A sample's force-extension curves enclose a loop during a repeatable closed loading-unloading cycle. What does the loop area represent?

• Work put in during the loading stage
• Work dissipated over the closed cycle
• Work returned during the unloading stage

An ideal Hooke's law spring has a straight force-extension graph from the origin to 10 N at an extension of 0.2 m. How much energy is stored, in joules?

During slow loading, area under a graph of applied stretching force against extension equals work done on the sample.

An ideal Hooke's law spring at final force F and extension x transfers all its energy to mass m, initially at rest. There is no height change or energy loss. Which equation determines speed v?

• half F x = half m v²
• half F x = half m v³
• half F x = half m v

In a repeatable closed loading-unloading cycle, 6 J of work is put into a sample and 4 J is returned. How much energy is dissipated, in joules?

A metal wire is modelled as ideal elastic with negligible energy dissipation. It is loaded and fully unloaded within its elastic range. What happens?

• It regains its length but returns less input work.
• It keeps a permanent extension while returning all input work.
• It regains its original length and returns the input work.

An ideal spring has a straight force-extension line from the origin to final force F and extension x. Lee calculates stored energy as F x. What is his error?

• He calculated the slope instead of the area under the line.
• He used the original length instead of the spring's extension.
• He used the surrounding rectangle's area instead of the triangle's area.

A spring transfers all 1 J of its stored energy to a 0.5 kg ball initially at rest. There is no height change or energy loss. What is the ball's final speed, in m/s?