A) Tension in the cord A ≈ 570 Newton
B) Tension in the cord B ≈ 700 Newton
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Further explanation
Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.
\(\large {\boxed {F = ma }\)
F = Force ( Newton )
m = Object's Mass ( kg )
a = Acceleration ( m )
Let us now tackle the problem !
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Given:
weight of the suspended object = w = 210 N
Asked:
tension in the cord A = T_A = ?
tension in the cord B = T_B = ?
Solution:
Let:
γ = 360° - 60° - 45° - 90° = 165°
α = 90° + 45° = 135°
β = 60°
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We will use Lami's Theorem in this question.
If the system is in equilibrium , then:
\(\large {\boxed{\frac{T_A}{\sin \alpha} = \frac{w}{\sin \gamma}}}\)
\(T_A = w \times \frac{\sin \alpha}{sin \gamma}\)
\(T_A = 210 \times \frac{\sin 135^o}{sin 165^o}\)
\(T_A = 210 \times ( 1 + \sqrt{3} )\)
\(T_A \approx 570 \texttt{ Newton}\)
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\(\large {\boxed {\frac{T_B}{\sin \beta} = \frac{w}{\sin \gamma}}}\)
\(T_B = w \times \frac{\sin \beta}{sin \gamma}\)
\(T_B = 210 \times \frac{\sin 60^o}{sin 165^o}\)
\(T_B = 210 \times \frac{1}{2}( 6 + 3\sqrt{2} )\)
\(T_B \approx 700 \texttt{ Newton}\)
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Learn more
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- The Acceleration Due To Gravity : https://brainly.com/question/4189441
- Newton's Law of Motion: https://brainly.com/question/10431582
- Example of Newton's Law: https://brainly.com/question/498822
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Answer details
Grade: High School
Subject: Physics
Chapter: Dynamics
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Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant
