How is it possible to lift heavy mass in water with ease?

Answer 1

There are at least two forces acting on any object in a gravitational field that is immersed in a fluid (Remember that gasses are fluids also; not only liquids.): 1) The force of gravity acting on an object (the object's weight) that is on or near the Earth's surface is constant for all practical purposes regardless of whether the object is immersed in a fluid or not. This is because the object's mass is the same in either case. The weight of the object would only change if its mass changes somehow, for example if the object corrodes in the fluid, if the object or part of it is soluble in the fluid, or if parts of the object are lost either spontaneously or during transfer. 2) The second force acting on an immersed object is a buoyancy force. 3) Additional forces may act on the object if someone or something pushes down or pulls up on the object or exerts a force against one side of it.

Recall that force is a vector, meaning that it has a magnitude and a direction. The gravi-tational force vector points from the center of mass of the object towards the center of the Earth. It is critical that we know the direction of and what causes the buoyancy force so that it may be calculated. As I'm sure you know from experience, the deeper under water something is the higher the pressure on that object. The same is true for a "pool" of air or any gas or mixture of gasses; the air pressure is greater at ground level and diminishes with altitude. When in a gravitational field, the liquid and gas pressures are due to gravity, which means that the denser the fluid, the greater the pressure at any given depth compared to a less dense fluid. (Gravity is responsible for a fluid's pressure in an open system. I want to clarify that we're not considering the case where a gas is compressed in a tank.)

When any object is immersed in a fluid, the pressures on the surfaces of the object vary with depth; the pressure is greater on a surface that is deeper and less on a surface that is shallower. Therefore, there is a pressure difference between the top and bottom surfaces of the submerged object that results in what is called a buoyancy force. You already know that the buoyancy force vector points upwards since the buoyancy force is what allows items to float. To be rigorous though, the origin of the buoyancy force is the geometric center (not necessarily the center of mass) of the object, and the vector's direction is perpendicular to the surface of the fluid directly over the geometric center of the object. This just means that if something is immersed in a pool of water, the buoyancy force would point from the geometric center of the object and would be perpendicular to the surface of the pool. Thus, the gravity and buoyancy force vectors on an immersed object are parallel but point in opposite directions such that they are counteracting one another. The last sentence is the answer to your question, however I would like to explain a little more.

Now we know what causes the buoyancy force and we know its direction, but how much is it? I will omit the mathematics that prove the magnitude of a buoyancy force. Any college physics textbook will certainly contain a complete mathematical description of it. The magnitude of a buoyancy force is exactly equal to the weight (not mass) of the fluid the submerged object displaces. Why the object's weight and not its mass? Because the buoyancy force on an object depends on the density of the fluid in which that object is immersed and on how much of the object is immersed while mass is an inherit property of an object that is the same regardless of where that object is. Hence, buoyancy has the dimensions of Pounds in the English system and Newtons in the kms system.

Let's look at one example to get an idea of how much difference buoyancy makes when a heavy object is submerged in water: I chose to use 1.00 yd3 of solid, fired, red brick. The density of these bricks is 143 lb./ft3. The densities of several types of brick were found on the public website "www.engineeringtoolbox.com" and the density of the brick chosen from that source was the same as what was given on two other public websites. Bricks are usually packaged in 1.00 yd3 units, one cube per palette, and the weight of the bricks is 143 lb./ft.3 • 27.0 ft.3 = 3,861 lb. since 1.00 yd3 = 3.00 ft. • 3.00 ft. • 3.00 ft. = 27.00 ft3.

Suppose that during the construction of a home addition, one cubic yard of bricks needed to be transferred from the materials staging area to a place nearer to where they were needed, and that the easiest way to move the bricks was to fly them over the pool using a small crane. As the bricks were moving over the pool, the braided steel cable connecting the crane hook to one of the steel bands wrapped around the bricks snapped and the entire lot of bricks fell into the pool, however all the bricks stayed together since all three steel bands wrapped around them remained in tact. The job foreman failed to inspect the carbon steel cable used to pick the bricks or he would have noticed that it was significantly corroded in one spot.

It is clear that the crane had to provide a minimum lifting force of 3,861 lb. to lift the bricks from their staging area. What is the minimum lifting force needed to lift the bricks off the bottom of the pool, which is six feet deep with a water temperature of 70.0 ˚F?

The weight of 1.00 ft3 of water at or near the Earth's surface at 70.0 ˚F is 62.30 lb. according to two, independent public sources. Since we know that the buoyancy force on an object submerged in water equals the weight of water displaced by that object, that the volume of water displaced by the bricks equals the volume of the bricks, and we know the density of water at 70.0 ˚F, we can easily calculate the buoyancy force on the bricks as

the weight of 27.0 ft3 water at 70.0 ˚F = 27.0 ft.3 • 62.30 lb./ft.3 = 1,682 lb. The force on the submerged bricks due to gravity is still 3,861 lb., so we simply subtract the buoyancy force from that since the forces are in exactly opposite directions. Remember to always subtract the buoyancy force from the gravitational force. Now we know that the minimum force needed to lift the bricks off the bottom of the pool is 3,861 lb. - 1,682 lb. = 2,179 lb.

This is the force needed to lift the bricks infinitely slowly just until any part of the cube of bricks breaks the water's surface. The moment any part of the bricks is no longer under water, there is no longer any buoyancy force on that part of the cube of bricks.

For fun and practice, calculate the buoyancy force on a helium weather balloon on the Earth's surface at sea level. The empty balloon and the equipment on it weighs 125 lb. Assume that the shape of the balloon is a perfect sphere with a radius of 5.00 ft.

I'll tell you that no balloon can rise forever. What causes the helium balloon described above to only rise to a certain altitude?

Answer 2

Archimedes principle