The weight of a 59.1-kg astronaut on a planet would be about
C) 1160 N
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Further explanation
Newton's gravitational law states that the force of attraction between two objects can be formulated as follows:
[tex]\large {\boxed {F = G \frac{m_1 ~ m_2}{R^2}} }[/tex]
F = Gravitational Force ( Newton )
G = Gravitational Constant ( 6.67 × 10⁻¹¹ Nm² / kg² )
m = Object's Mass ( kg )
R = Distance Between Objects ( m )
Let us now tackle the problem !
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Given:
mass of the astronaut = m = 59.1 kg
density of Earth = density of Planet = ρ
radius of Earth = R₁ = R
radius of Planet = R₂ = 2R
Asked:
weight of the astronaut on planet = w₂ = ?
Solution:
We will compare the weight of the astronaut on planet and earth as follows:
[tex]w_2 : w_1 = mg_2 : mg_1[/tex]
[tex]w_2 : w_1 = g_2 : g_1[/tex]
[tex]w_2 : w_1 = G\frac{m_2}{(R_2)^2} : G\frac{m_1}{(R_1)^2}[/tex]
[tex]w_2 : w_1 = G\frac{\rho V_2}{(R_2)^2} : G\frac{\rho V_1}{(R_1)^2}[/tex]
[tex]w_2 : w_1 = \frac{V_2}{(R_2)^2} : \frac{V_1}{(R_1)^2}[/tex]
[tex]w_2 : w_1 = \frac{\frac{4}{3} \pi (R_2)^3}{(R_2)^2} : \frac{\frac{4}{3} \pi (R_1)^3}{(R_1)^2}[/tex]
[tex]w_2 : w_1 = R_2 : R_1[/tex]
[tex]w_2 : w_1 = 2R : R[/tex]
[tex]w_2 : w_1 = 2 : 1[/tex]
[tex]w_2 = 2w_1[/tex]
[tex]w_2 = 2m g_1[/tex]
[tex]w_2 = 2(59.1)(9.8)[/tex]
[tex]w_2 \approx 1160 \texttt{ Newton}[/tex]
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Learn more
- Impacts of Gravity : https://brainly.com/question/5330244
- Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
- The Acceleration Due To Gravity : https://brainly.com/question/4189441
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Answer details
Grade: High School
Subject: Physics
Chapter: Gravitational Fields
