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Tension, Work and Energy Consumption

1. A 200 lb metal object is suspended in a liquid with a specific gravity of 1.6. The metal object has a weight density of 150 lb/ft^3. If the object is only 3/4 submerged, what is the tension in the support cable?

2. A vertical cylinder is closed by a freely moving piston at its top. The piston has a mass of 5 kg and an area of 300cm^2. Atmospheric pressure is 1X10^5Pa. As the gas is heated, the piston rises 8cm. How much work did the gas do during the expansion?

3. A certain steam engine has an output of 500 hp and its efficiency in the use of fuel is 14%. It burns fuel oil that has a heat of combustion of 10,000 cal/g. How many kg of oil does the engine consume each hour?

Solution Preview

1. A 200 lb metal object is suspended in a liquid with a specific gravity of 1.6. The metal object has a weight density of 150 lb/ft^3. If the object is only 3/4 submerged, what is the tension in the support cable?
First we need the volume of the metal object which is its weight divided by the weight density and that is 200 lb/150 lb/ft^3 = 1 1/3 ft^3 The object only displaces 3/4 of its volume as it is only 3/4 submerged. Therefore the volume displaced by the object is (3/4)(4/3) = 1 ft^3. That was nice of the questioner!

Now the buoyant force equals the weight of the liquid displaced and we have a specific gravity for that liquid of 1.6 grams/cc. Lets convert the volume displaced into cubic centimeters:
1 cubic foot = 2.832 x 10^4 cc The mass of the liquid displaced is then 2.832 x10^4 cc x (1.6 g/cc)
4.5312 x10^4 g or 45.312 Kg The ...

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