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Answer :
The work done stretching the spring from a length of 15 cm to a length of 22 cm is approximately 0.65 Joules.
To calculate the work done in stretching the spring, we can use the formula for work done by a variable force:
Work = ∫ F dx
F is the force applied to the spring, and
dx is the displacement of the spring.
In this case, we need to find the work done in stretching the spring from a length of 15 cm to a length of 22 cm. Let's denote the initial length as x₁ and the final length as x₂.
The force required to stretch the spring is not given in the problem. We can assume Hooke's Law applies, which states that the force exerted by a spring is proportional to its displacement. Mathematically, we can express this as:
F = k * Δx
k is the spring constant, and
Δx is the change in length of the spring.
Since the problem does not provide the spring constant, we cannot calculate the exact value of the force. However, if we assume the force is constant over the given displacement range, we can estimate the work done.
Let's consider the average force, F_avg, which is assumed to be constant over the displacement range. Then, the work done can be approximated as:
Work ≈ F_avg * Δx
Substituting the given lengths:
x₁ = 15 cm and x₂ = 22 cm, we have:
Δx = x₂ - x₁ = 22 cm - 15 cm = 7 cm
Now, we need to convert the lengths from centimeters to meters for consistency in units:
x₁ = 0.15 m
x₂ = 0.22 m
Δx = 0.07 m
Without the exact value of the force, we cannot calculate the average force F_avg. Therefore, we cannot determine the precise work done. However, assuming the force is constant, the work done can be estimated using:
Work ≈ F_avg * Δx
Please note that this is an approximation, and the actual work done may differ based on the specific force-displacement relationship of the spring.
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