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Chapter 9: Problem 101

A \(1.2-1 b\) kite with an area of \(6 \mathrm{ft}^{2}\) flies in a \(20-\mathrm{ft} / \mathrm{s}\) wind such that the weightless string makes an angle of \(55^{\circ}\) relative to the horizontal. If the pull on the string is 1.5 lb, determine the lift and drag coefficients based on the kite area.

Short Answer

Expert verified
To complete this problem, it's necessary to calculate the drag and lift forces, and then use these to find the coefficients. This problem does not give an exact numerical solution without knowing the air density, but the path to calculate the lift and drag coefficient would look the same even if it were given.

Step by step solution

01

Identify forces in the problem

We have three forces at play here - the lift (L), drag (D), and the tension in the string (T). Picture the scene with the kite flying in the air with the wind coming from left to right. The lift is the upward force, the drag is the backward force against the wind, and the tension along the string is due to the lift and drag. The angle (55 degrees) mentioned in the problem is made by the tension in the string with the horizontal direction.
02

Establish force relationships

Because the kite is at equilibrium, the sum of the forces in each direction must be zero. So, the force along the string in the direction of lift is Tsin(55), which is equal to the lift L. Similarly, force along the string in the direction of drag is Tcos(55), which is equal to the drag D. Liaise these equations as follows: L = Tsin(55) and D = Tcos(55). Plug the values given in the problem to solve for L and D.
03

Calculate Drag and Lift Coefficients

Apply formulas for the drag and lift coefficients after getting the values of L and D from step 2. The lift and drag coefficients are given by the ratios of lift and drag to the area of the kite, respectively. So, Lift Coefficient \(C_{l}\) = \(L / 6 ft^{2}\), and Drag Coefficient \(C_{d}\) = \(D / 6 ft^{2}\). Calculate these values to obtain the coefficients.

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