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The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm, potential energy stored in it will be :
- a)4U
- b)8U
- c)16U
- d)2U
Correct answer is option 'C'. Can you explain this answer?
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The potential energy of a long spring when stretched by2cmis U. If the...
Potential Energy of a Stretched Spring
When a spring is stretched or compressed from its equilibrium position, it stores potential energy. The potential energy stored in a spring is given by the equation:
U = (1/2) k x^2
Where U is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.
Given Information:
- The potential energy of a long spring when stretched by 2 cm is U.
- The spring is stretched by 8 cm.
Calculating Potential Energy:
Let's calculate the potential energy stored in the spring when it is stretched by 8 cm.
Using the given information, we can write the equation for potential energy as:
U = (1/2) k x^2
Substituting the given values:
U = (1/2) k (8 cm)^2
Simplifying the equation:
U = (1/2) k (64 cm^2)
U = 32 k cm^2
Therefore, the potential energy stored in the spring when stretched by 8 cm is 32 k cm^2.
Comparing Potential Energies:
Now, let's compare the potential energy stored in the spring when it is stretched by 8 cm with the potential energy when it is stretched by 2 cm.
Given: The potential energy of the spring when stretched by 2 cm is U.
Comparing the two potential energies:
32 k cm^2 = 16 times U (since (8 cm)^2 = 64 cm^2 and 64 cm^2 / (2 cm)^2 = 16)
Therefore, the potential energy stored in the spring when stretched by 8 cm is 16 times the potential energy when it is stretched by 2 cm.
Conclusion:
The potential energy stored in the spring when it is stretched by 8 cm is 16U. Therefore, the correct answer is option C.
When a spring is stretched or compressed from its equilibrium position, it stores potential energy. The potential energy stored in a spring is given by the equation:
U = (1/2) k x^2
Where U is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.
Given Information:
- The potential energy of a long spring when stretched by 2 cm is U.
- The spring is stretched by 8 cm.
Calculating Potential Energy:
Let's calculate the potential energy stored in the spring when it is stretched by 8 cm.
Using the given information, we can write the equation for potential energy as:
U = (1/2) k x^2
Substituting the given values:
U = (1/2) k (8 cm)^2
Simplifying the equation:
U = (1/2) k (64 cm^2)
U = 32 k cm^2
Therefore, the potential energy stored in the spring when stretched by 8 cm is 32 k cm^2.
Comparing Potential Energies:
Now, let's compare the potential energy stored in the spring when it is stretched by 8 cm with the potential energy when it is stretched by 2 cm.
Given: The potential energy of the spring when stretched by 2 cm is U.
Comparing the two potential energies:
32 k cm^2 = 16 times U (since (8 cm)^2 = 64 cm^2 and 64 cm^2 / (2 cm)^2 = 16)
Therefore, the potential energy stored in the spring when stretched by 8 cm is 16 times the potential energy when it is stretched by 2 cm.
Conclusion:
The potential energy stored in the spring when it is stretched by 8 cm is 16U. Therefore, the correct answer is option C.
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The potential energy of a long spring when stretched by2cmis U. If the...
Fo x = 2
Eq. (2)/eq. (1)
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The potential energy of a long spring when stretched by2cmis U. If the spring is stretched by8cm, potential energy stored in it will be :a)4Ub)8Uc)16Ud)2UCorrect answer is option 'C'. Can you explain this answer?
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