Buoyancy with the Cross-Sectional Area of a Rectangle

  • #1
Joe3502
6
0
Homework Statement:
Find the buoyant force acting on a rectangular object with a cross-sectional area of 6m^2 when 0.5m of the object is below the surface of the water.
Relevant Equations:
Fnet = Fb-Fg
Hi all,

My teacher assigned us a problem to do a few days ago and have attempted it many times, often leaving and coming back to see if I could figure it out. I imagine that you would take the cross-sectional area and multiply it by how far under the surface of the water the rectangular object is to get how much water it displaced. I am not sure if that is the right way to go about it, though.

Obviously, this is even harder because of the stay-at-home thing, but what's even worse is that my teacher hardly answers his email since the coming of this pandemic nor has he send any example problems or instructional videos. He does, however, post daily work but isn't mindful of those that need help.

Thank you very much for your time and stay safe,
Joe
 

Answers and Replies

  • #2
nrqed
Science Advisor
Homework Helper
Gold Member
3,765
295
Homework Statement:: Find the buoyant force acting on a rectangular object with a cross-sectional area of 6m^2 when 0.5m of the object is below the surface of the water.
Relevant Equations:: Fnet = Fb-Fg

Hi all,

My teacher assigned us a problem to do a few days ago and have attempted it many times, often leaving and coming back to see if I could figure it out. I imagine that you would take the cross-sectional area and multiply it by how far under the surface of the water the rectangular object is to get how much water it displaced. I am not sure if that is the right way to go about it, though.

Obviously, this is even harder because of the stay-at-home thing, but what's even worse is that my teacher hardly answers his email since the coming of this pandemic nor has he send any example problems or instructional videos. He does, however, post daily work but isn't mindful of those that need help.

Thank you very much for your time and stay safe,
Joe
What is the formula for the buoyant force?
 
  • #3
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2022 Award
39,212
8,527
I imagine that you would take the cross-sectional area and multiply it by how far under the surface of the water the rectangular object is to get how much water it displaced.
Yes.
 
  • #4
Joe3502
6
0
What is the formula for the buoyant force?
Fb = Vs*D*g

So if that is the case, then:
Fb = 0.5m * 1000kg/m^3 * 9.81m/s^2
Fb = 4905?
 
  • #5
Joe3502
6
0
Yes.
In that case, then 6m^2 * 0.5m = 3m^3 of water displaced.
 
  • #7
Adesh
735
188
Fb = Vs*D*g

So if that is the case, then:
Fb = 0.5m * 1000kg/m^3 * 9.81m/s^2
Fb = 4905?
Your value for ##V## is wrong.
 
  • #8
Adesh
735
188
In that case, then 6m^2 * 0.5m = 3m^3 of water displaced.
This is the correct value for ##V##, that is the volume of water displaced.
 
  • #9
Joe3502
6
0
This is the correct value for ##V##, that is the volume of water displaced.
How so?
 
  • #10
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2022 Award
39,212
8,527
How so?
In the formula Fb = Vs*D*g, Vs is the volume displaced. You calculated this in post #5. But in post #4 you plugged in the depth of immersion, 0.5m, instead.
 
  • #11
Joe3502
6
0
In the formula Fb = Vs*D*g, Vs is the volume displaced. You calculated this in post #5. But in post #4 you plugged in the depth of immersion, 0.5m, instead.
Ahhhhhhh thank you for catching my mistake.

Ok, so with that in mind:
Fb = 3m^3 * 1000kg/m^3 * 9.81m/s^2
Fb = 2.94 x 10^4 N?
 
  • #12
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2022 Award
39,212
8,527
Ahhhhhhh thank you for catching my mistake.

Ok, so with that in mind:
Fb = 3m^3 * 1000kg/m^3 * 9.81m/s^2
Fb = 2.94 x 10^4 N?
Yes.
 
  • #13
Joe3502
6
0
Thank you guys so much for helping me with this problem! I really appreciate it!
 

Suggested for: Buoyancy with the Cross-Sectional Area of a Rectangle

Replies
3
Views
789
Replies
22
Views
420
Replies
9
Views
446
  • Last Post
Replies
11
Views
301
Replies
5
Views
284
Replies
7
Views
407
Replies
11
Views
551
Replies
5
Views
316
Top