answer the following questions in complete sentences.
11. explain how gravity affects your weight on different planets.
12. describe a real - life example of magnetism that you have seen or used.
13. what did isaac newton relate with the force pulling an apple to the ground?
solve these problems using a calculator, and show your work!
14. two spherical objects have masses of 200 kg and 500 kg. their centers are separated by a distance of 25 m. find the gravitational attraction between them.
15. two spherical objects have masses of 1.5 x 10^5 kg and 8.5 x 10^2 kg. their centers are separated by a distance of 2500 m. find the gravitational attraction between them.
16. two spherical objects have masses of 3.1 x 10^5 kg and 6.5 x 10^3 kg. the gravitational attraction between them is 65 n. how far apart are their centers?

Question

Accepted Answer

### 11.
# Brief Explanations:
Weight is the force exerted on an object due to gravity. The gravitational acceleration ($g$) varies on different planets. Using the formula $W = mg$ (where $W$ is weight, $m$ is mass, and $g$ is gravitational - acceleration), since mass is constant but $g$ changes from planet to planet, weight also changes. For example, on Earth $g\approx9.8\ m/s^{2}$, while on Mars $g\approx3.71\ m/s^{2}$, so a person would weigh less on Mars than on Earth.
# Answer:
Weight is determined by the formula $W = mg$, where mass is constant but gravitational - acceleration varies on different planets, thus affecting weight.

### 12.
# Brief Explanations:
One common real - life example of magnetism is the use of a refrigerator magnet. The magnet sticks to the metal surface of the refrigerator due to the magnetic force between the magnet and the metal. The magnetic domains in the magnet align with the magnetic properties of the metal, creating an attractive force.
# Answer:
A refrigerator magnet is a real - life example of magnetism, as it sticks to the metal surface of a refrigerator due to magnetic force.

### 13.
# Brief Explanations:
Isaac Newton related the force pulling an apple to the ground (gravity on Earth) to the force that keeps the Moon in orbit around the Earth. He proposed the universal law of gravitation, which states that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
# Answer:
Isaac Newton related the force pulling an apple to the ground to the force that keeps the Moon in orbit around the Earth.

### 14.
# Explanation:
## Step1: Recall the gravitational - force formula
The formula for gravitational force is $F = G\frac{m_1m_2}{r^{2}}$, where $G = 6.67	imes10^{- 11}\ Nm^{2}/kg^{2}$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between their centers.
Given $m_1 = 200\ kg$, $m_2 = 500\ kg$, and $r = 25\ m$.
## Step2: Substitute the values into the formula
$F=6.67	imes 10^{-11}\frac{200	imes500}{25^{2}}$
$F = 6.67	imes10^{-11}\frac{100000}{625}$
$F=6.67	imes10^{-11}	imes160$
$F = 1.0672	imes10^{-8}\ N$
# Answer:
$1.0672	imes 10^{-8}\ N$

### 15.
# Explanation:
## Step1: Recall the gravitational - force formula
The formula for gravitational force is $F = G\frac{m_1m_2}{r^{2}}$, where $G = 6.67	imes10^{-11}\ Nm^{2}/kg^{2}$, $m_1 = 1.5	imes10^{5}\ kg$, $m_2 = 8.5	imes10^{2}\ kg$, and $r = 2500\ m$.
## Step2: Substitute the values into the formula
$F=6.67	imes 10^{-11}\frac{(1.5	imes10^{5})	imes(8.5	imes10^{2})}{2500^{2}}$
First, calculate the product of the masses: $(1.5	imes10^{5})	imes(8.5	imes10^{2})=1.5	imes8.5	imes10^{5 + 2}=12.75	imes10^{7}=1.275	imes10^{8}$
Then, calculate $2500^{2}=6250000 = 6.25	imes10^{6}$
$F=6.67	imes 10^{-11}\frac{1.275	imes10^{8}}{6.25	imes10^{6}}$
$F=6.67	imes10^{-11}	imes\frac{1.275}{6.25}	imes10^{8 - 6}$
$F=6.67	imes10^{-11}	imes0.204	imes10^{2}$
$F=6.67	imes0.204	imes10^{-11 + 2}$
$F = 1.36068	imes10^{-9}\ N$
# Answer:
$1.36068	imes 10^{-9}\ N$

### 16.
# Explanation:
## Step1: Recall the gravitational - force formula and rearrange it
The gravitational - force formula is $F = G\frac{m_1m_2}{r^{2}}$. Rearranging for $r$, we get $r=\sqrt{G\frac{m_1m_2}{F}}$
Given $G = 6.67	imes10^{-11}\ Nm^{2}/kg^{2}$, $m_1 = 3.1	imes10^{5}\ kg$, $m_2 = 6.5	imes10^{3}\ kg$, and $F = 65\ N$.
## Step2: Substitute the values into the formula
First, calculate the product of the masses: $m_1m_2=(3.1	imes10^{5})	imes(6.5	imes10^{3})=3.1	imes6.5	imes10^{5 + 3}=20.15	imes10^{8}=2.015	imes10^{9}$
Then, $G\frac{m_1m_2}{F}=6.67	imes10^{-11}	imes\frac{2.015	imes10^{9}}{65}$
$G\frac{m_1m_2}{F}=6.67	imes10^{-11}	imes0.031	imes10^{9}$
$G\frac{m_1m_2}{F}=6.67	imes0.031	imes10^{-11 + 9}$
$G\frac{m_1m_2}{F}=0.20677	imes10^{-2}$
$G\frac{m_1m_2}{F}=2.0677	imes10^{-3}$
$r=\sqrt{2.0677	imes10^{-3}}\approx0.0455\ m$
# Answer:
$0.0455\ m$

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11.

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12.