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Answer :
Sure, let's solve this step-by-step!
1. Understand the Problem:
We need to find the weight of an astronaut (who has a mass of 95 kg) on the planet Mercury, in pounds (lbs).
2. Use the Correct Formula:
The weight of an object on a planet is calculated using the formula for gravitational force:
[tex]\[
F = \frac{G \times m_1 \times m_2}{r^2}
\][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force (weight) in Newtons,
- [tex]\( G \)[/tex] is the gravitational constant ([tex]\(6.67430 \times 10^{-11} \, m^3 kg^{-1} s^{-2}\)[/tex]),
- [tex]\( m_1 \)[/tex] is the mass of the astronaut (95 kg),
- [tex]\( m_2 \)[/tex] is the mass of Mercury ([tex]\(3.3 \times 10^{23} \, kg\)[/tex]),
- [tex]\( r \)[/tex] is the radius of Mercury (2,439,500 m).
3. Calculate the Gravitational Force:
Plug in the values to find the force in Newtons:
[tex]\[
F = \frac{6.67430 \times 10^{-11} \times 95 \times 3.3 \times 10^{23}}{(2,439,500)^2}
\][/tex]
This calculation results in approximately 351.59 Newtons.
4. Convert to Pounds:
The problem states that 1 pound is equivalent to 4.45 Newtons. So to convert the weight from Newtons to pounds:
[tex]\[
\text{Weight in lbs} = \frac{351.59}{4.45}
\][/tex]
This calculation gives us approximately 79 lbs.
5. Conclude:
The weight of the astronaut on Mercury is approximately 79 lbs.
Therefore, the astronaut would weigh about 79 pounds on Mercury.
1. Understand the Problem:
We need to find the weight of an astronaut (who has a mass of 95 kg) on the planet Mercury, in pounds (lbs).
2. Use the Correct Formula:
The weight of an object on a planet is calculated using the formula for gravitational force:
[tex]\[
F = \frac{G \times m_1 \times m_2}{r^2}
\][/tex]
where:
- [tex]\( F \)[/tex] is the gravitational force (weight) in Newtons,
- [tex]\( G \)[/tex] is the gravitational constant ([tex]\(6.67430 \times 10^{-11} \, m^3 kg^{-1} s^{-2}\)[/tex]),
- [tex]\( m_1 \)[/tex] is the mass of the astronaut (95 kg),
- [tex]\( m_2 \)[/tex] is the mass of Mercury ([tex]\(3.3 \times 10^{23} \, kg\)[/tex]),
- [tex]\( r \)[/tex] is the radius of Mercury (2,439,500 m).
3. Calculate the Gravitational Force:
Plug in the values to find the force in Newtons:
[tex]\[
F = \frac{6.67430 \times 10^{-11} \times 95 \times 3.3 \times 10^{23}}{(2,439,500)^2}
\][/tex]
This calculation results in approximately 351.59 Newtons.
4. Convert to Pounds:
The problem states that 1 pound is equivalent to 4.45 Newtons. So to convert the weight from Newtons to pounds:
[tex]\[
\text{Weight in lbs} = \frac{351.59}{4.45}
\][/tex]
This calculation gives us approximately 79 lbs.
5. Conclude:
The weight of the astronaut on Mercury is approximately 79 lbs.
Therefore, the astronaut would weigh about 79 pounds on Mercury.
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