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 simple pendulum consists of a small object of mass m (the “bob”) suspended by a cord of length ℓ (Fig. 7–34) of negligible mass. A force F→ is applied in the horizontal direction (so F→ = Fî ), moving the bob very slowly so the acceleration is essentially zero. (Note that the magnitude of F→ will need to vary with the angle θ that the cord makes with the vertical at any moment.)

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(a) Determine the work done by this force, F→ , to move the pendulum from θ = 0 to θ₀ .