9. Work & Energy

A driver notices that her 950-kg car, when in neutral, slows down from 95 km/h to 65 km/h in about 7.0 s on a flat horizontal road. Approximately what power (watts and hp) is needed to keep the car traveling at a constant 80 km/h?

An outboard motor for a boat is rated at 35 hp. If it can move a particular boat at a steady speed of 35 km/h, what is the total force resisting the motion of the boat?

The true power is dissipated by the $R$ of any circuit. What does $R$ represent in this context?

Power is defined as the rate at which work is done. What is the value of power in terms of work $W$ and time $t$?

Which term describes the rate at which work is done ($\frac{W}{t}$)?

A hydroelectric power plant uses spinning turbines to transform the kinetic energy of moving water into electric energy with 80% efficiency. That is, 80% of the kinetic energy becomes electric energy. A small hydroelectric plant at the base of a dam generates 50 MW of electric power when the falling water has a speed of 18 m/s. What is the water flow rate - kilograms of water per second - through the turbines?

Suppose it takes 75 kW of power for your car to travel at a constant speed on the highway. What is this in horsepower?

A “60-watt equivalent” LED lightbulb is rated at 7.5 W and 800 lumens. How much power goes into light? (The rest goes into heat.)

Finish the solution of the problem.

$T-(1500\,\(\text{kg}\))(9.8\,\(\text{m/s}\)^2)=(1500\,\(\text{kg}\))\(\left\)(1.0\,\(\text{m/s}\)^2\(\right\))$

$P=T(2.0\,\(\text{m/s}\))$

A $20.0$-kg rock is sliding on a rough, horizontal surface at $8.00$ m/s and eventually stops due to friction. The coefficient of kinetic friction between the rock and the surface is $0.200$. What average power is produced by friction as the rock stops?

During a workout, football players ran up the stadium stairs in 75 s. The distance along the stairs is 83 m and they are inclined at a 33° angle. If a player has a mass of 88 kg, estimate his average power output on the way up. Ignore friction and air resistance.

A farmer uses a tractor to pull a 150 kg bale of hay up a 15° incline to the barn at a steady 5.0 km/h. The coefficient of kinetic friction between the bale and the ramp is 0.45. What is the tractor's power output?

A 70 kg human sprinter can accelerate from rest to 10 m/s in 3.0 s. During the same time interval, a 30 kg greyhound can go from rest to 20 m/s. What is the average power output of each? Average power over a time interval ∆t is ∆E/∆t.

Energy may be stored by pumping water to a high reservoir when demand is low and then releasing it to drive turbines (Fig. 20–15) during peak demand. Suppose water is pumped to a lake 105 m above the turbines at a rate of 1.00 x 10⁵ kg/s for 10.0 h at night. If all this energy is released during a 14-h day, at 75% efficiency, what is the average power output?