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The potential energy of a particle executing S.H.M. is 2.5 J when its displacement is half of amplitude. The total energy (in Joule) of the particle is :
Correct answer is '10'. Can you explain this answer?
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The potential energy of a particle executing S.H.M. is 2.5 J when its ...
Total energy 
Potential energy
So total energy
The correct answer is: 10
Potential energy
So total energy
The correct answer is: 10
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The potential energy of a particle executing S.H.M. is 2.5 J when its ...
The potential energy of a particle executing simple harmonic motion (S.H.M.) can be calculated using the formula:
Potential Energy = (1/2) * k * x²
Where:
- k is the spring constant (a measure of the stiffness of the spring)
- x is the displacement of the particle from its equilibrium position
In this case, we are given that the potential energy of the particle is 2.5 J when its displacement is half of the amplitude.
Let's assume that the amplitude of the S.H.M. is A. Therefore, when the displacement is half of the amplitude, it is A/2.
Using the given information, we can set up the equation:
2.5 = (1/2) * k * (A/2)²
Simplifying the equation:
2.5 = (1/2) * k * (A²/4)
Multiplying both sides by 4 to eliminate the fraction:
10 = k * (A²/4)
Multiplying both sides by 4/A²:
40/A² = k
Now, the total energy of the particle in S.H.M. is the sum of its kinetic energy and potential energy. Since total energy remains constant throughout the motion, it is equal to the maximum potential energy.
The maximum potential energy is given by:
Potential Energy = (1/2) * k * A²
Substituting the value of k from the previous equation:
Potential Energy = (1/2) * (40/A²) * A²
Simplifying the equation:
Potential Energy = 20
Therefore, the total energy of the particle is 20 J.
Potential Energy = (1/2) * k * x²
Where:
- k is the spring constant (a measure of the stiffness of the spring)
- x is the displacement of the particle from its equilibrium position
In this case, we are given that the potential energy of the particle is 2.5 J when its displacement is half of the amplitude.
Let's assume that the amplitude of the S.H.M. is A. Therefore, when the displacement is half of the amplitude, it is A/2.
Using the given information, we can set up the equation:
2.5 = (1/2) * k * (A/2)²
Simplifying the equation:
2.5 = (1/2) * k * (A²/4)
Multiplying both sides by 4 to eliminate the fraction:
10 = k * (A²/4)
Multiplying both sides by 4/A²:
40/A² = k
Now, the total energy of the particle in S.H.M. is the sum of its kinetic energy and potential energy. Since total energy remains constant throughout the motion, it is equal to the maximum potential energy.
The maximum potential energy is given by:
Potential Energy = (1/2) * k * A²
Substituting the value of k from the previous equation:
Potential Energy = (1/2) * (40/A²) * A²
Simplifying the equation:
Potential Energy = 20
Therefore, the total energy of the particle is 20 J.
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The potential energy of a particle executing S.H.M. is 2.5 J when its displacement is half of amplitude. The total energy (in Joule) of the particle is :Correct answer is '10'. Can you explain this answer?
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The potential energy of a particle executing S.H.M. is 2.5 J when its displacement is half of amplitude. The total energy (in Joule) of the particle is :Correct answer is '10'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The potential energy of a particle executing S.H.M. is 2.5 J when its displacement is half of amplitude. The total energy (in Joule) of the particle is :Correct answer is '10'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The potential energy of a particle executing S.H.M. is 2.5 J when its displacement is half of amplitude. The total energy (in Joule) of the particle is :Correct answer is '10'. Can you explain this answer?.
The potential energy of a particle executing S.H.M. is 2.5 J when its displacement is half of amplitude. The total energy (in Joule) of the particle is :Correct answer is '10'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The potential energy of a particle executing S.H.M. is 2.5 J when its displacement is half of amplitude. The total energy (in Joule) of the particle is :Correct answer is '10'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The potential energy of a particle executing S.H.M. is 2.5 J when its displacement is half of amplitude. The total energy (in Joule) of the particle is :Correct answer is '10'. Can you explain this answer?.
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