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Schach
2 months ago
7

Two planets having equal masses are in circular orbit around a star. Planet A has a smaller orbital radius than planet B. Which

statement is true?Planet A has more kinetic energy, less potential energy, and less mechanical energy (potential plus kinetic) than planet B.Planet A has more kinetic energy, less potential energy, and more mechanical energy (potential plus kinetic) than planet B.Planet A has more kinetic energy, more potential energy, and more mechanical energy (potential plus kinetic) than planet B.Planet A and planet B have the same amount of mechanical energy (potential plus kinetic).
Physics
1 answer:
serg [3.5K]2 months ago
6 0

Answer:

Explanation:

To approach this problem, we need to understand two key concepts.

First, the gravitational force on an object in orbit equals its mass multiplied by centripetal acceleration.

Secondly, Newton's law of universal gravitation defines the force between two masses: Fg = mMG/r², where Fg denotes gravitational force, m and M signify the masses, G represents the gravitational constant, and r indicates the distance separating the two masses.

Thus:

Fg = m v²/r

mMG/r² = m v²/r

v² = MG/r

Potential energy for each planet is expressed as:

PE = mgr = m (MG/r²) r = mMG/r

Kinetic energy for each planet is computed as:

KE = 1/2 mv² = 1/2 m (MG/r) = 1/2 mMG/r

Total mechanical energy is calculated as:

ME = PE + KE = 3/2 mMG/r

Since both planets share the same mass, the only variable is their orbital radius. Consequently, Planet A, with a smaller radius, possesses greater potential, kinetic, and mechanical energy.

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Explanation:

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Additionally, there is a gravitational force consistently acting downwards on the object, defined as g = 9.8 ms⁻²

For convenience, we will utilize a positive notation for downward acceleration and a negative notation for upward acceleration.

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The net force on the balloon can be expressed as:

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Ma = Mg - F                      (since the balloon moves downward, that means Mg > F)

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F = M (g-a)

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Case 2:

After releasing the ballast, the new mass becomes m. The new upward acceleration is -a/2:

The net force is expressed as:

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Determining the fraction of the mass initially dropped:

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