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## Physics Tutorials

### Archimedes Principle and Battery Indicators

Archimedes Principle is: any fluid applies a buoyant force to an object that is partially or completely immersed in it: the magnitude of the buoyant force equals the weight of the fluid that the object displaces.

FB=Wfluid

The Greek scientist Archimedes figured out this principle, which was a lingering question for so long. After this, Archimedes was known as one of the greatest scientists who ever lived.

#### Explanation

Buoyant force is the force that all fluids apply upwards when an object is immersed in it. When an object is immersed in a fluid, the fluid above the object exerts a downward pressure on the object. The fluid below the object exerts an upward pressure on the object. Pressure increases at lower depths, thus, the upward pressure exceeds the downward pressure. Thus, the fluid gives a total upward force, or buoyant force. The buoyant force equals the mass of the displaced fluid. The buoyant force equals mg. Note, Archimedes principle only works for a fully submerged object, not a partially submerged object. It can also apply to floating objects. Finally, a key point to remember is that: All solid objects will float in a fluid if the density of the object is less than or equal to the density of the liquid.

#### Application

Car batteries demonstrate an effective technique using Archimedes principle. A state-of-change indicator,

warns the owner when to recharge a battery. The battery holds a viewing point that shows a plastic rod entering into the battery acid. At the end of the rod is a “cage” containing a green ball. The cage has holes in it for acid to enter. If battery is charged, the density of the acid is high enough so the buoyant force places the ball at the top of cage, right below plastic rod. The viewing port indicates a green dot. As the battery starts to discharge, the acid density decreases. As mentioned, the buoyant force equals the weight of the acid displacement produced by the ball, the buoyant force also lessens. Due to this, the ball descends into one of the chambers, at an angular position. Since the ball cannot be seen, the viewing port shows a dark or black dot, indicating low battery charge.

#### Application

What is the maximum weight a solid, square, pinewood raft measuring 4.0 m on a side and 0.30 m thick support and still float in water?

Answer: We must figure out the raft’s weight and the buoyant force to stabilize the weight, to answer the question.

The density, of pine = 550 kg/m3

The volume of the wood = 4.0m*4.0m*0.30m=4.8m3 . Hence,

Weight of raft= (550 kg/m3)(4.8m3)(9.80 N/kg)=26 000 N.

When the raft is below surface level displacing 4.8 m3 of water, the maximum buoyant force exists and is equal to the weight of displaced water. Along with water’s density, it can be determined.

FB=Wfluid =(1000 kg/m3)(4.8 m3)(9.80 N/kg) = 47 000N

The buoyant force surpasses the weight of the raft by 21000 N. This is the maximum weight the raft will support and still float, according to Archimedes Principle.

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Ajit Srinivas