The magnitude of the net of force is about 37 Newton
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Further explanation
Centripetal Acceleration can be formulated as follows:
[tex]\large {\boxed {a = \frac{ v^2 } { R } }[/tex]
a = Centripetal Acceleration ( m/s² )
v = Tangential Speed of Particle ( m/s )
R = Radius of Circular Motion ( m )
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Centripetal Force can be formulated as follows:
[tex]\large {\boxed {F = m \frac{ v^2 } { R } }[/tex]
F = Centripetal Force ( m/s² )
m = mass of Particle ( kg )
v = Tangential Speed of Particle ( m/s )
R = Radius of Circular Motion ( m )
Let us now tackle the problem !
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Given:
period of the circular motion = T = 2.60 × 10⁸ = 8.20 × 10¹⁵ seconds
radius of the orbit = R = 3.00 × 10⁴ light years = 2.84 × 10²⁰ m
Unknown:
(a) centripetal acceleration = a = ?
(b) average speed = v = ?
Solution:
Question (a):
[tex]a = \omega^2 R[/tex]
[tex]a = (\frac{2\pi}{T})^2 R[/tex]
[tex]a = (\frac{2\pi}{8.20 \times 10^{15}})^2 \times 2.84 \times 10^{20}[/tex]
[tex]a \approx 1.67 \times 10^{-10} \texttt{ m/s}^2[/tex]
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Question (b):
[tex]v = \omega R[/tex]
[tex]v = (\frac{2\pi}{T}) R[/tex]
[tex]v = (\frac{2\pi}{8.20 \times 10^{15}}) \times 2.84 \times 10^{20}[/tex]
[tex]v \approx 2.18 \times 10^{5} \texttt{ m/s}[/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: Circular Motion
