A cylindrical log of radius 0.2 meter, 5 meters in length, and with a mass of 100 kilograms is placed vertically in a lake so that it is free to bob up and down. Assume that there is no water resistance. A weight of 100 kilograms of negligible volume is attached to the bottom of the log so that it remains vertical (so the total mass of the log and weight together is 200 kilograms). The mass density of water is 1000 kilograms per cubic meter. (For convenience, assume that the acceleration due to gravity is g =10m/s^2. There are two forces acting on the log: gravity and the buoyant force of the water. The buoyant force can be computed from Archimedes' principle: An object that is completely or partially submerged in a fluid is acted on by an upward (buoyant) force equal to the weight of the displaced fluid. Let t be time in seconds and let d(t) denote the depth (in meters) of the bottom of the log.

Required:
Compute the depth deq of the log in its equilibrium position, i. e. when the magnitude of the buoyant force is exactly equal the combined weight (in Newtons) of the log plus the mass.

Which one of the following research methods can show cause and effect

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?

Need people build a dam to create a reservoir that supplies water a nearby city needs. describe two ways this action will likely affect the water cycle in the local environment. (5 points) worth 20 points