Kinetic, potential and mechanical energy question.

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SUMMARY

The discussion centers on calculating the total loss of mechanical energy for a 5.5 x 104 kg airplane transitioning from an altitude of 9.9 km at 260 m/s to 2.1 km at 140 m/s. The relevant equations used are gravitational potential energy (Eg = mgh) and kinetic energy (Ek = 1/2 mv2). The user initially calculated the total mechanical energy loss as 4.98 x 109 Joules, while the expected answer is 5.5 x 109 Joules. The discrepancy suggests a potential error in the calculations or assumptions made during the process.

PREREQUISITES
  • Understanding of gravitational potential energy (Eg = mgh)
  • Knowledge of kinetic energy formula (Ek = 1/2 mv2)
  • Basic algebra for manipulating equations
  • Familiarity with units of energy (Joules)
NEXT STEPS
  • Review the calculation of gravitational potential energy at both altitudes
  • Reassess the kinetic energy calculations using the correct speeds
  • Explore the concept of mechanical energy conservation in physics
  • Practice similar problems involving energy loss in mechanical systems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and energy conservation principles, as well as educators looking for examples of energy calculations in real-world scenarios.

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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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