An empty plastic bottle of mass m is found to accelerate up at the rate of g/6 when placed deep inside water, what amount of sand must be put inside the bottle to accelerate it at the rate of g/6 downward?
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Force of buoyancy on the empty plastic bottle = m g + m * g/6
Volume * 1000 kg/m³ * g = 7 m g / 6
Volume = 7 m / 6000 m³
Let X kg of sand be put inside the empty bottle and bottle be sealed.
buoyancy force (same as before) = (m+X) * 5 g / 6
( 7 m / 6000 ) * 1000 * g = (m+X) 5 g / 6
7 m = 5 m + 5 X
X = 2 m / 5
You need to fill with sand, whose weight (mass) equal to 40% of the weight (mass) of empty bottle.
Volume * 1000 kg/m³ * g = 7 m g / 6
Volume = 7 m / 6000 m³
Let X kg of sand be put inside the empty bottle and bottle be sealed.
buoyancy force (same as before) = (m+X) * 5 g / 6
( 7 m / 6000 ) * 1000 * g = (m+X) 5 g / 6
7 m = 5 m + 5 X
X = 2 m / 5
You need to fill with sand, whose weight (mass) equal to 40% of the weight (mass) of empty bottle.
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