Average force of air resistance

In summary, the average force of air resistance exerted on the shuttle during its landing at a constant angle of 10 degrees to the earth was 3608N.
  • #1
bewocc
3
0
[SOLVED] Average force of air resistance

In early test flights for the space shuttle using a "glider" (mass of 1500kg including pilot), it was noted that after a horizontal launch at 750km/h at a height of 4500m, the glider eventually landed at a speed of 300km/h. What would it's landing speed have been in the absence of air resistance? What was the average force of air resistance exerted on the shuttle if it came in at a constant angle of 10 degrees to the earth?

I converted vi to 208.33 m/s and vf to 83.33 m/s.

I think I answered the first part correctly using 1/2mvi^2 + mgyi = 1/2mvf^2 + mgyf. I calcualted vf = 362.77 m/s. I double checked this using kinematic equations and got the same answer.

I'm having problems with the second part. I believe air resistance is a nonconservative force. The only equation that I came up with is:

wnc = change in KE + change in PE

From this I derived:

Fyi cos 10 = 1/2mvf^2 - 1/2mvi^2 + mgyf - mgyi

Using this I came up with the answer -21097 N but this doesn't seem right. What am I missing here?
 
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  • #2
I think I figured out where I went wrong.
d = yi/sin 10 making w = Fdcos 180 = -Fd = -F(yi/sin 10)

This would give me the following equation:

-F(yi/sin10) = (1/2mvf^2 - 1/2mvi^2) + (mgyf - mgyi)

Then solve for F. F = 3608N
 
  • #3


I would first like to commend you for your efforts in solving this problem. Your approach using the conservation of energy principle is correct, and the equation you derived is also correct. However, the value you obtained for the average force of air resistance (-21097 N) seems too large and may have resulted from a mistake in your calculations.

To calculate the average force of air resistance, we need to know the time taken for the shuttle to land, as the force of air resistance acts over a period of time. Without this information, it is difficult to accurately determine the average force of air resistance.

Additionally, the angle of descent (10 degrees) may also affect the force of air resistance. The force of air resistance is proportional to the surface area of the object facing the air flow, and at a 10 degree angle, the surface area may be larger and thus the force of air resistance may be greater.

To accurately determine the average force of air resistance, we would need more information such as the time taken for the shuttle to land and the exact angle of descent. Without this information, it is difficult to provide a precise answer.
 

1. What is the average force of air resistance?

The average force of air resistance is the opposing force that acts on an object as it moves through the air. It is caused by the collision of air molecules with the surface of the object and is dependent on the object's speed, size, and shape.

2. How is the average force of air resistance calculated?

The average force of air resistance can be calculated using the equation Fdrag = 1/2 ρAv2, where ρ is the density of air, A is the cross-sectional area of the object, and v is the velocity of the object. This equation is known as the drag equation.

3. What factors affect the average force of air resistance?

The average force of air resistance is affected by the speed, size, and shape of the object, as well as the density and viscosity of the air. Other factors such as air temperature, humidity, and elevation can also have an impact on air resistance.

4. How does air resistance affect the motion of an object?

Air resistance slows down the motion of an object by exerting an opposing force. As an object moves through the air, the force of air resistance increases until it is equal to the force of gravity, resulting in a state of dynamic equilibrium where the object moves at a constant speed.

5. Can the average force of air resistance be reduced?

Yes, the average force of air resistance can be reduced by making changes to the object's shape or surface texture to make it more aerodynamic. Additionally, reducing the speed of the object can also decrease the force of air resistance acting upon it.

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