91Ó°ÊÓ

The power output of a cyclist moving at a constant speed of $6.0 \mathrm{m} / \mathrm{s}\( on a level road is \)120 \mathrm{W} .$ (a) What is the force exerted on the cyclist and the bicycle by the air? (b) By bending low over the handlebars, the cyclist reduces the air resistance to \(18 \mathrm{N} .\) If she maintains a power output of \(120 \mathrm{W},\) what will her speed be?

A car with mass of \(1000.0 \mathrm{kg}\) accelerates from $0 \mathrm{m} / \mathrm{s}\( to \)40.0 \mathrm{m} / \mathrm{s}\( in \)10.0 \mathrm{s} .$ Ignore air resistance. The engine has a \(22 \%\) efficiency, which means that \(22 \%\) of the energy released by the burning gasoline is converted into mechanical energy. (a) What is the average mechanical power output of the engine? (b) What volume of gasoline is consumed? Assume that the burning of \(1.0 \mathrm{L}\) of gasoline releases 46 MJ of energy.

A motorist driving a 1200 -kg car on level ground accelerates from $20.0 \mathrm{m} / \mathrm{s}\( to \)30.0 \mathrm{m} / \mathrm{s}\( in a time of \)5.0 \mathrm{s}$ Neglecting friction and air resistance, determine the average mechanical power in watts the engine must supply during this time interval.

A \(62-\mathrm{kg}\) woman takes \(6.0 \mathrm{s}\) to run up a flight of stairs. The landing at the top of the stairs is \(5.0 \mathrm{m}\) above her starting place. (a) What is the woman's average power output while she is running? (b) Would that be equal to her average power input-the rate at which chemical energy in food or stored fat is used? Why or why not?

How many grams of carbohydrate does a person of mass 74 kg need to metabolize to climb five flights of stairs \((15 \mathrm{m}\) height increase)? Each gram of carbohydrate provides 17.6 kJ of energy. Assume \(10.0 \%\) efficiency-that is, \(10.0 \%\) of the available chemical energy in the carbohydrate is converted to mechanical energy. What happens to the other \(90 \%\) of the energy?

A top fuel drag racer with a mass of \(500.0 \mathrm{kg}\) completes a quarter- mile \((402 \mathrm{m})\) drag race in a time of \(4.2 \mathrm{s}\) starting from rest. The car's final speed is \(125 \mathrm{m} / \mathrm{s}\). What is the engine's average power output? Ignore friction and air resistance.

(a) Calculate the change in potential energy of \(1 \mathrm{kg}\) of water as it passes over Niagara Falls (a vertical descent of \(50 \mathrm{m}\) ). (b) \(\mathrm{At}\) what rate is gravitational potential energy lost by the water of the Niagara River? The rate of flow is $5.5 \times 10^{6} \mathrm{kg} / \mathrm{s} .\( (c) If \)10 \%$ of this energy can be converted into electric energy, how many households would the electricity supply? (An average household uses an average electrical power of about \(1 \mathrm{kW} .\) )

A pole-vaulter converts the kinetic energy of running to elastic potential energy in the pole, which is then converted to gravitational potential energy. If a pole-vaulter's center of gravity is \(1.0 \mathrm{~m}\) above the ground while he sprints at \(10.0 \mathrm{~m} / \mathrm{s},\) what is the maximum height of his center of gravity during the vault? For an extended object, the gravitational potential energy is \(U=m g h,\) where \(h\) is the height of the center of gravity. (In \(1988,\) Sergei Bubka was the first pole-vaulter ever to clear \(6 \mathrm{~m}\).)