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A property owner on a lake is given an aluminum dock for his property. Unfortunately the dock is too large and heavy to move over land. Instead the owner has this idea (which his family thinks is insane) to move the dock by water. The dock is 20 ft long, 3ft wide, and weighs 500 lbs. The owner decides to float the dock using 50 gallon plastic drums filled with air. (a) How many 50 gallon drums are required to float the dock

Respuesta :

Answer:

2 drums

Step-by-step explanation:

Given:

Length of dock = 20 ft

Width of dock = 3 ft

weight of dock = 500 lbs

Volume of plastic drum  = 50 gallons

also,

1 gallon = 1 gallon = 0.0.0038 m³

or

50 gallons = 50 × 0.0038 = 0.189 m³

Now,

The dock will float If the upthrust provided by the barrels is equal to or greater than the weight of the dock i.e the volume of water displaces is equal to volume of the barrel.

therefore,

mass of the water displaced =  volume of drum × Density of water

or

mass of the water displaced =  0.189 × 1000 = 189 kg

and,

1 kg = 2.20462 lbs

thus,

189 kg = 416.67318 lbs

therefore,

the number of drums required is = [tex]\frac{\textup{500}}{\textup{416.67}}[/tex]

or

the number of drums required = 1.199 ≈ 2 drums

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