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?

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 $\overrightarrow{F}$ is applied in the horizontal direction (so $\overrightarrow{F}$ = Fî ), moving the bob very slowly so the acceleration is essentially zero. (Note that the magnitude of $\overrightarrow{F}$ will need to vary with the angle θ that the cord makes with the vertical at any moment.) Determine the work done by this force, $\overrightarrow{F}$, to move the pendulum from θ = 0 to θ₀.

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A $6.0$-kg box moving at $3.0$ m/s on a horizontal, frictionless surface runs into a light spring of force constant $75$ N/cm. Use the work–energy theorem to find the maximum compression of the spring.

A surgeon is using material from a donated heart to repair a patient's damaged aorta and needs to know the elastic characteristics of this aortal material. Tests performed on a $16.0$-cm strip of the donated aorta reveal that it stretches $3.75$ cm when a $1.50$-N pull is exerted on it. If the maximum distance it will be able to stretch when it replaces the aorta in the damaged heart is $1.14$ cm, what is the greatest force it will be able to exert there?

A surgeon is using material from a donated heart to repair a patient's damaged aorta and needs to know the elastic characteristics of this aortal material. Tests performed on a $16.0$-cm strip of the donated aorta reveal that it stretches $3.75$ cm when a $1.50$-N pull is exerted on it. What is the force constant of this strip of aortal material?

(II) A spring has k = 65 N/m . Draw a graph like that in Fig. 7–11 and use it to determine the work needed to stretch the spring from x = 3.0cm to x = 7.5cm, where x = 0 refers to the spring’s unstretched length.