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A ball of mass m starting from rest, falls a vertical distance h before striking a vertical spring, which it compresses by a length delta. What is the spring constant of the spring? (Hint: Measure all the vertical distances from the point where the ball first touches the uncompressed spring, i.e., set this point as the origin of the vertical axis.)?
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A ball of mass m starting from rest, falls a vertical distance h befor...
Understanding the Problem
When the ball of mass m falls a distance h, it converts potential energy into kinetic energy. Upon striking the spring, it compresses the spring by a distance delta, converting kinetic energy into spring potential energy.
Energy Conservation Principle
- The potential energy (PE) lost by the ball as it falls is given by:
- PE_initial = m * g * h
- The kinetic energy (KE) just before hitting the spring is:
- KE = 0.5 * m * v^2
- The potential energy stored in the spring when compressed by delta is:
- PE_spring = 0.5 * k * delta^2
Here, k is the spring constant.
Setting Up the Equation
From the conservation of energy, we can equate the potential energy lost by the ball to the potential energy stored in the spring:
- m * g * h = 0.5 * m * v^2 + 0.5 * k * delta^2
Since the ball starts from rest, its initial kinetic energy is zero, leading to:
- m * g * h = 0.5 * k * delta^2
Finding the Spring Constant
To isolate k, rearrange the equation:
- k = (2 * m * g * h) / delta^2
This expression gives the spring constant in terms of the mass of the ball, the distance fallen, gravitational acceleration, and the compression of the spring.
Conclusion
- The spring constant k can be calculated using the formula derived above.
- Ensure to measure all distances from the point where the ball first touches the uncompressed spring to maintain consistency in your calculations.
When the ball of mass m falls a distance h, it converts potential energy into kinetic energy. Upon striking the spring, it compresses the spring by a distance delta, converting kinetic energy into spring potential energy.
Energy Conservation Principle
- The potential energy (PE) lost by the ball as it falls is given by:
- PE_initial = m * g * h
- The kinetic energy (KE) just before hitting the spring is:
- KE = 0.5 * m * v^2
- The potential energy stored in the spring when compressed by delta is:
- PE_spring = 0.5 * k * delta^2
Here, k is the spring constant.
Setting Up the Equation
From the conservation of energy, we can equate the potential energy lost by the ball to the potential energy stored in the spring:
- m * g * h = 0.5 * m * v^2 + 0.5 * k * delta^2
Since the ball starts from rest, its initial kinetic energy is zero, leading to:
- m * g * h = 0.5 * k * delta^2
Finding the Spring Constant
To isolate k, rearrange the equation:
- k = (2 * m * g * h) / delta^2
This expression gives the spring constant in terms of the mass of the ball, the distance fallen, gravitational acceleration, and the compression of the spring.
Conclusion
- The spring constant k can be calculated using the formula derived above.
- Ensure to measure all distances from the point where the ball first touches the uncompressed spring to maintain consistency in your calculations.
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A ball of mass m starting from rest, falls a vertical distance h before striking a vertical spring, which it compresses by a length delta. What is the spring constant of the spring? (Hint: Measure all the vertical distances from the point where the ball first touches the uncompressed spring, i.e., set this point as the origin of the vertical axis.)?
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A ball of mass m starting from rest, falls a vertical distance h before striking a vertical spring, which it compresses by a length delta. What is the spring constant of the spring? (Hint: Measure all the vertical distances from the point where the ball first touches the uncompressed spring, i.e., set this point as the origin of the vertical axis.)? for GATE Physics 2025 is part of GATE Physics preparation. The Question and answers have been prepared according to the GATE Physics exam syllabus. Information about A ball of mass m starting from rest, falls a vertical distance h before striking a vertical spring, which it compresses by a length delta. What is the spring constant of the spring? (Hint: Measure all the vertical distances from the point where the ball first touches the uncompressed spring, i.e., set this point as the origin of the vertical axis.)? covers all topics & solutions for GATE Physics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball of mass m starting from rest, falls a vertical distance h before striking a vertical spring, which it compresses by a length delta. What is the spring constant of the spring? (Hint: Measure all the vertical distances from the point where the ball first touches the uncompressed spring, i.e., set this point as the origin of the vertical axis.)?.
A ball of mass m starting from rest, falls a vertical distance h before striking a vertical spring, which it compresses by a length delta. What is the spring constant of the spring? (Hint: Measure all the vertical distances from the point where the ball first touches the uncompressed spring, i.e., set this point as the origin of the vertical axis.)? for GATE Physics 2025 is part of GATE Physics preparation. The Question and answers have been prepared according to the GATE Physics exam syllabus. Information about A ball of mass m starting from rest, falls a vertical distance h before striking a vertical spring, which it compresses by a length delta. What is the spring constant of the spring? (Hint: Measure all the vertical distances from the point where the ball first touches the uncompressed spring, i.e., set this point as the origin of the vertical axis.)? covers all topics & solutions for GATE Physics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball of mass m starting from rest, falls a vertical distance h before striking a vertical spring, which it compresses by a length delta. What is the spring constant of the spring? (Hint: Measure all the vertical distances from the point where the ball first touches the uncompressed spring, i.e., set this point as the origin of the vertical axis.)?.
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