Physics, 12.07.2019 21:30 bayeck

Ahoop of mass 2 kg, radius 0.5 m is rotating about its center with an angular speed of 3 rad's. a force of 10n is applied tangentially at the rim (a) determine the rotational kinetic energy oh the hoop (b) what is instantaneous change rate of the kinetic energy?

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Answer from: hannahkharel2

The rotational kinetic energy of the hoop and the instantaneous change rate of the kinetic energy are 2.25 J and 15 J.

Explanation:

Given that,

Mass = 2 kg

Radius = 0.5 m

Angular speed = 3 rad/s

Force = 10 N

(I). We need to calculate the rotational kinetic energy

Using formula of kinetic energy

$K.E =\dfrac{1}{2}\timesI\omega^2$

$K.E=\dfrac{1}{2}\times mr^2\times\omega^2$

$K.E=\dfrac{1}{2}\times2\times(0.5)^2\times(3)^2$

$K.E=2.25\ J$

(II). We need to calculate the instantaneous change rate of the kinetic energy

Using formula of kinetic energy

$K.E=\dfrac{1}{2}mv^2$

On differentiating

$\dfrac{K.E}{dt}=\dfrac{1}{2}m\times2v\times\dfrac{dv}{dt}$

$\dfrac{K.T}{dt}=mva$ ....(I)

Using newton's second law

F = ma

$a= \dfrac{F}{m}$

$a=\dfrac{10}{2}$

a=5 m/s^2

Put the value of a in equation (I)

$\dfrac{K.E}{dt}=mva$

$\dfrac{K.E}{dt}=mr\omega a$

$\dfrac{K.E}{dt}=2\times0.5\times3\times5$

$\dfrac{K.E}{dt}=15\ J/s$

Hence, The rotational kinetic energy of the hoop and the instantaneous change rate of the kinetic energy are 2.25 J and 15 J.

Answer from: Quest

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Answer from: Quest

-first use of geothermal energy occurred more than 10,000 years ago in north america by american paleo-indians

-the first industrial use of geothermal energy began near pisa, italy in late 18th century

-in 1904, italian scientist piero ginori conti invented the first geothermal electric power plant in which steam was used to generate the power

-with the above experiment, the first geothermal plant in usa started in 1922 with a capacity of 250 kilowatts

-however, in 1946 first ground-source geothermal heat pump installed at commonwealth building in portland, oregon

-during the 1960’s, pacific gas and electric began operation of first large scale geothermal power plant in san francisco, producing 11 megawatts

-in 1973, when oil crisis began many countries began looking for renewable energy sources and by 1980’s geothermal heat pumps (ghp) started gaining popularity in order to reduce heating and cooling costs

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hope this

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