A 700 kg plane is traveling at 90 m/s at an altitude of 1500 m. What is the total mechanical energy?
To determine the total mechanical energy of the plane, we need to consider both its kinetic energy and potential energy.
1. Calculate the kinetic energy (KE):
The formula for kinetic energy is KE = (1/2)mv², where m is the mass of the object and v is its velocity.
Given:
Mass (m) = 700 kg
Velocity (v) = 90 m/s
Plugging the values into the formula:
KE = (1/2) * 700 kg * (90 m/s)²
= (1/2) * 700 kg * 8100 m²/s²
= 3150000 J
The kinetic energy of the plane is 3,150,000 Joules.
2. Calculate the potential energy (PE):
The formula for potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Given:
Mass (m) = 700 kg
Height (h) = 1500 m
Acceleration due to gravity (g) ≈ 9.8 m/s²
Plugging the values into the formula:
PE = 700 kg * 9.8 m/s² * 1500 m
= 10,290,000 J
The potential energy of the plane is 10,290,000 Joules.
3. Calculate the total mechanical energy:
Total mechanical energy (E) is the sum of kinetic energy and potential energy:
E = KE + PE
= 3,150,000 J + 10,290,000 J
≈ 13,440,000 J
Therefore, the total mechanical energy of the plane is approximately 13,440,000 Joules.