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A mass of 6 kg is suspended by a rope of length 2 m from a ceiling a force of 16 newton is applied in a horizontal direction at the midpoint of the rope what is the angle between the rope and the vertical at the equilibrium?
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A mass of 6 kg is suspended by a rope of length 2 m from a ceiling a f...
To solve this problem, we need to analyze the forces acting on the mass when it is in equilibrium.
Understanding the Forces
- The gravitational force acting on the mass (weight) can be calculated as:
- Weight (W) = mass (m) × gravitational acceleration (g) = 6 kg × 9.81 m/s² = 58.86 N.
- There are two main forces acting on the mass at equilibrium:
- Tension (T) in the rope.
- Horizontal applied force (F) = 16 N.
Setting Up the Equations
- At equilibrium, the vertical and horizontal components of the forces must balance out.
- The vertical component of tension must equal the weight:
- T_vertical = W = 58.86 N.
- The horizontal component of tension must equal the applied force:
- T_horizontal = F = 16 N.
Using Trigonometry
- The angle (θ) between the rope and the vertical can be determined using the relationships of the components of tension:
- T_vertical = T * cos(θ)
- T_horizontal = T * sin(θ)
- Dividing the horizontal by vertical components gives:
- tan(θ) = T_horizontal / T_vertical
- tan(θ) = F / W = 16 N / 58.86 N.
Calculating the Angle
- Now plug in the values:
- tan(θ) = 16 / 58.86 ≈ 0.271.
- To find the angle (θ):
- θ = arctan(0.271) ≈ 15.2°.
Conclusion
- The angle between the rope and the vertical at equilibrium is approximately **15.2 degrees**. This angle results from the balance of the gravitational force and the horizontal force applied at the midpoint of the rope.
Understanding the Forces
- The gravitational force acting on the mass (weight) can be calculated as:
- Weight (W) = mass (m) × gravitational acceleration (g) = 6 kg × 9.81 m/s² = 58.86 N.
- There are two main forces acting on the mass at equilibrium:
- Tension (T) in the rope.
- Horizontal applied force (F) = 16 N.
Setting Up the Equations
- At equilibrium, the vertical and horizontal components of the forces must balance out.
- The vertical component of tension must equal the weight:
- T_vertical = W = 58.86 N.
- The horizontal component of tension must equal the applied force:
- T_horizontal = F = 16 N.
Using Trigonometry
- The angle (θ) between the rope and the vertical can be determined using the relationships of the components of tension:
- T_vertical = T * cos(θ)
- T_horizontal = T * sin(θ)
- Dividing the horizontal by vertical components gives:
- tan(θ) = T_horizontal / T_vertical
- tan(θ) = F / W = 16 N / 58.86 N.
Calculating the Angle
- Now plug in the values:
- tan(θ) = 16 / 58.86 ≈ 0.271.
- To find the angle (θ):
- θ = arctan(0.271) ≈ 15.2°.
Conclusion
- The angle between the rope and the vertical at equilibrium is approximately **15.2 degrees**. This angle results from the balance of the gravitational force and the horizontal force applied at the midpoint of the rope.
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A mass of 6 kg is suspended by a rope of length 2 m from a ceiling a force of 16 newton is applied in a horizontal direction at the midpoint of the rope what is the angle between the rope and the vertical at the equilibrium?
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A mass of 6 kg is suspended by a rope of length 2 m from a ceiling a force of 16 newton is applied in a horizontal direction at the midpoint of the rope what is the angle between the rope and the vertical at the equilibrium? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A mass of 6 kg is suspended by a rope of length 2 m from a ceiling a force of 16 newton is applied in a horizontal direction at the midpoint of the rope what is the angle between the rope and the vertical at the equilibrium? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mass of 6 kg is suspended by a rope of length 2 m from a ceiling a force of 16 newton is applied in a horizontal direction at the midpoint of the rope what is the angle between the rope and the vertical at the equilibrium?.
A mass of 6 kg is suspended by a rope of length 2 m from a ceiling a force of 16 newton is applied in a horizontal direction at the midpoint of the rope what is the angle between the rope and the vertical at the equilibrium? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A mass of 6 kg is suspended by a rope of length 2 m from a ceiling a force of 16 newton is applied in a horizontal direction at the midpoint of the rope what is the angle between the rope and the vertical at the equilibrium? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mass of 6 kg is suspended by a rope of length 2 m from a ceiling a force of 16 newton is applied in a horizontal direction at the midpoint of the rope what is the angle between the rope and the vertical at the equilibrium?.
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