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Alecsey [184]
1 year ago
13

The gravitational potential energy of a particle of mass m moving under the influence of a fixed mass M is given by - , where G

is the universal gravitational constant and r is the distance between the masses. What is the total energy of the mass m if it is in a circular orbit about mass M
Physics
1 answer:
djverab [1.8K]1 year ago
3 0

-GMm/2r is the total energy of the mass m if it is in a circular orbit about mass M.

Given

A particle of mass m moving under the influence of a fixed mass's M, gravitational potential energy of formula  -GMm/r, where r is the separation between the masses and G is the gravitational constant of the universe.

As the Gravity Potential energy of particle = -GMm/r

Total energy of particle = Kinetic energy + Potential Energy

As we know that

Kinetic energy = 1/2mv²

Also, v is equals to square root of GM/r

v = √GM/r

Put the value of v in the formula of kinetic energy

We get,

Kinetic Energy = GMm/2r

Total Energy = GMm/2r + (-GMm/r)

                     = GMm/2r - GMm/r

                     = -GMm/2r

Hence, -GMm/2r is the total energy of the mass m if it is in a circular orbit about mass M.

Learn more about Gravitational Potential Energy here brainly.com/question/15896499

#SPJ4

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Answer:

Yes, the car driver is exceeding the given limit.

Explanation:

<u>Given:</u>

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  • Speed limit of the highway, \rm v_o=75.0\ mi/h.

<h2><u>Converting the speed limit from mi/h to m/s:</u></h2>

We know,

1 mi = 1.60934 km.

1 km = 1000 m.

Therefore, 1 mi = 1.60934 × 1000 m = 1609.34 m.

1 hour = 60 minutes.

1 minute = 60 seconds.

Therefore, 1 hour = 60 × 60 seconds = 3600 seconds.

Using these values,

\rm 1\ \dfrac{mi}{h}=\dfrac{1609.34\ m}{3600\ s}=0.447\ m/s.

Therefore,

\rm v_o = 75.0\ mi/h=75.0\times 0.447=33.52\ m/s.

Clearly,

\rm v_o

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Atmospheric conditions near a mountain range are such that a cloud at an altitude of 2.00 km contains 3.20 ✕ 10^7 kg of water va
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Answer:

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Explanation:

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solution

we know work is mass × gravity force × height

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so we say that power =  mass  gravity force × height / time

now put all value and find time period

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time =  62.784 × 10^10 / 2.96 × 10^3

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