. The capacitance is a ... more

Capacitors conected in series

Connected in series, the capacitors each store instantaneous charge build-up equal to that of every other capacitor in the series. The total voltage ... more

Stored Energy (Electrical Charge)

Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. Here we can calculate for Stored Energy ... more

Energy stored in a system of three point charges

Electric potential energy, or electrostatic potential energy, is a potential energy that results from conservative Coulomb forces and is associated with ... more

Stored Energy (Potential Difference)

Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. Here we can calculate for Stored Energy ... 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/

Coulomb's constant

Coulomb’s constant, the electric force constant, or the electrostatic constant (denoted ke ) is a proportionality constant in equations relating ... more

Speed of light in matter

The speed of light in vacuum is the speed at which all massless particles and changes of the associated fields (including electromagnetic radiation such as ... more

Cross Section (discrete events)

The cross section is an effective area that quantifies the intrinsic likelihood of a scattering event when an incident beam strikes a target object, made ... more

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