Question

if your mass is 63.7 kg, and you are standing 7.5 m away from a boulder with a mass of 9,750.6 kg, what is the gravitational force between you and the boulder? newtons law of gravitation is $f_{\text{gravity}} = \frac{gm_1m_2}{r^2}$. the gravitational constant $g$ is $6.67 \times 10^{-11} \\, \text{n·m}^2/\text{kg}^2$.

a. $1.10 \times 10^4 \\, \text{n}$

b. $9.82 \times 10^{-8} \\, \text{n}$

c. $7.37 \times 10^{-7} \\, \text{n}$

d. $5.52 \times 10^{-6} \\, \text{n}$

Explanation:

Step1: Identify given values

We have \( m_1 = 63.7\space kg \), \( m_2 = 9750.6\space kg \), \( r = 7.5\space m \), \( G = 6.67\times 10^{-11}\space N\cdot m^2/kg^2 \) and the formula \( F_{gravity}=\frac{Gm_1m_2}{r^2} \).

Step2: Substitute values into formula

Substitute the values into the formula:
\[

$$\begin{align*} F_{gravity}&=\frac{(6.67\times 10^{-11})\times(63.7)\times(9750.6)}{(7.5)^2}\\ \end{align*}$$

\]

Step3: Calculate numerator

First, calculate the numerator:
\( (6.67\times 10^{-11})\times(63.7)\times(9750.6) \)
\( 63.7\times9750.6 = 63.7\times9750.6 = 620113.22 \)
Then, \( 6.67\times 10^{-11}\times620113.22 = 6.67\times620113.22\times 10^{-11} \)
\( 6.67\times620113.22 \approx 4136155.1774 \)
So numerator is \( 4136155.1774\times 10^{-11} = 4.1361551774\times 10^{-5} \)

Step4: Calculate denominator

Denominator is \( (7.5)^2 = 56.25 \)

Step5: Divide numerator by denominator

\( F_{gravity}=\frac{4.1361551774\times 10^{-5}}{56.25} \approx 7.35\times 10^{-7}\space N \approx 7.37\times 10^{-7}\space N \) (after rounding to appropriate significant figures)

Answer:

C. \( 7.37\times 10^{-7}\space N \)