What Is the Buoyant Force on an Object Submerged in Water?

[Saladsamurai]

I am not sure why this is not clicking...

An object hangs from a spring balance. The balance registers 30 N in the air and when it is immersed in water it reads 20 N. What is the buoyant force on this object? Draw a FBD to solve this.

FBD


$$\uparrow F_b$$
OBJECT
$$\downarrow F_W$$

Do I need to take into account any other forces?

It is multiple choice a) 20 N up
b) 10 N up
c) 10 N down
d) 20 N down

I am pretty sure it is not c or d...as that wouldn't seem like a "buoyant" force But I am not sure how to set up my Newton's 2nd equation?

Is it just $$\sum F=F_{weight}-F_{buoyant}=20$$
so F_buoyant=10N?

It just seems strange that we spent all day taking atmospheric pressure into account, but now we do not...

 

[PhanthomJay]

I am not sure why this is not clicking...

An object hangs from a spring balance. The balance registers 30 N in the air and when it is immersed in water it reads 20 N. What is the buoyant force on this object? Draw a FBD to solve this.

FBD


$$\uparrow F_b$$
OBJECT
$$\downarrow F_W$$

Do I need to take into account any other forces?

It is multiple choice a) 20 N up
b) 10 N up
c) 10 N down
d) 20 N down

I am pretty sure it is not c or d...as that wouldn't seem like a "buoyant" force But I am not sure how to set up my Newton's 2nd equation?

Is it just $$\sum F=F_{weight}-F_{buoyant}=20$$
so F_buoyant=10N?

It just seems strange that we spent all day taking atmospheric pressure into account, but now we do not...

Well, that's correct, but your free body diagram technically has 3 forces acting on the object: its weight down (30N), The buoyant force up (F_b), and tension in the scale's cord acting up (20N). So your FBD equation using Newtyon 1 is $$F_{net} = T + F_b -W = 0$$ from which 20 + F_b -30 = 0, that is, F_b = 10N up, whuch is what you got, but don't take shortcuts. Atmospheric pressure for all practical purposes cancels out of the equation, because the difference is rather small between the top and bottom of the object.

 

[ogb p]

I can understand why this concept may be confusing. Buoyant force is a complex concept that involves multiple factors such as density, volume, and gravity. In this scenario, the buoyant force is equal to the weight of the water displaced by the object, which is why it is crucial to take into account the object's volume.

To solve this problem, we need to use the formula for buoyant force, which is F_b = \rho Vg, where \rho is the density of the fluid (in this case, water), V is the volume of the object submerged in the fluid, and g is the acceleration due to gravity.

In this case, the volume of the object submerged in water is equal to its total volume, as it is fully submerged. Therefore, we can rewrite the formula as F_b = \rho V_{total}g.

Now, to set up the Newton's second law equation, we need to consider all the forces acting on the object. These forces are the weight of the object (F_{weight}), the buoyant force (F_b), and the normal force from the spring balance (F_{normal}).

Thus, our equation becomes \sum F = F_{normal} - F_{weight} - F_b = 0.

Since we know that the spring balance registers 30 N in the air and 20 N in water, we can plug these values into the equation to solve for the buoyant force. This gives us F_b = F_{normal} - F_{weight} = 20 - 30 = -10 N.

This means that the buoyant force is acting in the opposite direction of the weight of the object, which is downwards. Therefore, the correct answer is option d) 20 N down.

It is essential to take into account all the forces acting on an object to accurately determine the buoyant force. I hope this explanation helps clarify any confusion and helps you understand the concept better.