She weighs 599 N on Earth
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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:
weight of astronaut on the Moon = w_m = 99 N
acceleration of gravity on the moon = a_m = 1.62 m/s²
acceleration of gravity on the moon = a_e = 9.80 m/s²
Asked:
weight of astronaut on the Earth = w_e = ?
Solution:
[tex]w_e : w_m = m g_e : m g_m[/tex]
[tex]w_e : w_m = g_e : g_m[/tex]
[tex]w_e : 99 = 9.80 : 1.62[/tex]
[tex]w_e = \frac{9.80}{1.62} \times 99[/tex]
[tex]w_e \approx 599 \texttt{ N}[/tex]
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She weighs 599 N on Earth
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Grade: High School
Subject: Physics
Chapter: Gravitational Fields
