he electric motor of a model train accelerates the train from rest to 0.720 m/s in 29.0 ms. The total mass of the train is 840 g
1 answer:
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<h2>Answer: 56.718 min</h2>
Explanation:
According to the Third Kepler’s Law of Planetary motion<em> </em><em>“The square of the orbital period of a planet is proportional to the cube of the semi-major axis (size) of its orbit”. </em>
In other words, this law states a relation between the orbital period of a body (moon, planet, satellite) orbiting a greater body in space with the size
of its orbit.
This Law is originally expressed as follows:
(1)
Where;
is the Gravitational Constant and its value is
is the mass of Mars
is the semimajor axis of the orbit the spacecraft describes around Mars (assuming it is a <u>circular orbit </u>and a <u>low orbit near the surface </u>as well, the semimajor axis is equal to the radius of the orbit)
If we want to find the period, we have to express equation (1) as written below and substitute all the values:
(2)
(3)
(4)
Finally:
This is the orbital period of a spacecraft in a low orbit near the surface of mars
1) The forces are equal (Newton's third law of motion)
2) The force between the spheres will quadruple
3) The force of gravity exerted by the notebook on you is negligible
Explanation:
1)
In this part of the problem, we want to compare the gravitational force exerted by the larger mass sphere on the smaller mass sphere to the force exerted by the smaller mass sphere to the larger mass sphere.
We can do this by using Newton's third law of motion, which states that:
<em>"When an object A exerts a force (called </em><em>action</em><em>) on an object B, then object B exerts an equal and opposite force (called </em><em>reaction</em><em>) on object A"</em>
In this problem, we can identify the larger mass sphere as object A and the smaller mass sphere as object B. This law tells us that the two forces are equal in magnitude and opposite in direction: therefore, the gravitational force exerted by the larger mass sphere on the smaller mass sphere is equal to the force exerted by the smaller mass sphere to the larger mass sphere.
2)
The magnitude of the gravitational force between the two spheres is given by
where
G is the gravitational constant
are the masses of the two spheres
r is the separation between the two spheres
In this problem, we are asked to find what happens when the distance between the spheres is halved, therefore when the new distance is
Substituting into the equation, we find
So, the force between the two spheres will quadruple.
3)
We can give an estimate for the gravitational force exerted by your notebook on you.
As we said, the magnitude of the gravitational force is
Where:
is the gravitational constant
Let's estimate the following:
is your mass
is the mass of the notebook
, assuming the notebook is at 1 metre from you
Substituting,
We see that this force has an extremely small value: therefore, it is almost negligible in daily life, where other much stronger forces act on you.
Learn more about gravity:
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