The potential energy stored in the compressed spring of a dart gun, with a spring constant of 36.00 N/m, is 0.880 J. Find by how much is the spring is compressed.
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To find how much the spring is compressed, we can use the formula for the potential energy stored in a compressed spring:
Potential Energy = 1/2 * k * x^2
Where:
- Potential Energy is the energy stored in the spring (0.880 J in this case)
- k is the spring constant (36.00 N/m)
- x is the displacement of the spring (the amount it is compressed)
Rearranging the formula, we can solve for x:
x = sqrt((2 * Potential Energy) / k)
Let's substitute the given values and calculate:
x = sqrt((2 * 0.880 J) / 36.00 N/m)
x = sqrt(0.0489 J/N)
x ≈ 0.221 m
Therefore, the spring is compressed by approximately 0.221 meters.