What is the change in the gravitational potential energy of a Boeing 767 jet as it soars from the runway up to a cruising altitude of 10.2 km? Assume its mass is a constant 2.04×105 kg.
answer please in joules. thanks
m g h = 2.04*10^5 * 9.81 * 10.2*10^3
Potential Energy = mgh
where m is mass
g is gravity
h is height (should be in meters)
PE = mgh
PE = (2.04 x 10^5 kg)(9.8m/s^2)(10200m)
PE = 2.04 x 10^10 J
To calculate the change in gravitational potential energy, we can use the formula:
Change in gravitational potential energy (ΔPE) = mgh
Where:
m = mass of the object (in kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = change in height
In this case, the Boeing 767 jet has a mass of 2.04×10^5 kg and the change in height is from the runway to a cruising altitude of 10.2 km (or 10,200 m).
Let's calculate the change in gravitational potential energy step-by-step.
Step 1: Convert the cruising altitude from km to meters:
10.2 km = 10.2 × 1000 = 10,200 m
Step 2: Calculate the change in gravitational potential energy:
ΔPE = (2.04×10^5 kg) × (9.8 m/s^2) × (10,200 m)
Calculating this expression will give us the change in gravitational potential energy in joules (J).
To calculate the change in gravitational potential energy, we need to know the height difference (h) and the mass (m) of the object. In this case, the height difference is the difference between the cruising altitude and the runway level.
The gravitational potential energy (PE) is given by the equation: PE = mgh, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given:
Mass of the Boeing 767 jet (m) = 2.04 × 10^5 kg
Height difference (h) = cruising altitude - runway level = 10.2 km
First, we need to convert the height difference from kilometers to meters:
10.2 km = 10.2 × 1000 = 10200 m
Now, we can calculate the change in gravitational potential energy:
PE = mgh
PE = (2.04 × 10^5 kg) × (9.8 m/s^2) × (10200 m)
Simplifying the equation:
PE = 2.04 × 10^5 kg × 9.8 m/s^2 × 10200 m
Calculating the answer:
PE = 2.004 × 10^10 J
Therefore, the change in gravitational potential energy of the Boeing 767 jet as it soars from the runway up to a cruising altitude of 10.2 km is approximately 2.004 × 10^10 joules.