The uniform slender bar rests on a smooth horizon- tal surface when a force f is applied normal to the bar at point a. point a is observed to have an initial acceleration aa of 20 m/s2, and the bar has a corre- sponding angular acceleration of 18 rad /s2. deter- mine the distance b.

During spring semester at mit, residents of the parallel buildings of the east campus dorms battle one another with large catapults that are made with surgical hose mounted on a window frame. a balloon filled with dyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room. assume that the stretching of the hose obeys hooke's law with a spring constant of 89.0 n/m. if the hose is stretched by 5.80 m and then released, how much work does the force from the hose do on the balloon in the pouch by the time the hose reaches its relaxed length? unitst 3 number-1497 the tolerance is +/-5% open show work click if you would like to show work for this question:

Engines for propeller-driven aircraft are limited in their maximum rotational speed by the fact that the tip speed of the propeller must not approach the speed of sound in air (mach i). taking 6 ft as a typical diameter for a propeller of a light airplane and 1100 fils as the speed of sound, find the upper limit on the rpm (revolutions per minute) of the propeller shaft.

Derive the formula 2as=v² -u² where the formula have have usual meanings