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.
To find out by 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 (0.880 J in this case)
- k is the spring constant (36.00 N/m in this case)
- x is the displacement or compression of the spring (unknown in this case)
Rearranging the formula, we can solve for x:
x = square root((2 * PE) / k)
Substituting the given values into the formula:
x = square root((2 * 0.880 J) / 36.00 N/m)
Calculating this expression will give us the answer to the question.