9. Work & Energy

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?

A gardener pushes a 12 kg lawnmower whose handle is tilted up 37° above horizontal. The lawnmower's coefficient of rolling friction is 0.15. How much power does the gardener have to supply to push the lawnmower at a constant speed of 1.2 m/s? Assume his push is parallel to the handle.

(a) How much work must you do to push a 10 kg block of steel across a steel table at a steady speed of 1.0m/s for 3.0 s? (b) What is your power output while doing so?

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?

Astronomers using a 2.0-m-diameter telescope observe a distant supernova—an exploding star. The telescope's detector records 9.1 x 10¯¹¹ J of light energy during the first 10 s. It's known that this type of supernova has a visible-light power output of 5.0 x 10³⁷ W for the first 10 s of the explosion. How distant is the supernova? Give your answer in light years, where one light year is the distance light travels in one year. The speed of light is 3.0 x 10⁸ m/s .

When you ride a bicycle at constant speed, nearly all the energy you expend goes into the work you do against the drag force of the air. Model a cyclist as having cross-section area 0.45 m² and, because the human body is not aerodynamically shaped, a drag coefficient of 0.90 . Use 1.2 kg/m³ as the density of air at room temperature. (c) The food calorie is equivalent to 4190 J. How many calories does the cyclist burn if he rides over level ground at 7.3 m/s for 1 h?

(a) How much work does an elevator motor do to lift a 1000 kg elevator a height of 100 m? (b) How much power must the motor supply to do this in 50 s at constant speed?

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 90 kg firefighter needs to climb the stairs of a 20-m-tall building while carrying a 40 kg backpack filled with gear. How much power does he need to reach the top in 55 s?

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 .

In a hydroelectric dam, water falls 25 m and then spins a turbine to generate electricity. (b) Suppose the dam is 80% efficient at converting the water's potential energy to electrical energy. How many kilograms of water must pass through the turbines each second to generate 50 MW of electricity? This is a typical value for a small hydroelectric dam.