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A 15 kg mass attached to a massless spring whose force constant is 2500n/m has amplitude of 4 cm. Assuming energy is quantized find number of system n if E =nhf?
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A 15 kg mass attached to a massless spring whose force constant is 250...
Given:
- Mass of the object (m) = 15 kg
- Force constant of the massless spring (k) = 2500 N/m
- Amplitude of the motion (A) = 4 cm = 0.04 m
- Energy of the system (E) = nhf
To find:
- Number of the system (n)
Explanation:
1. Potential Energy of the System:
The potential energy of a mass-spring system is given by the equation:
PE = 1/2 kx^2
where k is the force constant of the spring and x is the displacement from the equilibrium position.
In this case, the maximum potential energy of the system occurs at the maximum displacement, which is equal to the amplitude of the motion (A).
PE_max = 1/2 kA^2
2. Kinetic Energy of the System:
The kinetic energy of a mass-spring system is given by the equation:
KE = 1/2 mv^2
where m is the mass of the object and v is the velocity of the object.
At the maximum displacement, the velocity of the object is zero. Therefore, the kinetic energy of the system is zero.
KE_max = 0
3. Total Energy of the System:
The total energy of the system is the sum of the potential energy and the kinetic energy.
E = PE + KE
At the maximum displacement, the total energy of the system is equal to the maximum potential energy.
E_max = PE_max
4. Calculation of Number of the System:
Given that the energy is quantized and E = nhf, where n is the number of the system, h is Planck's constant, and f is the frequency of the system.
Since E_max = PE_max, we can substitute the equations for potential energy and total energy:
E_max = 1/2 kA^2
Substituting the given values:
E_max = 1/2 * 2500 N/m * (0.04 m)^2
Simplifying the equation:
E_max = 2 N/m * (0.04 m)^2
E_max = 2 * 0.0016 N * m
E_max = 0.0032 N * m
Now, we can equate E_max to nhf:
0.0032 N * m = nhf
Since the values of Planck's constant (h) and the frequency (f) are not given, we cannot determine the value of n directly. However, if the values of h and f are provided, we can solve for n using this equation.
Conclusion:
The number of the system (n) cannot be determined without the values of Planck's constant (h) and the frequency (f).
- Mass of the object (m) = 15 kg
- Force constant of the massless spring (k) = 2500 N/m
- Amplitude of the motion (A) = 4 cm = 0.04 m
- Energy of the system (E) = nhf
To find:
- Number of the system (n)
Explanation:
1. Potential Energy of the System:
The potential energy of a mass-spring system is given by the equation:
PE = 1/2 kx^2
where k is the force constant of the spring and x is the displacement from the equilibrium position.
In this case, the maximum potential energy of the system occurs at the maximum displacement, which is equal to the amplitude of the motion (A).
PE_max = 1/2 kA^2
2. Kinetic Energy of the System:
The kinetic energy of a mass-spring system is given by the equation:
KE = 1/2 mv^2
where m is the mass of the object and v is the velocity of the object.
At the maximum displacement, the velocity of the object is zero. Therefore, the kinetic energy of the system is zero.
KE_max = 0
3. Total Energy of the System:
The total energy of the system is the sum of the potential energy and the kinetic energy.
E = PE + KE
At the maximum displacement, the total energy of the system is equal to the maximum potential energy.
E_max = PE_max
4. Calculation of Number of the System:
Given that the energy is quantized and E = nhf, where n is the number of the system, h is Planck's constant, and f is the frequency of the system.
Since E_max = PE_max, we can substitute the equations for potential energy and total energy:
E_max = 1/2 kA^2
Substituting the given values:
E_max = 1/2 * 2500 N/m * (0.04 m)^2
Simplifying the equation:
E_max = 2 N/m * (0.04 m)^2
E_max = 2 * 0.0016 N * m
E_max = 0.0032 N * m
Now, we can equate E_max to nhf:
0.0032 N * m = nhf
Since the values of Planck's constant (h) and the frequency (f) are not given, we cannot determine the value of n directly. However, if the values of h and f are provided, we can solve for n using this equation.
Conclusion:
The number of the system (n) cannot be determined without the values of Planck's constant (h) and the frequency (f).
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A 15 kg mass attached to a massless spring whose force constant is 2500n/m has amplitude of 4 cm. Assuming energy is quantized find number of system n if E =nhf?
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A 15 kg mass attached to a massless spring whose force constant is 2500n/m has amplitude of 4 cm. Assuming energy is quantized find number of system n if E =nhf? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A 15 kg mass attached to a massless spring whose force constant is 2500n/m has amplitude of 4 cm. Assuming energy is quantized find number of system n if E =nhf? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 15 kg mass attached to a massless spring whose force constant is 2500n/m has amplitude of 4 cm. Assuming energy is quantized find number of system n if E =nhf?.
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