Experiments using "optical tweezers" measure the elasticity of individual dna molecules. for small enough changes in length, the elasticity has the same form as that of a spring. a dna molecule is anchored at one end, then a force of 1.5 nn (1.5×10−9n) pulls on the other end, causing the molecule to stretch by 5.0nm (5.0×10−9m). what is the spring constant of that dna molecule?

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?

Madison lives near the ocean. she’s formed a hypothesis that increased concentrations of salt in the air speeds the corrosion of certain metals. if madison plans to test this hypothesis, she will have to deal with the following variables in her experiment: dependent variable: independent variable: one possible confounding variable:

How does changing the frequency affect the energy of the wave?