An aluminum foil sheet with a mass of 5 g must be compressed to a volume of how many cubic centimeters in order to sink?A container with a volume of 25 cubic cm must be filled with how many grams of gallium in order to have a density greater than one?A cylinder with a volume of 150 cubic cm must be filled with how many grams of substance in oder to float in water?thnks
If the crane lifts the bucket at a constant speed, it must be exerting a force exactly equal to the weight of the bucket and sand at any given momentThe work is the product of the force and the distance traveled, or the integral of force with respect to distanceSo what we really need is an expression for the weight of the bucket and sand in terms of y, the vertical position of the bucketWe know that the weight of the bucket and sand is W 100 + 500 - 3t 600 - 3t pounds, where t is elapsed time in secondsThe position of the bucket and sand is y 2t feet, again with t in secondsSo t y/2 W 600 - 3y/2 600 - 1.5y, and you need to integrate this over the 80 feet the bucket is lifted.
You can actually do this without calculus, since the bucket is losing sand at a constant rateThe total work will be the same as lifting the average amount of sand in the bucketThe total time this take is 80feet/2ft/s40 seconds Therefore halfway is 20 secondsAt this point the bucket weighs 600-320540 lbs Work ForceDmgD540lbs32ft/s^280ft1,382,4lbft^2/s^2
W ∫ F?ds F(t) 100 + 500 - 3t bucket + sand s 2t ; ds 2 dt W 2 ∫ 600 - 3t dt from 0 to 40 (takes 40 seconds to lift at 2 fps) 2(600t - 3/2 t?) 0 to 40 2(600(40) - 3/2(40)?) 43200 Answer: 43200 ft lbs
I won't do these for you, but I will give you some clues:) 1To get your aluminium sheet to sink in water, it has to displace a volume of water that is less than its own massto answer this question, then, what volume of water is equal to 5g? 2What mass of gallium would displace 25 cubic cm of water? 3Well, if you didn't put anything in the container, it would float on waterbut what's the most you could put in the container and still have it float? A mass that would displace less than 150 cubic cm of waterso, less than xxx?gramsFor all of your answers, start by assuming that the water is pure water (not water containing any substance in solution, which would change the density of the water and change your answers).
