By Ernest R. McDowell, Don Greer

Few airplane designs have had as abnormal or advanced a historical past because the P-40 sequence. in truth one wonders why the Air Corps elected to provide the H-75P a designation except a splash quantity within the P-36 sequence because it was once primarily a re-engined P-36A. Spin-offs from the P-36 layout may consequence not just within the P-40 however the XP-37, XP-42, XP-46, XP-53, XP-60, and XP-62 plus those given Y designations and numerous sprint numbers.

Ignoring the Curtiss Hawk biplanes, the genealogy of the P-40 would appear to have its faucet roots within the XP-934 Curtiss quick of 1932 classic. even though a few event within the low-wing monoplane variety used to be received whilst the corporate produced its famed Shrike sequence of assault planes, the quick, or XP-31 because it used to be exact by way of the Air Corps, used to be their first low-wing pursuit layout. via a type of unusual quirks, the speedy in the beginning used to be powered by means of an in-line engine which gave method to a extra robust radial, simply the opposite of the P-36 to P-40 layout improvement. The XP-31 was once no longer profitable with both engine and the layout was once quickly deserted (It did earn the doubtful contrast of being the final U.S. pursuit aircraft with a hard and fast touchdown gear). The Curtiss Company's fortunes took a downward flip within the pursuit box whilst the Boeing P-26A used to be chosen via the Air Corps over the XP-31.

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Few plane designs have had as atypical or advanced a history because the P-40 sequence. in truth one wonders why the Air Corps elected to offer the H-75P a designation except a splash quantity within the P-36 sequence because it used to be essentially a re-engined P-36A. Spin-offs from the P-36 layout may end result not just within the P-40 however the XP-37, XP-42, XP-46, XP-53, XP-60, and XP-62 plus those given Y designations and diverse sprint numbers.

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9. Do the following: (a) Using Green's theorem, prove that -~ (xdy- ydx) = A where A is the area enclosed by the curve c. 10. (a) Show that -~ (xydy- y2dx) = A~ (b) -~ (xyZdy - y3dx) ----Ix ,i c where A is the area bounded by C, (Y, y) is its centroid, and Ix its moment of inertia about x axis. 11. If er, eo, and e0 are the unit vectors in spherical coordinates, show that the unit vectors in Cartesian coordinates can be written as i = (e, sin0 + e0 cos 0)cos 4~ - e0 sin~b j = (er sin 0 + e0cos 0) sin4~ + e~bcos ~b k = e,.

32) 20 ADVANCED DYNAMICS Ht / /// Fig. 6 r ~ ~ v ~ m V Relationship between angular and linear momentums. 3 To illustrate the meaning of Eq. 32), let us consider a block as a particle sliding on a straight rod without friction at a uniform velocity of 30 ft/s, as shown in Fig. 7. The rod is in the x - y plane, which is perpendicular to the gravitational force. The angular velocity of the rod is 50 rad/s. The position of the block is 6 in. away from the rotating axis. Determine the force between the block and the rod if the mass of the block is 1/30 slug.

One is a fixed reference frame; the x axis is oriented along the acceleration. The other is moving with a constant velocity along the negative x direction of the fixed reference frame. However, they coincide at the beginning of observation. (a) Find the velocity and position of the particle as a function of time in both reference frames. (b) Find the work done by the force during a time interval t in both frames. (c) Are the results of (b) different in the two frames? If so, are the laws of mechanics different in the two inertial frames of reference?