Calculating Plane Energy for a Safe Takeoff

[sbpleecniadl]

Hi, my professor wants me to solve this problem using energy formulas. I am a little confused on how I am supposed to do this. If anyone wants to give me a lead in the right direction, it would be greatly appreciated. Here is the problem:
"You and a friend charter a small plane to take a tour of the desert. Unfortunately, there are mechanical difficulties during the flight and the pilot is forced to make a crash landing on the top of a mesa that stands 250m above the surrounding plain. The pilot fixes the plane and wants to take off again, but the only reasonably smooth road that could be used for a runway is not long enough. The pilot estimates that the maximum speed the plane is likely to reach before going off the edge of the mesa is about 45 mph, but the plane needs an airspeed of about 120mph before the wing’s lift becomes significantly larger than the plane’s weight. Noting that the side of the mesa is essentially a vertical cliff, the pilot thinks about deliberately driving the plane off the edge and diving downward and forward. By doing this he hopes to pick up enough air speed to pull out of the dive before hitting the ground. Seeing how your life is at stake in this attempt, you decide to do your own calculations.

Thank you

 

[xanthym]

Hi, my professor wants me to solve this problem using energy formulas. I am a little confused on how I am supposed to do this. If anyone wants to give me a lead in the right direction, it would be greatly appreciated. Here is the problem:
"You and a friend charter a small plane to take a tour of the desert. Unfortunately, there are mechanical difficulties during the flight and the pilot is forced to make a crash landing on the top of a mesa that stands 250m above the surrounding plain. The pilot fixes the plane and wants to take off again, but the only reasonably smooth road that could be used for a runway is not long enough. The pilot estimates that the maximum speed the plane is likely to reach before going off the edge of the mesa is about 45 mph, but the plane needs an airspeed of about 120mph before the wing’s lift becomes significantly larger than the plane’s weight. Noting that the side of the mesa is essentially a vertical cliff, the pilot thinks about deliberately driving the plane off the edge and diving downward and forward. By doing this he hopes to pick up enough air speed to pull out of the dive before hitting the ground. Seeing how your life is at stake in this attempt, you decide to do your own calculations.

Thank you

{Mass of Airplane & Contents} = M
{Kinetic Energy Required for Flight} = (1/2)M(120 mph)^2 =
= (1/2)M(53.6448 m/sec)^2 = (1439)M
{Kinetic Energy Available from Runway Takeoff} = (1/2)M(45 mph)^2 =
= (1/2)M(20.1168 m/sec)^2 = (202.3)M
{Additional Kinetic Energy Required from Cliff Drop for Flight} = (1439)M - (202.3)M = (1237)M

{Potential Energy Available from Cliff Drop} = M*g*h = M(9.8)(250 m) = (2450)M

Since available Potential Energy exceeds additional Kinetic Energy required for flight:
Pilot's Plan Is Predicted To Be Successful.


~~

 

[thepatientmental]

Hello! Solving this problem using energy formulas involves using the principles of potential and kinetic energy. Let's break it down step by step.

First, we need to calculate the potential energy of the plane when it is at the top of the mesa. We can use the formula PE = mgh, where m is the mass of the plane, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the mesa (250m). This will give us the potential energy of the plane at the top of the mesa.

Next, we need to calculate the kinetic energy of the plane when it reaches the edge of the mesa. We can use the formula KE = 1/2mv^2, where m is the mass of the plane and v is the velocity of the plane (45 mph or 20.11 m/s). This will give us the kinetic energy of the plane just before it goes off the edge.

Now, we need to determine the minimum airspeed needed for the plane to take off. The pilot estimates this to be 120 mph or 53.58 m/s. We can use the same formula for kinetic energy to calculate the minimum kinetic energy needed for the plane to take off.

Finally, we need to compare the potential energy and the minimum kinetic energy. If the potential energy is greater than the minimum kinetic energy, then the plane will not be able to take off. In this case, the pilot's plan of diving off the edge will not work. However, if the minimum kinetic energy is greater than the potential energy, then the plane will have enough energy to take off.

I hope this helps guide you in the right direction. Remember to always double check your calculations and assumptions, and make sure to communicate with your professor if you need further clarification. Good luck!