# Find Torques frm Gravity & Buoyancy on Beam Cross-Sections

• jchan79
In summary, the conversation discusses the representation of the cross-section of an underwater beam as a combination of a rectangle and two narrow triangles, with one of the triangles having negative mass. The individual is seeking assistance in finding the torques from gravity and buoyancy on these figures. The homework statement then introduces the concept of a beam with low density in water and its unstable orientation, and asks for the critical density at which this transition occurs. The equation for balancing vertical forces is also provided.
jchan79
Homework Statement
If a beam with square cross-section and very low density is placed in water, it will turn one pair of its long opposite faces horizontal. This orientation, however, becomes unstable as we increase its density. Find the critical density when this transition occurs. The density of water is ##\rho_w = 1000 kg/m^3##.
Relevant Equations
Balancing vertical forces: ##\rho_w = \frac{\rho_{block}l^2}{xh}## where l is the side length of the square cross-section and h is the depth of the beam that is submerged in the water.
The hint says that "The cross-section of the underwater part of the beam could be represented as a superposition of a rectangle and two symmetrically positioned narrow triangles (one of them of negative mass)." How do I find the torques from gravity and buoyancy on these figures?

jchan79 said:
Homework Statement: If a beam with square cross-section and very low density is placed in water, it will turn one pair of its long opposite faces horizontal. This orientation, however, becomes unstable as we increase its density. Find the critical density when this transition occurs. The density of water is ##\rho_w = 1000 kg/m^3##.
Homework Equations: Balancing vertical forces: ##\rho_w = \frac{\rho_{block}l^2}{xh}## where l is the side length of the square cross-section and h is the depth of the beam that is submerged in the water.

The hint says that "The cross-section of the underwater part of the beam could be represented as a superposition of a rectangle and two symmetrically positioned narrow triangles (one of them of negative mass)." How do I find the torques from gravity and buoyancy on these figures?
Please post or describe the diagram you have drawn using the hint.

## What is the difference between torque from gravity and torque from buoyancy?

Torque from gravity is the rotational force exerted on an object due to its weight and the force of gravity, while torque from buoyancy is the rotational force exerted on an object due to the pressure difference between the top and bottom surfaces of the object in a fluid.

## How do you calculate torque from gravity on a beam cross-section?

To calculate torque from gravity on a beam cross-section, you need to find the weight of the beam and the distance from the center of gravity to the point where the torque is being measured. Then, multiply the weight by the distance to get the torque value.

## What is the equation for torque from buoyancy on a beam cross-section?

The equation for torque from buoyancy on a beam cross-section is T = ρgVh, where T is the torque, ρ is the density of the fluid, g is the acceleration due to gravity, V is the volume of the beam, and h is the distance from the center of buoyancy to the point where the torque is being measured.

## How does the shape of a beam cross-section affect torque from gravity and buoyancy?

The shape of a beam cross-section can affect torque from gravity and buoyancy by changing the distribution of weight and buoyancy forces. For example, a rectangular cross-section will have a different torque value compared to a triangular cross-section with the same dimensions.

## What are some real-world applications of calculating torque from gravity and buoyancy on beam cross-sections?

Calculating torque from gravity and buoyancy on beam cross-sections is important in engineering and construction, as it helps determine the stability and strength of structures. It is also used in designing ships and submarines to ensure they are able to withstand the forces of buoyancy and gravity. Additionally, understanding torque is crucial in industries such as aerospace and automotive, where it is used in the design and performance of vehicles and aircraft.

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