A force of 3 N stretches a spring by 1 m. (a) Find the spring constant k.
(b) A mass of 4 kg is attached to the spring. At t-0, the mass is pulled down a distance 1 m from equilibrium and released with a downward velocity of 0.5 m/s. Assuming that damping is negligible, determine an expression for the position y of the mass at time t. (Assume that y is the distance in meters from the equilibrium position, where distances are measured positive in the downward direction. Enter your answer as an equation involving y andt.) V 3
Find the circular frequency of the system and the amplitude, phase, and period of the motion. circular frequency-1 X s-1 amplitude phase 6 period

Aplane takes off from an airport and flies to town a, located d1 = 215 km from the airport in the direction 20.0° north of east. the plane then flies to town b, located d2 = 230 km at 30.0° west of north from town a. use graphical methods to determine the distance and direction from town b to the airport. (enter the distance in km and the direction in degrees south of west.)

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?

Explain why you think this diagram shows what happened to the carbon in the biodome.