The United States Patent and Trademark Office rejects claims for perpetual motion machines (in which energy output is as great or greater than energy input) without even investigating them. Why is this?

The metabolic power for typing is 150 W for Lili, not a lot as you know probably. How long does it take to burn off the energy in a slice of apple pie, which energy content is 1680 kJ (400 food calorie), in minutes?  (Try to stay active, working/studying in front of a computer is not the best exercise you can do for your body.) Your answer needs to have 3 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.

In Arizona, photovoltaic (PV) panels can generate an average annual power of 1 MW/acre. If there are 311 sunny days per year in Arizona, but only 160 sunny days per year in Pennsylvania, how much average power (in MW/acre) could the same PV panels generate in Pennsylvania? Please include two decimal places in your answer. Note: assume that a cloudy day delivers 0 watts/acre of solar power. This is not true, but it simplifies the problem for us.

Iceland has both high geothermal activity, with high temperatures near the surface, and abundant cold surface water. Iceland has many power plants that take advantage of the proximity of these natural hot and cold reservoirs. One plant uses an underground source at 122°C as the hot reservoir and a nearby lake at 5°C as the cold reservoir. The plant draws 16 MW from the hot reservoir to produce 1.8 MW of electricity. How does the actual efficiency of the plant compare to the theoretical maximum efficiency?

A sleeping 68 kg man has a metabolic power of 75 W . How many Calories does he burn during an 8.0 hour sleep? Express your answer using two significant figures.

A crate of mass 9.8 kg is pulled up a rough incline with an initial speed of 1.54 m/s. The pulling force is 102 N parallel to the incline, which makes an angle of 20.5° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5.04 m. (a) How much work is done by the gravitational force on the crate? נ| (b) Determine the increase in internal energy of the crate-incline system owing to friction. נן (c) How much work is done by the 102-N force on the crate? J (d) What is the change in kinetic energy of the crate? J (e) What is the speed of the crate after being pulled 5.04 m? m/s