A plastic film moves over two drums. During a 4-s interval the speed of the tape

Question

A plastic film moves over two drums. During a 4-s interval the speed of the tape is increased uniformly from v0 = 2ft/s to v1 = 4ft/s. Knowing that the tape does not slip on the drums, determine (a) the angular acceleration of drum B, and (b) the number of revolutions executed by drum B during the 4-s interval. 5) A rocket weighs 2600 lb, including 2200 lb of fuel, which is consumed at the rate of 25 lb/s and ejected with a relative velocity of 13000 ft/s. Knowing that the rocket is fired vertically from the ground, determine its acceleration (a) as it is fired, and (b) as the last particle of fuel is being consumed.

Explanation / Answer

a) a = (v1 - v0) / t = (4 - 2) / 4 = 0.5 ft/s2

alpha = a/r = 0.5 / (15 / 12) = 0.4 rad/s2

b)w0 = v0 / r = 2 / (15/12)

= 1.6 rad/s

theta = w0 * t + 1/2 * alpha * t2 = 1.6 * 4 + 1/2 * 0.4 * 42

= 9.6 rad = 9.6 / 2 * pi

= 1.529 rev

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