A catapult launcher for a small, 4 lb, unmanned aerial vehicle (UAV) is shown be

Question

A catapult launcher for a small, 4 lb, unmanned aerial vehicle (UAV) is shown below. The UAV is attached to an unstretched spring (k = 50 lb/ft) at point B. To "cock" the launcher, the UAV and spring are then pulled back to point A (spring stretched 10 inches). After the UAV is released at point A, it slides along the launcher rail and exits the launcher at point C. Neglecting air drag, aerodynamic lift and friction between the UAV and the rail determine the speed of the UAV at point C. Neglecting air drag and aerodynamic lift, but including friction between the UAV and the rail (mu k = 0. 2) determine the speed of the UAV at point C.

Explanation / Answer

a) Ei= 1/2 kx^2 = 0.5 * 50* (10/12)^2 =17.36 b) Ef = 1/2 m v^2 + mgh Ei = Ef 17.36 = 0.5 * 4/32*v^2 + 4*(70/12)*sin(20) solve for v v=12.25 ft/s c) similar except now Ei + W friction = Ef W friction = - u N d = - u mg cos 20 d = - 0.2 * 4 * cos(20)*70/12 so 17.36 - 0.2 * 4 * cos(20)*70/12= 0.5 * 4/32*v^2 + 4*(70/12)*sin(20) v= 8.94 ft/s

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