calculate the energy content of
a. a 16000lb elevator at a height of 100ft
b. a 200kg horse moving at 10m/s
c. a gram of nuclear fuel containing 20pg of mass convertible to E.
To calculate the energy content for each scenario, we can use the principles of potential energy, kinetic energy, and Einstein's mass-energy equivalence equation (E = mc^2). Let's break down each scenario one by one:
a. Energy content of a 16000 lb elevator at a height of 100 ft:
1. Converting the weight from pounds to Newtons:
16000 lb = 16000 lb * 4.448 N/lb = 71232 N (rounded to nearest whole number)
2. Calculating the potential energy:
Potential energy = Weight * Height difference
Potential energy = 71232 N * 100 ft = 7123200 N·ft
Note: If you prefer to use SI units, you can convert the potential energy from foot-pounds (ft·lb) to Joules (J) by multiplying by a conversion factor of 1.3558 J/ft·lb.
b. Energy content of a 200 kg horse moving at 10 m/s:
1. Calculating the kinetic energy:
Kinetic energy = 0.5 * Mass * Velocity^2
Kinetic energy = 0.5 * 200 kg * (10 m/s)^2 = 10000 J
c. Energy content of a gram of nuclear fuel containing 20 pg of mass convertible to energy:
1. Converting the mass from picograms (pg) to kilograms:
20 pg = 20 pg / 10^12 kg/pg = 2e-14 kg
2. Calculating the energy using E = mc^2:
Energy = Mass * (Speed of Light)^2
Energy = 2e-14 kg * (3e8 m/s)^2 = 1.8e-3 J
Note: The energy obtained is a very small value due to the conversion factor from mass to energy.
Keep in mind that these calculations assume certain assumptions, such as neglecting factors like friction and air resistance. Additionally, the energy content mentioned here is the potential or kinetic energy associated with the given scenarios, not the total energy content of the elevator, horse, or nuclear fuel.