A robot unloads a finished component from a machine and places it on a gravity c

Question

A robot unloads a finished component from a machine and places it on a gravity conveyor. The conveyor accelerates from rest until it reaches the bottom of the conveyor 4.5 seconds later. The component is traveling at a velocity of 1.35 m/s when it reaches the bottom of the conveyor where it is then stopped by hitting a buffer. The component sits stationary awaiting packaging.

A) The conveyor section length is later modified and extended by a further 1.5m, Determine the new velocity of the components when they reach the buffer.

Explanation / Answer

For the first part, use equation vf = v0 + at, where v0 = 0, t = 4.5 s and vf = 1.35 m/s a = 1.35/4.5 = 0.3 m/s^2 Knowing acceleration and new distance, you can determine the new final speed using equation: vf^2 = v0^2 + 2a*d The problem states that it is extended by an additional 1.5 m, so you'll have to first determine the initial length before the extension: d = vf^2/2a = (1.35)^2/(2*.3) = 3.0375 m Now you add 1.5 to that distance above and use the formula to determine vf: vf = root(2*.3*4.5375) = 1.65m/s

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