Search results
An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0. This typically occurs when a system is in contact with an ... more
An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0. This typically occurs when a system is in contact with an ... more
Electrical work is the work done on a charged particle by an electric field. The equation for 'electrical’ work is equivalent to that of ... more
Electrical work is the work done on a charged particle by an electric field. The equation for 'electrical’ work is equivalent to that of ... more
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total ... 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/
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total ... more
The Gibbs free energy is a thermodynamic potential that measures the “usefulness” or process-initiating work obtainable from a thermodynamic ... more
Compressed air energy storage is a way to store energy generated at one time for use at another time using compressed air. In order to achieve a near ... more
In astrodynamics, the vis viva equation, also referred to as orbital energy conservation equation, is one of the fundamental equations that govern the ... more
In astrodynamics, the vis viva equation, also referred to as orbital energy conservation equation, is one of the fundamental equations that govern the ... more
In astrodynamics, the vis viva equation, also referred to as orbital energy conservation equation, is one of the fundamental equations that govern the ... more
Potential energy is the energy of a body or a system with respect to the position of the body or the arrangement of the particles of the system. The amount ... more
An isobaric process is a thermodynamic process in which the pressure stays constant: ΔP = 0. The heat transferred to the system does work, but also changes ... more
Every single thermodynamic system exists in a particular state. When a system is taken through a series of different states and finally returned to its ... more
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.
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.
According to Hooke’s Law, Elastic potential energy is stored in a simple harmonic oscillator at position x,for example, the energy saved in an object ... more
In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is the work needed to accelerate a body of a given mass ... more
Escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero. It is the speed needed to ... more
Energy–maneuverability theory is a model of aircraft performance. It was developed by Col. John Boyd, and is useful in describing an aircraft’s ... more
Electrons can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency ... more
In the gravitational two-body problem, the specific orbital energy (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual ... more
Elastic energy is the potential mechanical energy stored in the configuration of a material or physical system as work is performed to distort its volume ... more
Auger electron spectroscopy is a common analytical technique used specifically in the study of surfaces and, more generally, in the area of materials ... more
Gibbs free energy is a thermodynamic potential that measures the “usefulness” or process-initiating work obtainable from a thermodynamic system ... more
A flywheel is a rotating mechanical device that is used to store rotational energy. Flywheel energy storage works by accelerating a rotor to a very high ... more
In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that is done by the force of ... more
Potential function for electrostatic forces between two bodies is the work required to move a charge from a point to any point in the electrostatic force ... more
The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around ... more
A regenerative brake is an energy recovery mechanism which slows a vehicle or object by converting its kinetic energy into a form which can be either used ... more
...can't find what you're looking for?
Create a new formula
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?