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Two masses are 1.15 m apart. Mass 1 is 75.0 kg and mass 2 is 68.4 kg. What is the gravitational force between the two masses?

[tex]\[
\begin{array}{c}
\vec{F}=G \frac{m_1 m_2}{r^2} \\
G=6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2 \\
m_1 = 75.0 \, \text{kg} \\
m_2 = 68.4 \, \text{kg} \\
r = 1.15 \, \text{m}
\end{array}
\][/tex]

[tex]\[
\vec{F}=[?] \times 10^{[?]} \, \text{N}
\][/tex]

Sagot :

GinnyAnswer
Certainly! Let's solve the problem step by step using the provided formula to calculate the gravitational force between two masses.

### Information Provided:
- Mass 1 ([tex]\( m_1 \)[/tex]) = 75.0 kg
- Mass 2 ([tex]\( m_2 \)[/tex]) = 68.4 kg
- Distance between the masses ([tex]\( r \)[/tex]) = 1.15 m
- Gravitational constant ([tex]\( G \)[/tex]) = [tex]\( 6.67 \times 10^{-11} \)[/tex] [tex]\( \text{N} \cdot \text{m}^2/\text{kg}^2 \)[/tex]

### Formula:
The gravitational force ([tex]\( F \)[/tex]) is given by:
[tex]\[ \vec{F} = G \frac{m_1 m_2}{r^2} \][/tex]

### Steps to Calculate:

1. Substitute the values into the formula:
[tex]\[ F = 6.67 \times 10^{-11} \times \frac{75.0 \times 68.4}{(1.15)^2} \][/tex]

2. Calculate the value of [tex]\( m_1 \times m_2 \)[/tex]:
[tex]\[ m_1 \times m_2 = 75.0 \times 68.4 = 5130 \][/tex]

3. Calculate the value of [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = (1.15)^2 = 1.3225 \][/tex]

4. Apply these values in the formula:
[tex]\[ F = 6.67 \times 10^{-11} \times \frac{5130}{1.3225} \][/tex]
Calculate the fractional division:
[tex]\[ \frac{5130}{1.3225} = 3877.56 \][/tex]

5. Then, multiply by [tex]\( 6.67 \times 10^{-11} \)[/tex]:
[tex]\[ F = 6.67 \times 10^{-11} \times 3877.56 \approx 2.587304347826087 \times 10^{-7} \][/tex]

6. Express the force in scientific notation:
[tex]\[ F \approx 2.59 \times 10^{-7} \, \text{N} \][/tex]

### Final Answer:
[tex]\[ \vec{F} \approx 2.59 \times 10^{-7} \, \text{N} \][/tex]

So, the gravitational force between the two masses is approximately [tex]\( 2.59 \times 10^{-7} \)[/tex] Newtons.
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