9. Work & Energy

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?

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?

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?

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. (b) 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. (a) What is the force constant of this strip of aortal material?

A 50 g rock is placed in a slingshot and the rubber band is stretched. The magnitude of the force of the rubber band on the rock is shown by the graph in FIGURE P9.56. The rubber band is stretched 30 cm and then released. What is the speed of the rock?