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Though longitudinally stable when stationary, a bike may become longitudinally unstable under sufficient acceleration or deceleration. The normal ... more
Though longitudinally stable when stationary, a bike may become longitudinally unstable under sufficient acceleration or deceleration. The normal ... more
A compound pendulum (or physical pendulum) is one where the rod is not massless, and may have extended size; that is, an arbitrarily shaped rigid body ... more
In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In a Freefall in Uniform Gravitational Field with ... more
Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... more
Vertical pressure variation is the variation in pressure as a function of elevation. The vertical variation is especially significant, as it results from ... 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
The Richardson number (Ri) is named after Lewis Fry Richardson (1881 – 1953). It is the dimensionless number that expresses the ratio of potential to ... more
A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. A so-called “simple ... more
Free fall is any motion of a body where its weight is the only force acting upon it. Falling in air, as long as the force of gravity on the object is much ... more
In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating ... more
Darcy’s law states that the volume of flow of the pore fluid through a porous medium per unit time is proportional to the rate of change of excess ... more
A seiche (/ˈseɪʃ/ SAYSH) is a standing wave in an enclosed or partially enclosed body of water. Seiches and seiche-related ... more
A water rocket is a type of model rocket using water as its reaction mass. Such a rocket is typically made from a used plastic soft drink bottle. The water ... 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.
The gravity of Earth, which is denoted by g, refers to the acceleration that the Earth imparts to objects on or near its surface due to gravity. In SI ... more
A seiche (/ˈseɪʃ/ SAYSH) is a standing wave in an enclosed or partially enclosed body of water. Seiches and seiche-related ... more
Offsets are vertical distances from the initial tangent to the curve, play a significant role in vertical curve design.
Vertical Curves are the ... more
By definition, hydraulic conductivity is the ratio of velocity to hydraulic gradient indicating permeability of porous media.
Civil engineers ... more
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
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/
In various scientific contexts, a scale height is a distance over which a quantity decreases by a factor of e (approximately 2.71828, the base of natural ... more
Gravity gives weight to physical objects and causes them to fall toward the ground when dropped.
If Μ is a point mass or the mass of a sphere with
... more
Clairaut’s theorem is a general mathematical law applying to spheroids of revolution. The formula can be used to relate the gravity at any point on ... 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
The surface gravity, g, of an astronomical or other object is the gravitational acceleration experienced at its surface. The surface gravity may be thought ... more
Bernoulli’s principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with an increase in dynamic ... more
Vertical Curves are the second of the two important transition elements in geometric design for highways, the first being Horizontal Curves. A vertical ... more
Trail, or caster, is the horizontal distance from where the steering axis intersects the ground to where the front wheel touches the ground. The ... more
In physics, assuming a flat Earth with a uniform gravity field, and no air resistance, a projectile launched with specific initial conditions will have a ... more
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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.
