Need help finding the buoyant force in this problem

[TheKShaugh]

Hi everyone,

This question is killing me, I don't know why but I just can't get my head around it.

Homework Statement

A team of 6 scouts plans to cross a lake on a raft they designed.

The scouts have wooden beams with an average density of .80. The beams measure 30cm x 30cm x 3m.

The average mass for the team members is 65kg, and for their safety, they want the top of the raft to be at least 3 cm above the surface of the water.

How many beams will they need to complete their project successfully?

Homework Equations

I'm not sure if I need to post them. f = mg is the main one.

The Attempt at a Solution

My tutor gave me this method:

Fg(scouts) = 65 x 9.8 x 6

V(beam) = .27m^3

Fg(beam) = 800 x 9.8 x .27

Fg(raft) = Fg(beam) x n [n = number of beams]

Fg(total) = Fg(scouts) + Fg(raft)

Fb = 2381 x n

Fb = Fg(total) = Fg(scouts) + Fg(raft).

Solve for n.

Now I'm just a lowly high school student so my math isn't all that great, and when I do this I end up getting 0. The equation as I write it out is

2381n = -3822 - 2116n = -3822 - 2116n

6713n = -3822 +3822

6713n = 0

Could anyone help me out with this question?

Thanks,

Kevin

 

[SteamKing]

Your algebra has taken a wrong turn.

Fg = -3822 - 2116n

Fb = 2381n

From statics, we know that Fb + Fg = 0 (there is no net force on a floating object)

so, 2381n -3822 - 2116n = 0

Solve for n

 

[haruspex]

2381n = -3822 - 2116n = -3822 - 2116n

6713n = -3822 +3822

Try that step again.

 

[TheKShaugh]

Your algebra has taken a wrong turn.

Fg = -3822 - 2116n

Fb = 2381n

From statics, we know that Fb + Fg = 0 (there is no net force on a floating object)

so, 2381n -3822 - 2116n = 0

Solve for n

Thank you. You truly are the king of kings.