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A smooth rod is mounted just above a tabletop . A 10 kg collar which is able to slide on the rod with negligible friction is fastened to a spring whose other end is attached to a pivot at O does spring has negligible mass a relaxed length of 10cm and the spring constant of 500 Newton per metre the collar is released from rest at point a what is its velocity as it passes point B?
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A smooth rod is mounted just above a tabletop . A 10 kg collar which i...
Analysis:
To find the velocity of the collar as it passes point B, we need to apply the principles of conservation of energy and Hooke's law.
Conservation of Energy:
When the collar is released from rest at point A, it possesses potential energy due to its displacement from the equilibrium position of the spring. As the collar moves towards point B, this potential energy is converted into kinetic energy.
Hooke's Law:
According to Hooke's law, the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The equation for Hooke's law is given by F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.
Calculations:
1. Calculate the potential energy of the collar at point A:
- The potential energy of the collar is given by PE = (1/2)kx^2, where k is the spring constant and x is the displacement from the equilibrium position.
- At point A, the displacement is 10 cm = 0.1 m.
- Substitute the values into the equation: PE = (1/2)(500 N/m)(0.1 m)^2 = 2.5 J.
2. Apply the principle of conservation of energy:
- At point A, the total energy of the system is equal to the potential energy of the collar.
- As the collar moves towards point B, its potential energy is converted into kinetic energy.
- At point B, all the potential energy is converted into kinetic energy.
- Therefore, the kinetic energy of the collar at point B is equal to the potential energy at point A.
- The equation for kinetic energy is KE = (1/2)mv^2, where m is the mass of the collar and v is its velocity.
- Substitute the values into the equation: 2.5 J = (1/2)(10 kg)v^2.
- Simplify the equation: v^2 = 0.5 m^2/s^2.
- Take the square root of both sides: v ≈ 0.707 m/s.
Answer:
The velocity of the collar as it passes point B is approximately 0.707 m/s.
To find the velocity of the collar as it passes point B, we need to apply the principles of conservation of energy and Hooke's law.
Conservation of Energy:
When the collar is released from rest at point A, it possesses potential energy due to its displacement from the equilibrium position of the spring. As the collar moves towards point B, this potential energy is converted into kinetic energy.
Hooke's Law:
According to Hooke's law, the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The equation for Hooke's law is given by F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.
Calculations:
1. Calculate the potential energy of the collar at point A:
- The potential energy of the collar is given by PE = (1/2)kx^2, where k is the spring constant and x is the displacement from the equilibrium position.
- At point A, the displacement is 10 cm = 0.1 m.
- Substitute the values into the equation: PE = (1/2)(500 N/m)(0.1 m)^2 = 2.5 J.
2. Apply the principle of conservation of energy:
- At point A, the total energy of the system is equal to the potential energy of the collar.
- As the collar moves towards point B, its potential energy is converted into kinetic energy.
- At point B, all the potential energy is converted into kinetic energy.
- Therefore, the kinetic energy of the collar at point B is equal to the potential energy at point A.
- The equation for kinetic energy is KE = (1/2)mv^2, where m is the mass of the collar and v is its velocity.
- Substitute the values into the equation: 2.5 J = (1/2)(10 kg)v^2.
- Simplify the equation: v^2 = 0.5 m^2/s^2.
- Take the square root of both sides: v ≈ 0.707 m/s.
Answer:
The velocity of the collar as it passes point B is approximately 0.707 m/s.
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A smooth rod is mounted just above a tabletop . A 10 kg collar which is able to slide on the rod with negligible friction is fastened to a spring whose other end is attached to a pivot at O does spring has negligible mass a relaxed length of 10cm and the spring constant of 500 Newton per metre the collar is released from rest at point a what is its velocity as it passes point B?
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A smooth rod is mounted just above a tabletop . A 10 kg collar which is able to slide on the rod with negligible friction is fastened to a spring whose other end is attached to a pivot at O does spring has negligible mass a relaxed length of 10cm and the spring constant of 500 Newton per metre the collar is released from rest at point a what is its velocity as it passes point B? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A smooth rod is mounted just above a tabletop . A 10 kg collar which is able to slide on the rod with negligible friction is fastened to a spring whose other end is attached to a pivot at O does spring has negligible mass a relaxed length of 10cm and the spring constant of 500 Newton per metre the collar is released from rest at point a what is its velocity as it passes point B? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A smooth rod is mounted just above a tabletop . A 10 kg collar which is able to slide on the rod with negligible friction is fastened to a spring whose other end is attached to a pivot at O does spring has negligible mass a relaxed length of 10cm and the spring constant of 500 Newton per metre the collar is released from rest at point a what is its velocity as it passes point B?.
A smooth rod is mounted just above a tabletop . A 10 kg collar which is able to slide on the rod with negligible friction is fastened to a spring whose other end is attached to a pivot at O does spring has negligible mass a relaxed length of 10cm and the spring constant of 500 Newton per metre the collar is released from rest at point a what is its velocity as it passes point B? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A smooth rod is mounted just above a tabletop . A 10 kg collar which is able to slide on the rod with negligible friction is fastened to a spring whose other end is attached to a pivot at O does spring has negligible mass a relaxed length of 10cm and the spring constant of 500 Newton per metre the collar is released from rest at point a what is its velocity as it passes point B? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A smooth rod is mounted just above a tabletop . A 10 kg collar which is able to slide on the rod with negligible friction is fastened to a spring whose other end is attached to a pivot at O does spring has negligible mass a relaxed length of 10cm and the spring constant of 500 Newton per metre the collar is released from rest at point a what is its velocity as it passes point B?.
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