Need help answering problems related to Buoyance/Buoyance Force

  • Thread starter Sam
  • Start date
  • Tags
    Force
In summary, the first problem involves calculating the buoyant force needed to hold a 100kg man under water in the ocean, taking into account his density and the specific gravity of sea water. The second problem involves finding the buoyant force on a helium balloon in air using Archimedes' law. Both problems provide hints and involve solving for the force needed to counteract the buoyant force.
  • #1
Sam
14
0
I have two homework problems that I am unable to answer related to buoyancy/force. Please help! Thanks!

1. How much force (in Newtons) does it take to hold a 100kg man completely under water in the ocean? His density is 903 kg/m^3, and the specific gravity of sea water is 1.07.

They give the following hint: Buoyant force is greater than the weight: B.F. = Weight + Force Down

2. What is the buoyant force in N on a 6.6 m^3 helium balloon in air at standard conditions? The density of air is 1.3 kg/m^3

They give the following hint: According to Archimedes you only need to know the weight of the air displaced.
 
Physics news on Phys.org
  • #2
Sam,
what have you got so far and where are you stuck? If you haven't started yet, then I think Archimedes' law is a good starting point.
 
  • #3
Here's what I have so far...

I have the following, but I know my answer isn't correct because it's an online course and will let you know when you are correct:

Let:

Mm = mass of man in kg (given at 100 kg)
Vm = volume displaced by man in m^3 = Mm/Dm
Sg = specific gravity of seawater (given at 1.07)
Dw = Density of pure water 1 gm/cm^3 = 1000kg/m^3
Ds = Density of seawater
Fb = Buoyancy force
g = acceleration of gravity in m/s^2 = (9.8 m/s^2)

Here's how I tried to solve:

Fb = Vm*Dw*g
= (Mm/Dm)*Sg*Dw*g
= (100 kg/903kg/m^3)*1.07*(1000kg/m^3)*9.8m/s^2 N

Ok, so the buoyant force exceeds his weight. To keep him submerged you'd have to push him down with the difference force F=1161 - 980 or about 181 N.

What did I do wrong?
 
  • #4


Hmmm... looks OK to me. With the following changes, which don't change the result:

Fb = Vm*Sg*Dw*g
= (Mm/Dm)*Sg*Dw*g
= (100 kg/903kg/m^3)*1.07*(1000kg/m^3)*9.8m/s^2 no N

Since they say B.F. = Weight + Force Down, maybe they expect the answer to have a minus sign. Suggest you try that.
 

1. What is buoyancy force?

Buoyancy force is the upward force exerted by a fluid on an object that is partially or completely submerged in it. This force is equal to the weight of the fluid that the object displaces.

2. How is buoyancy force calculated?

Buoyancy force is calculated using Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid it displaces. This can be represented by the equation FB = ρVg, where ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity.

3. What factors affect buoyancy force?

The factors that affect buoyancy force include the density of the fluid, the volume of the displaced fluid, and the acceleration due to gravity. The shape and size of the object also play a role, as well as the depth at which it is submerged in the fluid.

4. How does buoyancy force relate to an object's weight?

Buoyancy force acts in the opposite direction of an object's weight. If the buoyancy force is greater than the weight of the object, the object will float. If the weight is greater than the buoyancy force, the object will sink. When the two forces are equal, the object will be suspended in the fluid.

5. How is buoyancy force important in everyday life?

Buoyancy force plays a crucial role in many everyday activities, such as swimming, boating, and scuba diving. It also explains why some objects float while others sink in water. In addition, the concept of buoyancy is used in designing ships and other watercraft to ensure they do not sink, and in the design of hot air balloons and blimps.

Similar threads

  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
15
Views
977
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
753
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
668
  • Introductory Physics Homework Help
Replies
6
Views
1K
Back
Top