what is the force of gravity on 50 kg couch 4.0 × 10^8m from the earth’s center of mass? (the mass of the earth is approximately 6.0 × 10^24kg.)

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Accepted Answer

# Explanation:
## Step1: Write the formula for gravitational force
The formula for gravitational force is $ F = G\frac{m_1m_2}{r^2} $, where $ G = 6.67\times10^{- 11}\space N\cdot m^{2}/kg^{2}$, $m_1$ is the mass of the Earth ($m_1 = 6.0\times10^{24}\space kg$), $m_2$ is the mass of the couch ($m_2=50\space kg$), and $r$ is the distance from the Earth's center of mass ($r = 4.0\times10^{8}\space m$).
## Step2: Substitute the values into the formula
Substitute $G = 6.67\times10^{-11}$, $m_1 = 6.0\times10^{24}$, $m_2 = 50$, and $r = 4.0\times10^{8}$ into $F = G\frac{m_1m_2}{r^2}$:
$$
\begin{align*}
F&=(6.67\times 10^{-11})\frac{(6.0\times 10^{24})\times(50)}{(4.0\times 10^{8})^{2}}\
&=(6.67\times 10^{-11})\frac{3.0\times 10^{26}}{1.6\times 10^{17}}\
&=(6.67\times 10^{-11})\times1.875\times 10^{9}\
&=12.50625\space N
\end{align*}
$$

# Answer:
$12.5\space N$ (rounded to three significant figures)

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Question

Explanation:

Step1: Write the formula for gravitational force

Step2: Substitute the values into the formula

Answer: