# Fluid Mechanics - Bouyancy Question

• wesDOT
Therefore, you will need to add enough lead to the block so that the total force is greater than its weight. This will ensure that the block sinks, along with the lead. However, be careful not to add too much lead, as it will exceed the weight of the fluid displaced and cause the block to sink too quickly. In summary, to find the minimum mass of lead needed for the block to sink, you must take into account the buoyant force on the lead and make sure the total force is greater than the weight of the block.

## Homework Statement

A block of wood floats on water. The density of the
wood is .634g/cm^3. Its mass is 243 g. Find the minimum mass (g) of lead we
must attach to the block so that it will sink, along with the lead. The density of lead is
11.3 g/cm^3. Caution: you must take into account the buoyant force on the lead, as well
as on the wood.

## Homework Equations

B=pgV=Mg(weight of fluid displaced)

## The Attempt at a Solution

I know that I must apply bouyancy principles to Newton's Second Law but I am not sure exactly how to set up my equations. How should I attack this problem?

You might consider drawing a free-body diagram first, to show the forces acting on the wood and lead. Or at least making a list of the forces involved. (You can consider the wood and lead combined to be a single free body - don't worry about the force of the lead pushing on the wood or vice-versa) The buoyant force ($$B = \rho g V$$) will be one force, but what else is there?

Once you've done that, you can add up all the forces to get the total force. Remember that in order for the wood and lead to sink, the total force should be downward rather than upward.