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The force exerted by a diving board is conservative, provided the internal friction is negligible. Assuming friction is negligible, describe changes in the potential energy of a diving board as a swimmer dives from it, starting just before the swimmer steps on the board until just after his feet leave it.

Consider the following scenario. A car for which friction is not negligible accelerates from rest down a hill, running out of gasoline after a short distance. The driver lets the car coast farther down the hill, then up and over a small crest. He then coasts down that hill into a gas station, where he brakes to a stop and fills the tank with gasoline. Identify the forms of energy the car has, and how they are changed and transferred in this series of events. (See Figure 7.34.)

Figure 7.34 A car experiencing non-negligible friction coasts down a hill, over a small crest, then downhill again, and comes to a stop at a gas station.

Describe the energy transfers and transformations for a javelin, starting from the point at which an athlete picks up the javelin and ending when the javelin is stuck into the ground after being thrown.

Boxing gloves are padded to lessen the force of a blow.

(a) Calculate the force exerted by a boxing glove on an opponent’s face, if the glove and face compress 7.50 cm during a blow in which the 7.00-kg arm and glove are brought to rest from an initial speed of 10.0 m/s.

(b) Calculate the force exerted by an identical blow in the gory old days when no gloves were used and the knuckles and face would compress only 2.00 cm.

(c) Discuss the magnitude of the force with glove on. Does it seem high enough to cause damage even though it is lower than the force with no glove?

Do devices with efficiencies of less than one violate the law of conservation of energy? Explain

A hydroelectric power facility (see Figure 7.38) converts the gravitational potential energy of water behind a dam to electric energy.

(a) What is the gravitational potential energy relative to the generators of a lake of volume$\mathbf{50}\mathbf{.}\mathbf{0}{\mathbf{\text{km}}}^{\mathbf{3}}$ $\left(\text{mass}=5.00×{10}^{13}\text{kg}\right)$, given that the lake has an average height of 40.0 m above the generators?

(b) Compare this with the energy stored in a 9-megaton fusion bomb.

List the energy conversions that occur when riding a bicycle.

Most electrical appliances are rated in watts. Does this rating depend on how long the appliance is on? (When off, it is a zero-watt device.) Explain in terms the definition of power.

In Example 7.7, we found that the speed of a roller coaster that had descended 20.0m was only slightly greater when it had an initial speed of 5.00m/s than when it started from rest. This implies that $\mathit{Δ}\mathbf{\text{PE}}\mathbf{≫}\mathit{Δ}{\mathbf{\text{KE}}}_{\mathbf{\text{i}}}$.Confirm this statement by taking the ratio of $\mathit{Δ}\mathbf{\text{PE}}$to $\mathit{Δ}{\mathbf{\text{KE}}}_{\mathbf{\text{i}}}$. (Note that mass cancels.)

A 100-g toy car is propelled by a compressed spring that starts it moving. The car follows the curved track in Figure 7.39. Show that the final speed of the toy car is 0.687 m/s if its initial speed is 2.00 m/s and it coasts up the frictionless slope, gaining 0.180 m in altitude.