An intrepid treasure-salvage group has discovered a steel box, containing gold doubloons and other valuables, resting in 80 ft of seawater. They estimate the weight of the box and treasure (in air) at 7000 lbf. Their plan is to attach the box to a sturdy balloon, inflated with air to 3 atm pressure. The empty balloon weighs 250 lbf. The box is 2 ft wide, 5 ft long, and 18 in high. What is the proper diameter of the balloon to ensure an upward lift force on the box that is 20% more than required

the proper diameter is 6.137 ft

Explanation:

first we find the volume of box using the relation, which is;

V = 2 x 5 x 1.5 = 15 ft³

we  find the buoyant force on the box by calculating the weight of water displaced.

FB = V x y

where  y is the specific weight of sea water(62.4 lbf/ft³)

so we Substitute

FB = 15 x 62.4 = 936 lbf  

now we find the upward force required by the balloon

FR = (W - FB) x 120%

= 1.2 (W - FB)

where W is the weight of the box treasure(7000 lb)

so we  Substitute,

FB = 1.2( 7000 - 936 ) = 7276.8 lbf

Because the universal gas constant contains a Rankine in its units, we make use of Rankine for our temperature

so we find the density of air at 3 atm using ideal gas relation,

Pair = p/RT

Here, p is the pressure acting (3 atm), R is the universal gas constant (1716 ft²/S²-R), and T is the temperature (520°R),

Substitute so we substitute

Pair = (3 * 2116.22) / (1516 * 520)

= 0.007114  lbf.ft³

next we find the specific weight of air;

Yair = Pair * g

g is acceleration due to gravity(32.2 ft/s²)

Yair =  

0.007114 * 32.2

= 0.23 Ibf /ft³

Now we find diameter of the balloon by balancing the net force required

FR = (y - yair) * V - Wb

= (y - yair) x (π/6)d³ - Wb  

d is the diameter of the balloon.

so we Substitute, 7276.8 lbf for FR,

62.4 Ibf/ft³ for  y, 0.23 for lbf/ft³ for Yair, 350 lb for Wb

so

7276.8 = (62.4 - 0.23)πd³  - 250

d³ = 231.23 ft³

d = 6.137 ft   

Therefore, the proper diameter is 6.137 ft

d. learned preferences i believe is your answer

relativism, roughly put, is the view that truth and falsity, right and wrong, standards of reasoning, and procedures of justification are products of differing conventions and frameworks of assessment and that their authority is confined to the context giving rise to them. more precisely, “relativism” covers views which maintain that—at a high level of abstraction—at least some class of things have the properties they have (e.g., beautiful, morally good, epistemically justified) not simpliciter, but only relative to a given framework of assessment (e.g., local cultural norms, individual standards), and correspondingly, that the truth of claims attributing these properties holds only once the relevant framework of assessment is specified or supplied. relativists characteristically insist, furthermore, that if something is only relatively so, then there can be no framework-independent vantage point from which the matter of whether the thing in question is so can be established.

relativism has been, in its various guises, both one of the most popular and most reviled philosophical doctrines of our time. defenders see it as a harbinger of tolerance and the only ethical and epistemic stance worthy of the open-minded and tolerant. detractors dismiss it for its alleged incoherence and uncritical intellectual permissiveness. debates about relativism permeate the whole spectrum of philosophical sub-disciplines. from ethics to epistemology, science to religion, political theory to ontology, theories of meaning and even logic, philosophy has felt the need to respond to this heady and seemingly subversive idea. discussions of relativism often also invoke considerations relevant to the very nature and methodology of philosophy and to the division between the so-called “analytic and continental” camps in philosophy. and yet, despite a long history of debate going back to plato and an increasingly large body of writing, it is still difficult to come to an agreed definition of what, at its core, relativism is, and what philosophical import it has. this entry attempts to provide a broad account of the many ways in which “relativism” has been defined, explained, defended and criticized.

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