Buoyancy in Different Gravitational Fields
Will a boat that floats in water on Earth still
float in water on a planet with more gravity?
What you must understand is that the buoyant force equals the WEIGHT if the
displaced water. Increasing gravity will increase the weight of both the
boat AND the water. The boat will still float.
Dr. Ken Mellendorf
Illinois Central College
Good question. When an object floats, the net force on that object is
zero. The downward force on a boat due to gravity is balanced out by
the weight of the water displaced by the boat. This is Archimedes'
Principle. Since the same gravity is acting on both the water and the
boat, the amount of water the boat displaces will be independent of
gravity, and the boat will still float.
Yes, the boat will float on that planet exactly as it does on earth
independent of the strength of gravity on that planet.
That is because, as Archimeded pointed out, the buoyant force on an
object in a liquid is equal to the WEIGHT of the water
displaced. If the gravity is increased, the buoyant force increases
since the weight of the water increases. The weight of the boat, of
course, increases in exactly the same ratio, so the boat will float
while displacing exactly the same volume of fluid as long as the
density of the fluid does not change.
Best, Dick Plano, Professor of Physics emeritus, Rutgers University
The bouyant force acting on a floating object is equal to the weight of
the fluid displaced. So since the weight of the water increases as
well as the weight of the boat, the bouyant force would increase right
along with the weight of the boat, so it would still float at the same
Mathematically, you can show this by doing a free body diagram summing
forces in the vertical direction. Using W = m*g, and setting the
weight equal to the bouyant force, we obtain W=B for an object floating
at rest. This becomes m(boat)*g = m(displaced water)*g. You can see
that g divides out of the equation, so no matter what value it has, the
boat would float at the same height in the water.
Yes. The submerged fraction of the boat will weigh more, and the
displaced water will weigh more, but the equality of those weights
will be unaffected. (Water is nearly incompressible, so its density
will increase only very slightly.)
Things will not be exactly the same, however. If you push the boat down
further into the water and let it pop up, it will pop up faster on a
planet with higher gravity. All the forces involved will be greater,
and they will be acting on an object of the same mass.
Yes it will!
What the boat relies on to float is taking up more space for its
weight than an equal amount of water. So a 5000 ton ship will take
up more space than 5000 tons of water. The ship will sink down just
far enough into the water to displace 5000 tons of water, (hence the
term "displacement"), and the rest of the ship will sit above the water.
Since you asked about an increased amount of gravity, remember that
it will affect both the ship and the water the same. So the 5000
ton ship now weighs 10,000 tons, but the water it displaces also
weighs twice as much, so it does not have to sink any further to
displace that 10,000 tons of water.
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Update: June 2012