A spring attached to the ceiling is stretched 100 mm when a mass of 2 kg is hung on its end.How much work must be done to compress the spring by 6 cm?

Question

Quizplus · Accepted Answer

The work done to compress or stretch a spring can be calculated using the formula $W = \frac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is the displacement from the equilibrium position. First, we need to find the spring constant $k$. The force exerted by the spring when stretched 100 mm (or 0.1 m) by a 2 kg mass is equal to the weight of the mass, $F = mg = 2 \times 9.8 = 19.6 \, \text{N}$. Using Hooke's law, $F = kx$, we can solve for $k$: $k = \frac{F}{x} = \frac{19.6}{0.1} = 196 \, \text{N/m}$. To compress the spring by 6 cm (or 0.06 m), we use the work formula with the found value of $k$: $W = \frac{1}{2} \times 196 \times (0.06)^2 = 0.35 \, \text{J}$.

A Spring Attached to the Ceiling Is Stretched 100 Mm