# Find out more aboutFloating and Stability

Virtual Lab: Stability and Center of Buoyancy game 1

### Stability and Center of Buoyancy

Finally, we can look at stability and buoyancy together.

If the floating wood block is pushed down at one end slightly, the block tilts in the direction of the downward push. This changes the shape of the displaced water and shifts the location of the center of buoyancy.

In the diagram (above right), there is more displaced water on the left side. Therefore, the center of buoyancy is located to the left of center.

 The buoyant force acting upward through the center of buoyancy is the restoring force. When the downward push is removed, the buoyant force and the weight acting through the center of gravity rotate the block back to its original position. The floating block is stable. block weight buoyant force

If a coin is placed on top and in the middle of a wood block floating in water, the block sinks into the water until an upward buoyant force is created that is equal to the weight of the block and the coin together. Then it stops sinking, because the upward buoyant force exactly balances the downward combined weight of the block and coin.

 block/coin weight buoyant force

Notice in the diagram here that the volume of the displaced water has increased, since the block is riding lower in the water than it was withouth the coin. The location of the center of buoyancy is at the geometric center of this volume of displaced water.

The weight of the block and the coin together acts downward through the center of gravity. The corresponding buoyant force acts upward through the center of buoyancy.

If the block-with-coin is pushed down at one end slightly, it tilts in the direction of the downward push just as it did without the coin.

 block/coin weight buoyant force

Once again, the center of buoyancy shifts to the left of center. The buoyant force acting upward through the center of buoyancy is the restoring force. When the downward push is removed, the restoring force tilts the block back to its original position.

The floating block with the coin on top in the middle is stable because it returned to its equilibrium position.

If the coin is moved off center toward one end of the block, the center of gravity of the block and coin together moves off center toward the coin.

 Virtual Lab: Stability and Center of Buoyancy game 2 Click here to try for yourself

Because the center of gravity is now off center, the floating block-with-coin tilts downward on the side with the coin. This changes the shape of the displaced water and shifts the location of the center of buoyancy.

This does not change the total volume of displaced water, however, because the weight of the block and coin together is still the same.

 block/coin weight buoyant force

In the diagram (far right), there is more displaced water on the left side. Therefore, the center of buoyancy is located to the left of center. The block continues to tilt until the center of buoyancy is directly beneath the center of gravity.

At this point, the upward buoyant force acting at the center of buoyancy exactly balances the downward force of the combined block-and-coin weight acting through the center of gravity.

Note: The coin stays on the block because the equilibrium angle is not steep enough to cause it to slide downward. If the coin were placed nearer the end, the floating block might tilt enough for the coin to slide into the water.

Pushing down on the side of the block near the coin will cause the block to tilt downward even more. As a result, the shape of the displaced water changes, shifting the location of the center of buoyancy to the left of the center of gravity. This is shown in the diagram below.

 block/coin weight buoyant force

This creates a buoyant force that acts upward at the center of buoyancy as a restoring force. When the downward push is removed, the restoring force tilts the block back to its original tilted position.

The block with the off-center coin is stable.

A floating object that is round does not change the shape of its displaced water when it rotates or tilts. Therefore, it cannot use its buoyant force as a restoring force.

If the floating object in the diagram above rotates, the center of gravity and the center of buoyancy stay in the same relative location.

 object/coin weight buoyant force

However, if a coin is placed on top of a round floating object, the situation is unstable. In actuality, it is very difficult to place a coin exactly over the center of gravity. The smallest offset is all that is necessary to start the object and the coin to rotate. As it does so, the center of gravity of the object and coin together moves outside of the center of buoyancy.

Virtual Lab: Stability and Center of Buoyancy game 3