Compare the energy scales of mechanical, chemical, and mass energy by calculatin

Question

Compare the energy scales of mechanical, chemical, and mass energy by calculating (a) the energy associated with dropping 1 kg of coal through a vertical distance of 100 m, (b) burning 1 kg of coal, and (c) converting the mass of 1 kg of coal into energy An elevator has a rated capacity of 2, 000 pound mass (907 kg). It can transport people at the rated capacity between the first and the fifth floors in 7 seconds with a vertical distance of 15 ft (4.6 m) between each floor. Estimate the power requirement for such an elevator. One cubic meter of water is poured off a 100-m high bridge. If the change in gravitational potential energy is converted into electricity with an efficiency of 90%, how long can this energy illuminate a standard 60-W light bulb? One gram of methane is burned, and the heat is used to raise the temperature of 1 kg of water. If the initial temperature of the water is 25 degree C, what is the final temperature?

Explanation / Answer

a) energy associated with dropping 1 kg of coal through a vertical distance of 100 m is gravitational potential energy

then energy associated is U = m*g*h = 1*9.8*100 = 980 J

b) burnign of a kg of coal gives chemical energy of 29.3*10^6 J

C) Using mass - energy relation

E = m*c^2 = 1*(3*10^8)^2 = 9*10^16 J

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