alculate 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 in each scenario, we can use the formula for potential energy and kinetic energy.
a. Calculate the energy content of the elevator at a height of 100ft:
The potential energy (PE) of an object is given by the formula: PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Given that the elevator weighs 16000lb, we first need to convert this to mass in pounds.
1 pound (lb) = 0.453592 kg
So, the mass of the elevator would be 16000 lb * 0.453592 kg/lb = 7257.472 kg.
Now, we can calculate the potential energy:
PE = mgh
PE = 7257.472 kg * 9.8 m/s² * 100 ft * 0.3048 m/ft (to convert ft to meters)
PE ≈ 2,135,477 Joules
Therefore, the energy content of the elevator at a height of 100ft is approximately 2,135,477 Joules.
b. Calculate the energy content of the horse moving at 10m/s:
The kinetic energy (KE) of an object is given by the formula: KE = (1/2)mv², where m is the mass and v is the velocity.
Given that the mass of the horse is 200 kg and its velocity is 10 m/s, we can calculate the kinetic energy:
KE = (1/2)mv²
KE = (1/2) * 200 kg * (10 m/s)²
KE = 10,000 Joules
Therefore, the energy content of the horse moving at 10m/s is 10,000 Joules.
c. Calculate the energy content of a gram of nuclear fuel containing 20pg of mass convertible to energy:
The famous equation from Einstein's special theory of relativity is E = mc², where E is the energy, m is the mass, and c is the speed of light.
Given that the mass convertible to energy is 20 pg (picograms), we need to convert this to kilograms:
1 pg = 1e-12 kg
So, the mass convertible to energy would be 20 pg * 1e-12 kg/pg = 2e-11 kg.
Now, we can calculate the energy content:
E = mc²
E = 2e-11 kg * (3e8 m/s)² (speed of light)
E = 1.8e6 Joules
Therefore, the energy content of a gram of nuclear fuel containing 20pg of mass convertible to energy is approximately 1.8 million Joules.