Calculating Air Resistance on a Space Shuttle Glider During Test Flights

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In early testflights for the space shuttle using a "glider" (mass of 1000kg including pilot), it was noted that after a horizontal launch at 500km/h at an altitude of 3500m, the glider eventually landed at a speed of 200km/h.

a) What would its landing spped have been in the absence of air resistance?

I use the PE + KE = KE principle and get that the speed should be 294 m/s. No problem here.



b) What was the average force of air resistance exerted on it if it came in a constant glide of 10 degrees to the earth?

I first tried to solve this by solving for the time it takes to fall vertically to the ground 3500 = 1/2 x 9.8 x t^2 Then Since I know the difference between the inital speed and final speed and the time, i can calculate the avg. acceleration, then put it into the F = ma formula. I get a resonable answer, but since I assume that there is no air resistance on the vertical fall, i get about 1000 N wrong. There must be another method of solving this.

Plz help!

 

[mrjeffy321]

OK, here is an idea, see what you think.

you know its total energy, or at least the energy that it should have when it gets to the ground, and you also know the energy it actually has when it gets to the ground. from that you find the amount of energy lost, we will assume it was all lost to air resistance.
you also know the distance it travels, from a certain hieght to the ground at a 10 degree incline, so you can find the distance of its path.

using the formula,
W = F*d
where W is the work done, F is the average force, and d is the distance,
the work is equal to the amount of energy lost due to air resistance, and the distance (d) is equal to the hypotenuse of the 10 degree triangle you solved earler, then just simple solve for the average force (F).

This method assumes that no other energy was lost to anything else, ie. heat, sound, vibration, ... (which in reality is false).

 

[thepatientmental]

To calculate the average force of air resistance on the glider, we can use the equation F = 1/2 * ρ * v^2 * A * Cd, where ρ is the density of air, v is the velocity of the glider, A is the cross-sectional area of the glider, and Cd is the drag coefficient.

First, we need to calculate the velocity of the glider at the time of landing, which can be done using the conservation of energy principle as you mentioned in part (a). The glider's initial kinetic energy (KE) at launch can be calculated as KE = 1/2 * m * v^2, where m is the mass of the glider and v is the launch velocity. The final kinetic energy at landing can be calculated as KE = 1/2 * m * v^2, where v is the landing velocity.

Next, we can use the equation PE + KE = KE to calculate the potential energy (PE) at launch. The potential energy at landing can be assumed to be zero since the glider is at ground level.

After solving for the launch velocity, we can use this value to calculate the landing velocity. Once we have the landing velocity, we can plug it into the equation F = 1/2 * ρ * v^2 * A * Cd to calculate the average force of air resistance on the glider during its descent.

It's important to note that this is just an approximation and there may be other factors at play that could affect the force of air resistance, such as wind speed and direction. However, this method should give you a reasonable estimate of the average force of air resistance on the glider during its test flight.