Answer :
Sure, let's solve the problem step by step.
We are given:
- Distance between the two masses, [tex]\( r = 8.90 \)[/tex] m
- Mass 1, [tex]\( m_1 = 157 \)[/tex] kg
- Mass 2, [tex]\( m_2 = 5.61 \)[/tex] kg
- Gravitational constant, [tex]\( G = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 \cdot \text{kg}^{-2} \)[/tex]
We need to find the gravitational force [tex]\( \vec{F} \)[/tex] between the two masses using the formula:
[tex]\[ \vec{F} = G \frac{m_1 m_2}{r^2} \][/tex]
Let's plug in the values into the formula:
1. First, calculate [tex]\( m_1 \times m_2 \)[/tex]:
[tex]\[ m_1 \times m_2 = 157 \times 5.61 = 880.77 \, \text{kg}^2 \][/tex]
2. Next, calculate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = (8.90)^2 = 79.21 \, \text{m}^2 \][/tex]
3. Now, compute the gravitational force:
[tex]\[ \vec{F} = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 \cdot \text{kg}^{-2} \times \frac{880.77 \, \text{kg}^2}{79.21 \, \text{m}^2} \][/tex]
4. Simplify the fraction:
[tex]\[ \frac{880.77}{79.21} \approx 11.12 \][/tex]
5. Multiply the results:
[tex]\[ \vec{F} = 6.67 \times 10^{-11} \times 11.12 \][/tex]
[tex]\[ \vec{F} \approx 7.42 \times 10^{-10} \, \text{N} \][/tex]
So, the gravitational force between the two masses is approximately:
[tex]\[ \vec{F} \approx 7.42 \times 10^{-10} \, \text{N} \][/tex]
Expressing this force in the required form:
[tex]\[ \vec{F} = 74.17 \times 10^{-11} \, \text{N} \][/tex]
Therefore, the final answer is:
[tex]\[ \vec{F} = 7.42 \times 10^{-10} \, \text{N} \][/tex]
or
[tex]\[ \vec{F} = 74.17 \times 10^{-11} \, \text{N} \][/tex]
I hope that helps! If you have any further questions, feel free to ask.
We are given:
- Distance between the two masses, [tex]\( r = 8.90 \)[/tex] m
- Mass 1, [tex]\( m_1 = 157 \)[/tex] kg
- Mass 2, [tex]\( m_2 = 5.61 \)[/tex] kg
- Gravitational constant, [tex]\( G = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 \cdot \text{kg}^{-2} \)[/tex]
We need to find the gravitational force [tex]\( \vec{F} \)[/tex] between the two masses using the formula:
[tex]\[ \vec{F} = G \frac{m_1 m_2}{r^2} \][/tex]
Let's plug in the values into the formula:
1. First, calculate [tex]\( m_1 \times m_2 \)[/tex]:
[tex]\[ m_1 \times m_2 = 157 \times 5.61 = 880.77 \, \text{kg}^2 \][/tex]
2. Next, calculate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = (8.90)^2 = 79.21 \, \text{m}^2 \][/tex]
3. Now, compute the gravitational force:
[tex]\[ \vec{F} = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 \cdot \text{kg}^{-2} \times \frac{880.77 \, \text{kg}^2}{79.21 \, \text{m}^2} \][/tex]
4. Simplify the fraction:
[tex]\[ \frac{880.77}{79.21} \approx 11.12 \][/tex]
5. Multiply the results:
[tex]\[ \vec{F} = 6.67 \times 10^{-11} \times 11.12 \][/tex]
[tex]\[ \vec{F} \approx 7.42 \times 10^{-10} \, \text{N} \][/tex]
So, the gravitational force between the two masses is approximately:
[tex]\[ \vec{F} \approx 7.42 \times 10^{-10} \, \text{N} \][/tex]
Expressing this force in the required form:
[tex]\[ \vec{F} = 74.17 \times 10^{-11} \, \text{N} \][/tex]
Therefore, the final answer is:
[tex]\[ \vec{F} = 7.42 \times 10^{-10} \, \text{N} \][/tex]
or
[tex]\[ \vec{F} = 74.17 \times 10^{-11} \, \text{N} \][/tex]
I hope that helps! If you have any further questions, feel free to ask.
