9. Work & Energy

An ideal spring with original length of $10\mathrm{cm}$ and spring constant of $2500\mathrm{N}/\mathrm{m}$ is stretched $2.0\mathrm{cm}$ to a length of $12\mathrm{cm}$. How much work must you do on the spring to stretch it an additional $3.0\mathrm{cm}$?

A spring-loaded toy gun shoots a $50\mathrm{g}$ metal ball at $4.0\mathrm{m}/\mathrm{s}$. How much energy was stored in the spring when it was cocked, and ready to shoot?

Justin slides a $500\mathrm{g}$ block of wood across a frictionless tabletop at $5.0\mathrm{m}/\mathrm{s}$. It collides with a horizontal spring which compresses $12\mathrm{cm}$ as the block comes to rest. What is the spring constant of the spring?

A $20.0\mathrm{cm}$ massless spring with spring constant $340\mathrm{N}/\mathrm{m}$ is suspended from the ceiling. A student carefully hangs a $450\mathrm{g}$ mass from the free end. How long is the spring now?