Archimedes principle?

Question

1.Suppose Spaceman Spiff flies his spaceship into Lake Superior on Wednesday, August 23rd 2000. The spaceship is 234 kg and, due to its air tight protective forcefield we can consider it to be a sphere (volume = (4/3)πR3). When Spaceman Spiff flies into Lake Superior he floats with only the small caution light floating (negligible mass) above the surface. What is circumference of the spaceship in cm? Remember that the circumference of a circle is 2πR.
2. Explain why fresh water boats can travel in the ocean while some ocean faring boats cannot travel in fresh water.
3. Suppose I give you an object that I say is made out of gold (density of 19.3 g/cm3). The object has a volume of 10mL and has a mass of 180 grams. Am I lying if say it is made out of solid gold?

Answer 1

1. The spaceship is displacing a mass of water equal to its own mass, 234kg. This mass of water occupies a volume of 0.234 m3 (density is 1000kg/m3).

0.234 = (4/3)Pi R3
R=0.382m

3. If the object is pure gold, its density has to be 19.3g/mL. The object you're given has a density of 180g/10mL or 18 g/mL, which means it's not pure gold.

Answer 2

OMG! R U in my class? I have the exact same take-home test!!

Seriously, you shouldn't let strangers on the Internet do your homework for you. They might derive perverse pleasure from giving you the wrong answer.

Now, for a straight answer (or at least some hints), Lake Superior is fresh water which conveniently weighs 1 gram per cubic centimeter. So, set V in the volume equation to 234,000 and see how big R is.

For question 2, consider that sea water weighs 1.025 grams per cubic centimeter, instead of 1.000 grams like fresh water. If you still can't figure it out, design a spaceship for the evil beings of the planet Glork (Spaceman Spiff's arch-nemeses) to just barely float in the ocean. Divide 234,000 by 1.025 to find out how many cubic centimeters their spaceship has to displace, and work that through your volume equation. You'll find they need a smaller spaceship. Now, put that spaceship into Lake Superior, and remember that their spaceship weighs just as much as Spaceman Spiff's...it goes "bloop" and sinks to the bottom.

For part 3, well, just figure out how much 10mL of gold weighs. Remember that 1 cubic centimeter = 1 mL, and do the math.

Answer 3

1.
(4/3)πR^3 = 234,000
R^3 = 234,000/((4/3)π)
R = (234,000/((4/3)π))^(1/3)
C = 2π(234,000/((4/3)π))^(1/3)
C = 240.19 cm

2. Because salt water is more dense than fresh water a floating object doesn't sink as far down before its weight is displaced.

3.
10 ml = 10 cc
(180 g)/(10 cc) = 18 g/cc
The object is not solid gold.

Answer 4

Hi 2) Because salt water is denser and supports more of a ship out of the water.