A pendulum consists of a large balanced mass hanging on the end of a long wire. At the point where a 28-kg pendulum has the greatest potential energy, the angle between the pendulum’s weight and the wire is 89°.What is the wire’s length if the magnitude of the torque exerted by the pendulum’s weight at this position is 1.84 × 104 N•m?

When applying kirchhoff's rules, one of the essential steps is to mark each resistor with plus and minus signs to label how the electric potential changes from one end of the resistor to the other. the circuit in the drawing contains four resistors, each marked with the associated plus and minus signs. however, one resistor is marked incorrectly. which one is it?

John throws .4 kg ball with velocity of 18 m/s. hits .2 kg bottle and bottle flies 25 m/s. how fast is ball traveling after hitting the bottle?

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?