Exploring the Relationship between Buoyancy Force and Gravitational Force

In summary, the body in water has 2.4 times greater mass and has 2.4 times greater buoyancy Force, which causes it to float. The gravitational force between the body in air and the body in water is not enough to keep the body in water from floating.
  • #1
Callmelucky
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Homework Statement
Picture below. Both bodies are made of same material but the body placed in water had 2.4 times greater mass. What is the relationship between buoyancy Force and gravitational force between body in water and body in air?
Relevant Equations
F(buoyancy) = density(of fluid) * g * Volume(of object), F(gravitational) = m * g
Picture below. Both bodies are made of same material but the body placed in water had 2.4 times greater mass. What is the relationship between buoyancy Force and gravitational force between body in water and body in air?I have no clue how to solve this.
I know that body with greater mass has 2.4 times greater buoyancy Force, 2.4 times greater mass and gr. force, 2.4 larger volume. But I don't know how to solve the problem.

The worst thing is that I only need to answer if F(buoyancy) of body in water is <, =, > than gravitational force of body in air or if there is not enough data to answer the question.
Answer at the end of textbook is F(buoyancy) of body in water > F(gravitational) of body in air.

if some can please explain I'd be very grateful.
Thank you.
 

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  • #2
What can you infer from the fact that the scale is in equilibrium? What is the relationship between the net forces acting on the two bodies?
 
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  • #3
nasu said:
What can you infer from the fact that the scale is in equilibrium? What is the relationship between the net forces acting on the two bodies?
well, I guess that Fb+Fg1 = Fg2, but I still don't get it.
 
  • #4
Callmelucky said:
well, I guess that Fb+Fg1 = Fg2
Don't guess. Draw two free body diagrams, one for each mass, and show all the forces acting on the mass in each diagram.
 
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  • #5
kuruman said:
Don't guess. Draw two free body diagrams, one for each mass, and show all the forces acting on the mass in each diagram.
🤦‍♂️🙆‍♂️ How stupid I am. I got it. Thank you.
I didn't solve enough problems with drawing forces, so I don't have that habit.
I will have to fix that.
 
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  • #6
Callmelucky said:
🤦‍♂️🙆‍♂️ How stupid I am. I got it. Thank you.
I didn't solve enough problems with drawing forces, so I don't have that habit.
I will have to fix that.
I'm glad that you got it.
 
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FAQ: Exploring the Relationship between Buoyancy Force and Gravitational Force

What is the relationship between buoyancy force and gravitational force?

The buoyancy force and gravitational force are interrelated through the principle of buoyancy, which states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object. The gravitational force, on the other hand, pulls the object downward. The relationship between these forces determines whether an object will float, sink, or remain neutrally buoyant.

How do you calculate the buoyancy force acting on an object?

The buoyancy force (F_b) can be calculated using the formula: F_b = ρ × V × g, where ρ (rho) is the density of the fluid, V is the volume of the fluid displaced by the object, and g is the acceleration due to gravity. This formula derives from Archimedes' principle.

What factors affect the magnitude of the buoyancy force?

The magnitude of the buoyancy force is affected by three primary factors: the density of the fluid (ρ), the volume of the fluid displaced by the object (V), and the acceleration due to gravity (g). Changes in any of these factors will alter the buoyancy force experienced by the object.

How does the gravitational force impact an object's buoyancy?

The gravitational force impacts an object's buoyancy by determining the object's weight, which acts downward. If the buoyancy force is greater than the gravitational force, the object will float. If the gravitational force is greater, the object will sink. When both forces are equal, the object will remain neutrally buoyant, neither sinking nor floating.

Can an object have a buoyancy force if it is not submerged in a fluid?

No, an object cannot have a buoyancy force if it is not submerged in a fluid. Buoyancy arises from the pressure difference exerted by the fluid on the object, which requires the object to be at least partially submerged. Without a fluid medium, there is no displaced fluid volume to generate a buoyant force.

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