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Power average (related to Work)

Power is the rate of doing work. It is equivalent to an amount of energy consumed per unit time. The same amount of work is done when carrying a load up a ... more

Mechanical Power (Displacement)

Power is the rate at which work is done. It is equivalent to an amount of energy consumed per unit time.
The same amount of work is done when ... more

Worksheet 292

What is the cost of running a 0.600-kW computer 6.00 h per day for 30.0 d if the cost of electricity is $0.120 per kW ⋅ h ?

Multiplication

where t is the total consumption time, td is the days of consumption and th the hours of consumption per day

Power-average (related to Work)

where P is Power consumption rate, E is the energy supplied by the electricity company and t is consumption time

keywords:
ballistics

Multiplication

where C is the total cost and CkW is the cost per kilowatt hour

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/

Power-mechanics (Velocity)

Power is the rate at which work is done. It is equivalent to an amount of energy consumed per unit time. Power in mechanical systems is the combination of ... more

Power - rotational systems (torque)

Power is the rate at which work is done. It is equivalent to an amount of energy consumed per unit time. Power in mechanical systems is the combination of ... more

Power (aerodynamic drag)

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force ... more

Power in a reference system(aerodynamic drag)

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force ... more

Group work calculator

Estimate how long it will take to complete a work by two people, from their individual working capacities.

... more

Electric Potential Energy with Time (related to Electrical Work)

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

Compressed air energy storage (Work for compression)

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

Potential energy

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

Apparent power

The power factor of an AC electrical power system is defined as the ratio of the real power flowing to the load, to the apparent power in the circuit. In a ... more

Carnot cycle

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

Electric Potential Energy (related to Electrical Work)

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

Kinetic energy (related to object's momentum)

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

Tractive Force - Steam locomotives

As used in mechanical engineering, the term tractive force can either refer to the total traction a vehicle exerts on a surface, or the amount of the total ... more

Spring work

When a force is applied on a spring, and the length of the spring changes by a differential amount dx, the work done is Fdx. For linear elastic springs, ... more

Law of Conservation of Mechanical Energy - General version

Energy can be neither created nor destroyed.
Total energy is constant in any process. It may change in form or be transferred from one system to ... more

Material Removal Rate

Machining is any of various processes in which a piece of raw material is cut into a desired final shape and size by a controlled material-removal process. ... more

Thermodynamic efficiency (Rankine cycle)

Rankine cycle is a model that is used to predict the performance of steam engines. The Rankine cycle is an idealised thermodynamic cycle of a heat engine ... more

Ideal gas - isobaric process

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

Internal energy isobaric process

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

Ripple voltage (full-wave rectifier))

The most common meaning of ripple in electrical science is the small unwanted residual periodic variation of the direct current (DC) output of a power ... more

Ripple voltage (half-wave rectifier))

The most common meaning of ripple in electrical science is the small unwanted residual periodic variation of the direct current (DC) output of a power ... more

Beale number

In mechanical engineering, the Beale number is a parameter that characterizes the performance of Stirling engines. It is often used to estimate the power ... 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/

Worksheet 341

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.

Division
Potential energy

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.

Multiplication

then we calculate the number of hours worked in the 20 years.

Multiplication

Then we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.

Multiplication
Multiplication

The efficiency is the resulting potential energy divided by the consumed energy.

Division
Shaft work

Energy transmission with a rotating shaft is very common in engineering practice. Often the torque T applied to the shaft is constant which means that the ... more

Internal energy isobaric process in terms of volume

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

Isentropic Relations for an Ideal Gas - Temperature and Pressure

In thermodynamics, an isentropic process is an idealized thermodynamic process that is adiabatic and in which the work transfers of the system are ... more

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