Kinetic, potential and mechanical energy question.

AI Thread Summary
The discussion revolves around calculating the total loss of mechanical energy for an airplane transitioning from an altitude of 9.9 km and speed of 260 m/s to an altitude of 2.1 km and speed of 140 m/s. The formulas for gravitational potential energy (E_g = mgh) and kinetic energy (E_k = 1/2 mv^2) are provided as essential tools for the calculation. The user initially calculates the total mechanical energy at both states but arrives at a result of 4.98 x 10^9 Joules, which is lower than the expected 5.5 x 10^9 Joules. Other participants suggest reviewing the calculations for potential errors, indicating that the approach taken is fundamentally correct. The discussion emphasizes the importance of careful calculation in energy loss assessments.
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Homework Statement


A 5.5 x 10^4 kg airplane, traveling at an altitude of 9.9 km, has a speed of 260 m/s relative to the ground. Nearing the end of the flight, the plane slows to a speed of 140 m/s while descending to an altitude of 2.1 km. Determine the plane's total loss of mechanical energy during this change of speed and altitude.

Homework Equations


E_g = mgh
E_k = \frac{1}{2}mv^2


The Attempt at a Solution


I have no idea how to start to solve this problem. If someone could point me in the right direction, it would be great.
 
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The mechanical energy is just the sum of gravitational PE and kinetic energy. You have the formulas for both--just crank it out.
 
Doc Al said:
The mechanical energy is just the sum of gravitational PE and kinetic energy. You have the formulas for both--just crank it out.

Thanks dude!
 
Ok, I did this:

a)
Eg = mgh
Ek = mv^2, where v I put 260 m/s
Et1 = Eg + Ek

b)
Same thing as above but with the second values.
Elost = Et1 - Et2.

The answer is supposed tob e 5.5 x 10^9 Joules but i get 4.98 x 10^9 Joules. What did I do wrong? Did I go about this the right way?
 
Looks like the right way to me. If you post the details of your calculation, perhaps we can spot an error. (Or confirm your answer.)
 
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