Conservation of Energy airplane pilot

In summary: So the work done by air resistance is mgh+1/2*mv^2. In summary, an airplane pilot fell 400 m after jumping without his parachute opening. He landed in a snowbank, creating a crater 2 m deep, but survived with only minor injuries. The work done by the snow to bring him to a stop is equal to his kinetic energy at his terminal velocity of 65 m/s. The average force exerted by the snow on him to stop him can be found by dividing the work done by the snow by the distance over which it was done. The work done by air resistance as he fell is equal to the difference between his initial potential energy and the work done by the snow. This can
  • #1
physicsss
319
0
An airplane pilot fell 400 m after jumping without his parachute opening. He landed in a snowbank, creating a crater 2 m deep, but survived with only minor injuries. Assume that the pilot's mass was 50 kg and his terminal velocity was 65 m/s.

(a) Estimate the work done by the snow in bringing him to rest.

Is it just work done by gravity, which is mgh, h being 402 m?

(b) Estimate the average force exerted on him by the snow to stop him.

No idea...

(c) Estimate the work done on him by air resistance as he fell.

No clue...
 
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  • #2
Work-energy theorem: The net work done on an object is equal to the change in kinetic energy of the object.

Assume that the snow exerted the only force on the pilot as he came to a stop. Since he was at a terminal velocity, there's no need to use kinematics.

b)
Once you find the work done by the snow, use the standard equation for work to find the force

c)
at terminal velocity, air resistance equals weight.
 
  • #3
physicsss said:
An airplane pilot fell 400 m after jumping without his parachute opening. He landed in a snowbank, creating a crater 2 m deep, but survived with only minor injuries. Assume that the pilot's mass was 50 kg and his terminal velocity was 65 m/s.

(a) Estimate the work done by the snow in bringing him to rest.


Is it just work done by gravity, which is mgh, h being 402 m?

No, there is also work done by air resistance- because he has a maximum velocity of 65 m/s. That's the speed with which he hits the snow so the work the snow does is equal to his kinetic energy at that speed.

(b) Estimate the average force exerted on him by the snow to stop him.

No idea...

You know the work done by the snow from (a) and you know that work is "force times distance"...

(c) Estimate the work done on him by air resistance as he fell.

No clue...

NOW use your idea from (a). His potential energy is what you said there- the total work done to bring him to a stop is equal to that. You calculated the work done by the snow in (a). The work done by the air resistance is the difference between his initial potential energy and the work done by the snow.

(Rember than the work done by the snow was the same as his kinetic energy at his terminal speed. That is, the work done by the air is the initial potential energy less the kinetic energy at terminal speed.)
 
  • #4
Is a) W=mgh+1/2*mv^2 , where h = height of crater and v = terminal velocity?
 
  • #5
physicsss said:
Is a) W=mgh+1/2*mv^2 , where h = height of crater and v = terminal velocity?
Yes, if by h you mean the depth of the crater (2 m).
 
  • #6
For part c, is it mgh, where h is 400m, minus what I got for a) ??
 
  • #7
physicsss said:
For part c, is it mgh, where h is 400m, minus what I got for a) ??
Almost. When it just hits the ground it has a KE that is less than its original PE (measured from the ground). The "missing" energy is that lost to air resistance.
 
  • #8
mgh, where h is 402m, minus what I got for a) ??
 
  • #9
wait... is Work done by friction=mgh-1/2*mv^2-mgd, where h is 400m and v is 65m/s, and d=2.0m?
 
Last edited:
  • #10
physicsss said:
mgh, where h is 402m, minus what I got for a) ??
That would work.
 
  • #11
physicsss said:
wait... is Work done by friction=mgh-1/2*mv^2-mgd, where h is 400m and v is 65m/s, and d=2.0m?
I would drop the mgd term. Assume that air resistance just acts while the object is falling, but not after it hits the snow.
 

Related to Conservation of Energy airplane pilot

1. What is the conservation of energy principle in relation to airplane pilots?

The conservation of energy principle in relation to airplane pilots states that energy cannot be created or destroyed, but it can be transferred or transformed from one form to another. This means that the total energy of a system, such as an airplane, remains constant.

2. How does the conservation of energy affect airplane pilots during flight?

During flight, the conservation of energy principle is crucial for airplane pilots as they must constantly monitor and manage the energy of the aircraft. This includes factors such as the fuel consumption, altitude, speed, and air resistance, to ensure that the plane has enough energy to complete its journey safely.

3. Can airplane pilots use the conservation of energy to save fuel?

Yes, airplane pilots can use the conservation of energy principle to save fuel. By making efficient use of the plane's energy, such as maintaining a steady speed and altitude and reducing air resistance, pilots can minimize the amount of fuel needed for the flight.

4. How do airplane manufacturers incorporate the conservation of energy into designing aircraft?

Airplane manufacturers use the conservation of energy principle in various ways when designing aircraft. They aim to create streamlined and aerodynamic designs to reduce air resistance and improve fuel efficiency. They also incorporate advanced technologies, such as regenerative braking and solar panels, to capture and reuse energy during flight.

5. What are the potential consequences if an airplane pilot does not adhere to the conservation of energy principle?

If an airplane pilot does not adhere to the conservation of energy principle, it can result in various consequences. These can include running out of fuel mid-flight, losing control of the aircraft, or not being able to reach the intended destination. It can also lead to increased fuel consumption and environmental impact.

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