Buoyancy in Different Gravitational Fields ```Name: Al Status: educator Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: Will a boat that floats in water on Earth still float in water on a planet with more gravity? Replies: Al, 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 Physics Instructor Illinois Central College Hi Al 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. Robert Froehlich Hi Al, 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 height. 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. David Brandt 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. Tim Mooney 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. Ryan Belscamper Click here to return to the Physics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}