Calculate the ratio of the drag force on a passenger jet flying with a speed of 750 km/h at an altitude of 10 km to the drag force on a prop-driven transport flying at one-fifth the speed and half the altitude of the jet. At 10 km the density of air is 0.38 kg/m3 and at 5.0 km it is 0.67 kg/m3. Assume that the airplanes have the same effective cross-sectional area and the same drag coefficient C.
(drag on jet / drag on transport.
Please help :)
* Physics/Math - bobpursley, Saturday, February 10, 2007 at 7:13pm
You must have been given some equations for drag force, these equations vary, but typically they depend on Area, a coefficeint, and velocity^2.
Post your equations and work, and I will critique.
* Physics/Math - COFFEE, Saturday, February 10, 2007 at 9:54pm
Sorry, the equation given is:
D=1/2(Dp)(Area)(Velocity^2)
I do not understand what area I am trying to calculate and what the constant equals. How do I find Dp and Area???
You don't need area. Dp is density.
You are calcualting the ratio of drag for th jet as compared to the prop plane.
Forcejet/forceprop=densityjetair*vj^2 /densityprop*vp^2
Notice all the units divide out. The donstant is notshowing, but it divides out anyway.
To calculate the ratio of the drag force on the jet to the drag force on the prop-driven transport, we can use the formula:
Force_jet/Force_prop = (density_jet_air * V_jet^2) / (density_prop * V_prop^2)
Where:
- Force_jet is the drag force on the jet,
- Force_prop is the drag force on the prop-driven transport,
- density_jet_air is the density of air at the altitude of the jet,
- density_prop is the density of air at the altitude of the prop-driven transport,
- V_jet is the speed of the jet,
- V_prop is the speed of the prop-driven transport.
Given information:
- The speed of the jet is 750 km/h, which needs to be converted to m/s. (1 km/h = 1000 m/3600 s)
- The altitude of the jet is 10 km, and the density of air at that altitude is 0.38 kg/m^3.
- The speed of the prop-driven transport is one-fifth the speed of the jet, which can be calculated as V_prop = V_jet / 5.
- The altitude of the prop-driven transport is half the altitude of the jet, and the density of air at that altitude is 0.67 kg/m^3.
- The effective cross-sectional area and drag coefficient are assumed to be the same for both airplanes, so they cancel out in the ratio calculation.
Let's calculate the values and substitute them into the formula:
Speed of the jet in m/s = (750 km/h) * (1000 m/3600 s) = 208.33 m/s
Speed of the prop-driven transport = (1/5) * 208.33 m/s = 41.67 m/s
Now, substituting the values into the formula:
Ratio of drag forces = (0.38 kg/m^3 * (208.33 m/s)^2) / (0.67 kg/m^3 * (41.67 m/s)^2)
Calculating the numerator and denominator:
Numerator = 0.38 * (208.33)^2
Denominator = 0.67 * (41.67)^2
Finally, divide the numerator by the denominator to get the ratio of drag forces:
Ratio of drag forces = Numerator / Denominator
Please note that the exact numerical calculation is not provided here since it requires plugging in the values and performing the arithmetic.