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A planet orbits a star along an elliptical path from point X to point Y, as shown in the figure. In which of the following syste

8090 [49]

Answer:

The correct answer is Option D, the closed system containing the planet and the star.

Explanation:

To start, we need to define mechanical energy: the energy an object has from its motion and position.

The fundamental principle in physics is that the total energy in a closed system stays constant, even if it transforms. By saying "closed system," we refer to a system isolated from its surroundings. Energy never leaves the system; it only moves from one part to another.

This statement only applies to closed systems, however. An open system that interacts with its environment works differently. Energy may enter and leave the system through interaction with external forces, and this includes mechanical energy. For this reason, Option A and Option B are incorrect.

The remaining two options, C and D, only vary with the objects in the closed system. Option D includes the star; Option C does not.

However, we should take a closer look at Option C. Can an object have potential energy with itself? No, it cannot. It only has potential energy with other bodies. If the system is defined as the planet only, the only type of energy present is kinetic energy. We know a planet orbiting a star has more kinetic energy near and more gravitational potential energy further from its star. Thus it has less kinetic energy further from its star and less mechanical energy. Because of this, Option C is incorrect.

The only answer left is Option D. If we define the planet and star as a closed system, we find no net external force acting on it. Consequently, it obeys the law of conservation of energy. From prior reasoning, we know mechanical energy includes potential energy and kinetic energy and that the amounts of these energies vary with its orbit. As a result, mechanical energy is always conserved and always the same. In the end, the correct answer is Option D.

4 0

3 years ago

Estimate the kinetic energy of the earth with respect to the sun as the sum of two terms.

nekit [7.7K]

The definition of kinetic energy allows to find the result for the relationship between the energy of the sun and the Earth is:

The kinetic energy ratio is $\frac{K_{Sum} }{K_{Earth}} = 5.3 \ 10^2$

<h3 /><h3 /><h3> Kinetic enrgy.</h3>

Kinetic energy is the energy due to the movement of bodies, it is given by the relation

K = ½ m v²

where K is the kinetic energy, m the mass of the body and v the velocity of the body.

In a compound motion it is common to separate energy into parts to simplify calculations.

Translational kinetic energy. Due to the linear movement of the body

$K_{tras} =\frac{1}{2} m v^2$

Rotational kinetic energy. Due to the rotational movement of the body.

$K_{rot} = \frac{1}{2} I w^2$

Where I is the inrtia momentum and w the angular velocity.

They indicate that we compare the kinetic energy of the sun and the Earth.

The Earth has two movements, one of rotation about its axis with a period of T = 24 h and one of translation with respect to the Sun with a period of T= 365 days, therefore the kinetic energy of the Earth.

$K_{earth} = K_{tras} + K_{rot}$

Linear and rotational speed are related.

v = w r

The Earth is an almost spherical body therefore the moment of inertia of a solid sphere.

I = $\frac{2}{5 } m r^2$

Let's subatitute.

$K_{earth} = \frac{1}{2} \ m r^2_{tras} w^2_{tras} + \frac{1}{2} ( \frac{2}{5} m r^2_{earth}) w^2_{rot}$

The movement of the Earth around the sun is almost circular, therefore we can use the relations of the uniform circular movement, where the angle for one revolution is 2π radians and the time is called the period.

$w = \frac{2 \pi}{T}$

Let's substitute.

$K_{earth} = \frac{1}{2} m ( \frac{2\pi r^2_{tras}}{T_{tras}})^2 \ + \frac{1}{5} m (\frac{2\pi r^2_{earth} }{T^2_{rot}})^2$

$K_{earth} = 4 \pi^2 \ m \ ( \frac{1}{2} [ \frac{r_{tras}}{T_{tras}y} ]^2 + \frac{1}{5} [ \frac{r_{rot}}{T_{rot}}]^2)$

Data for Earth are tabulated:

Mass m = 5.98 1024 kg

Radius r = 6.37 10⁶ m

Radius orbits tras = 1.496 10¹¹ m

Rotation period $T_{rot}$ = 24 h ( $\frac{3600s}{1h}$ ) = 8.64 10⁴s

Translation period $T_{tras}$ = 365 d ( $\frac{24h}{1 d}$ ) ( $\frac{3600s}{1h}$ ) = 3.15 10⁷ s

Let's calculate.

$K_{earth} = 4 \pi^2 5.98 \ 10^{24} ( \frac{1}{2} ( \frac{1.496 \ 10^{11}}{3.15 \ 10^7 } )^2 \ + \frac{1}{5}( \frac{6.37 \ 10^6 }{8.64 \ 10^4})^2 )$

$K_{earth} = 2.36 \ 10^{26 } \ (1.128 \ 10^7 + 1.087 \ 10^3)$

$K_{earth}= 2.66 \ 10^{33} J$

Let's analyze the kinetic energy for the Sun, this is inside the solar system therefore it has no translation movement and is approximately a sphere with a rotation period of $T_{Sum}$ = 27 days.

The kinetic energy of the sun is;

$K_{sum} = K_{rot} = \frac{1}{2} I w^2$

$K_{sum} = \frac{1}{2} (\frac{2}{5} M R^2) (\frac{2\pi}{T_{sum}})^2$

$K_{sum} = \frac{4\pi^2 }{5} M (\frac{R}{T_{rot}})^2$

The tabulated data for the sun are:

Mass m = 1,991 1030 kg.

Radius R = 6.96 10⁸ m

Period T = 27 d ( $\frac{24h}{1 d}$ ) ( $\frac{3600s}{1h}$ ) = 2.33 10⁶ s

Let's calculate.

$K_{sum} = 1.40 \ 10^{36} J$

The relationship of the kinetic energy of the sun and the Earth is:

$\frac{K_{sum}}{K_{earth}} = \frac{1.40 \ 10^{36}}{2.66 \ 10^{33}}$

$\frac{K_{sum}}{K_{earth}} = 5.3 \ 10^2$

In conclusion using the definition of kinetic energy we can shorten the result for the relationship between the energy of the sun and the Earth is:

The kinetic energy ratio is: $\frac{K_{Sum}}{K_{Earth}} = 5 \ 10^2$

Learn more about kinetic energy here: brainly.com/question/25959744

5 0

3 years ago

What do you know about water

Romashka-Z-Leto [24]

Answer:

It is vital for all known forms of life.
It provides no calories nor organic nutrients.
It forms precipitation in the form of rain and aerosols in the form of fog.
It's chemical symbol is H₂O

Explanation:

HOPE THAT HELPS

PLEASE MARK AS BRAINLIEST

7 0

3 years ago

Which action best demonstrates the transformation of mechanical energy to heat energy and light energy?

Vinvika [58]

Well, first off, mechanical energy is the sum of kinetic and potential energy in an object that is used to do work. In other words, it is energy in an object due to its motion or position, or both. Heat energy is the result of the movement of tiny particles called atoms, molecules or ions in solids, liquids and gases. Light energy is the only form of energy that we can actually see directly. It is formed through chemical, radiation, and mechanical means. Striking a match stick (mechanical energy) creates fire, which has a ton of heat energy, and produces light too, so the answer, is A. I hope i could help!

5 0

3 years ago

What are the prediction made by the second and third apparitions?

julsineya [31]

This is too late too answer?

3 0

3 years ago