6) A bottle filled with soda rests on the conveyor of a grocery check-out. The b

Question

6) A bottle filled with soda rests on the conveyor of a grocery check-out. The bottle weights 2 lbs, the CG is 8 inches from the base of the bottle, and the diameter of the bottle is 3 inches. Determine the largest acceleration the conveyor can have without causing the bottle to tip.
7) If the bottle on the conveyor of the above problem has a friction coefficient against the conveyor of .2, what is the greatest acceleration the conveyor can have without slipping?

8) Evaluate the results of Problems 6 and 7 above to determine whether the bottle will tip over on the conveyor, or slip on the conveyor, when the acceleration gets too high

Explanation / Answer

6) Balancing moments, W*(d/2) = F*(h) where F = ma and W = mg
So, gd/2 = ah
a = gd/2h = 9.81*3/(2*8) = 1.84 m/s^2

7) Fric force = W
W*(d/2) = (F-W)h

gd/2 = (a-g)h

a = gd/(2h) + g = 1.84 + 0.2*9.81 = 3.8 m/s^2

8) If W(d/2) > (F-W)h, bottle will slip. otherwise it'll tip.

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