Biologists use optical tweezers to manipulate micron-sized objects using a beam of light. in this technique, a laser beam is focused to a very small-diameter spot. because small particles are attracted to regions of high light intensity, the focused beam can be used to "grab" onto particles and manipulate them for various experiments. in one experiment, a 10 mw laser beam is focused to a spot that has a diameter of 0.67 μmpart a: what is the intensity of the light in this spot? part b: what is the amplitude of the electric field?

The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 ? t ? 8. (a) when is the position function decreasing? (round you

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?

Henry, whose mass is 95 kg, stands on a bathroom scale in an elevator. the scale reads 830 n for the first 2.4 s after the elevator starts moving, then 930 n for the next 2.4 s. part a what is the elevator's speed 4.8 s after starting? express your answer with the appropriate units.