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Answer:
The radius of the new planet is ~2.04 * 10⁶ m, or 2,041,752 m.
Explanation:
We can use Newton's Law of Universal Gravitation:
Let's look at Newton's 2nd Law:
We can set these equations equal to each other:
The mass of the second mass (astronaut) cancels out. We are left with:
We are solving for the radius of the new planet, so we can rearrange the equation:
Substitute in our known values given in the problem (<u><em>G = 6.67 * 10⁻¹¹ </em></u><em> ; </em><u><em>M = 7.5 * 10²³</em></u><em> ; </em><u><em>a = 12</em></u>).
The radius of the new planet is ~2.04 * 10⁶ m.
Using KE=1/2mv^2
v=
so v=10
v=
so v=10
Answer:
a) Gravitational potential energy = 399 J
b) Gravitational potential energy = 66.5 J
c) Gravitational potential energy = 0 J
Explanation:
Hi there!
Please, see the attached figure for a better understanding of the problem.
a) When the ropes are horizontal, the height of the child, relative to the child's lowest position, is 2.10 m (see figure).
The gravitational potential energy is calculated as follows:
PE = mgh
Where:
PE = potential energy.
mg = weight of the child
h = height.
Then when the ropes are horizontal, the potential energy will be:
PE = 190 N · 2.10 m = 399 J
b) When the ropes make a 34.0° with the vertical, the height of the child is 2.10 m minus x (see figure). To find x, we can use trigonometry of right triangles:
cos angle = adjacent side / hypotenuse
cos 34.0° = x / 2.10 m
x = 2.10 m · cos 34.0° = 1.75 m
Then, the height of the child relative to the lowest position is
(2.10 m - 1.75 m) = 0.35 m
Therefore, the gravitational potential energy will be:
PE = 190 N · 0.35 m
PE = 66.5 J
c) When the child is at the bottom of the circular arc the height is zero (the child is at the lowest position), then, the gravitational potential energy will be zero.
