How Much Lead Is Needed to Sink a Floating Log?

[moniquert]

Homework Statement

A 2.04 kg piece of wood floats on water of density 1006.2 kg/m3. If the density of wood is 486.0 kg/m3 and the density of lead is 11300 kg/m3, what minimum mass of lead, hung from it by a string, will cause it to sink?

Homework Equations

Bouyant force= (density of water)(Volume displaced)(gravity 9.81)
Volume= (Pie)(r)squared(height)
Density= mass/volume

The Attempt at a Solution

I found the weight of the log by doing (9.81)(2.04)=20.0124N. Then i found volume of the log (2.04)/486=0.004197531 metres cubed. Then i found bouyant force upwards (1006.2)(.004197531)(9.81)= 41.43308N. Then I subtracted them to get how much weight is required for it just to stay a float 21.42N. I don't Know what to do after that help please.

 

[silvashadow]

Well, you have mass of lead. Find Fb which should be equal to weight of lead. Also, judging from the volume in 2, you didn't mention that is was a cylinder in 1.

 

[moniquert]

I don't have the mass of lead only the density. and how do you know its a cylinder? and if it is a cylinder i still can't find the volume that way because i don't have the radius or height.

 

[silvashadow]

2. Homework Equations
Bouyant force= (density of water)(Volume displaced)(gravity 9.81)
Volume= (Pie)(r)squared(height)
Density= mass/volume

Isn't that volume of cylinder?

 

[moniquert]

I know that's a volume of a cylinder but i don't have the radius or height to use that equation so i just used the density=mass/volume

 

[silvashadow]

Well, you are right up to the last part of 21.398N. You also need to account for the Fb of the lead underwater.

 

[moniquert]

To find the fb of lead would i just do density of lead times volume of the log? I don't know how to solve for the Fb of lea what numbers to use. (11300)(0.004197531)(9.81)=465.3N

 

[silvashadow]

Also, try reading these:
https://www.physicsforums.com/showthread.php?t=22103
https://www.physicsforums.com/showthread.php?t=46779

 

[kamerling]

To find the fb of lead would i just do density of lead times volume of the log? I don't know how to solve for the Fb of lea what numbers to use. (11300)(0.004197531)(9.81)=465.3N

The buoyant force of the lead is the weight of the water that it displaces.

 

[Doc Al]

The Attempt at a Solution

I found the weight of the log by doing (9.81)(2.04)=20.0124N. Then i found volume of the log (2.04)/486=0.004197531 metres cubed. Then i found bouyant force upwards (1006.2)(.004197531)(9.81)= 41.43308N. Then I subtracted them to get how much weight is required for it just to stay a float 21.42N. I don't Know what to do after that help please.

You're on the right track, but it's a bit trickier than that.

It's always good idea to draw a diagram and label all the forces involved. The diagram would show the submerged wood and a piece of lead (also submerged) hanging down from it by a string.

What forces act on the wood? The buoyant force acting up; the weight and string tension acting down. You've calculated what the string tension must be.

What forces act on the lead? String tension and buoyant force acting up; the weight acting down. Use this information to calculate the volume and thus the mass of lead needed.

 

[bobbyjack]

Forget the string and think of the lead and wood just below the surface. The total buoyant force on the lead and wood must be equal to the weight of the lead and wood. The buoyant force is the weight of the displaced water; the volume of the displaced water is the same as the volume of the lead and wood. Set this up and see what you have.

You're on the right track, but it's a bit trickier than that.

It's always good idea to draw a diagram and label all the forces involved. The diagram would show the submerged wood and a piece of lead (also submerged) hanging down from it by a string.

What forces act on the wood? The buoyant force acting up; the weight and string tension acting down. You've calculated what the string tension must be.

What forces act on the lead? String tension and buoyant force acting up; the weight acting down. Use this information to calculate the volume and thus the mass of lead needed.

 

[Doc Al]

That's a perfectly fine way to go as well.