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.
PE=1/2 k x^2
solve for x
To find how much the spring is compressed, we can use the formula for potential energy stored in a spring:
Potential energy (PE) = (1/2) * k * x^2
Where:
PE is the potential energy stored in the spring (given as 0.880 J),
k is the spring constant (given as 36.00 N/m),
x is the amount the spring is compressed (the unknown).
We can rearrange the formula and solve for x:
x^2 = (2 * PE) / k
x = √((2 * PE) / k)
Now we can substitute the given values into the formula to calculate the compression of the spring:
x = √((2 * 0.880 J) / 36.00 N/m)
x = √(1.76 J / 36.00 N/m)
x = √0.0489 m^2
x ≈ 0.221 m
Therefore, the spring is compressed by approximately 0.221 meters.