An alpha particle is a nucleus of helium. it has twice the charge and four times the mass of the proton. when they were very far away from each other, but headed toward directly each other, a proton and an alpha particle each had an initial speed of 3.1×10−3 c, where c is the speed of light. what is their distance of closest approach? there are two conserved quantities. make use of both of them. (c = 3.00 × 108 m/s, k = 1/4πε 0 = 8.99 × 109 n · m2/c2, e = 1.60 × 10-19 c, m proton = 1.67 x 10-27 kg)

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?

The temperature at a point (x, y) is t(x, y), measured in degrees celsius. a bug crawls so that its position after t seconds is given by x = 6 + t , y = 8 + 1 3 t, where x and y are measured in centimeters. the temperature function satisfies tx(3, 9) = 5 and ty(3, 9) = 4. how fast is the temperature rising on the bug's path after 3 seconds? (round your answer to two decimal places.)

Which of the following is the phase that results when the moon is on the opposite side of the earth from the sun? a. quarter moon b. crescent moon c. new moon d. full moon