Abungee cord can stretch, but it is never compressed. when thedistance between the two ends of the cord is less than its unstretched lengthl0, the cord folds and its tension is zero. for simplicity, neglect the cord’s ownweight and inertia as well as the air drag on the ball and the cord. a bungee cord has lengthl0 = 33 m when unstretched; when it’s stretched to l > l0, thecord’s tension obeys hooke’s law with "spring" constant 39 n/m. to test the cord’sreliability, one end is tied to a high bridge of height 94 m above the surface of a river) and the other end is tiedto a steel ball of mass75 kg. the ball is dropped off the bridge with zero initial speed. fortunately, the cord works and the ball stops in the air a fewmeters before it hits the water — and then the cord pulls itback up. the acceleration of gravity is 9.8 m/s2 . calculate theball’s height above the water’s surface at this lowest point of its trajectory. what is the tension of the bungee cord when the ballis at its lowest point?

Aheat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. the same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. heat pumps are widely used for home heating. you can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat qh, warming the indoors. perhaps this seems a little silly, but consider the following. electricity can be directly used to heat a home by passing an electric current through a heating coil. this is a direct, 100% conversion of work to heat. that is, 19.0 \rm kw of electric power (generated by doing work at the rate 19.0 kj/s at the power plant) produces heat energy inside the home at a rate of 19.0 kj/s. suppose that the neighbor's home has a heat pump with a coefficient of performance of 4.00, a realistic value. note: with a refrigerator, "what you get" is heat removed. but with a heat pump, "what you get" is heat delivered. so the coefficient of performance of a heat pump is k=qh/win. an average price for electricity is about 40 mj per dollar. a furnace or heat pump will run typically 200 hours per month during the winter. what does one month's heating cost in the home with a 16.0 kw electric heater? what does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?