# How Is the Shear Modulus of a Sponge Calculated?

• mikefitz
In summary, a large sponge with forces of magnitude 17 N applied to opposite faces of area 43 cm2 and a thickness of 3 cm has a delta x of 4.43 mm. The shear modulus of the sponge is calculated to be approximately 0.28 Pa. However, there may be an error in the conversion factor and further assistance may be needed from the Engineering forum.
mikefitz
A large sponge has forces of magnitude 17 N applied in opposite directions to two opposite faces of area 43 cm2 (see the figure below ). The thickness of the sponge (L is ")3 cm. The deformation angle (g is ")8.4°. (a) What is delta x? (b) What is the shear modulus of the sponge?

delta x = 4.43 mm

stress = 17N/430mm = .03953N/mm^2
strain = delta L/L, 4.43/30= .1476

shear modulus = stress/strain
=.03953/.1476=.28 Pa?

what did I do wrong?

mikefitz said:
A large sponge has forces of magnitude 17 N applied in opposite directions to two opposite faces of area 43 cm2 (see the figure below ). The thickness of the sponge (L is ")3 cm. The deformation angle (g is ")8.4°. (a) What is delta x? (b) What is the shear modulus of the sponge?

delta x = 4.43 mm

stress = 17N/430mm = .03953N/mm^2
strain = delta L/L, 4.43/30= .1476

shear modulus = stress/strain
=.03953/.1476=.28 Pa?

what did I do wrong?
I see for one thing that you have an incorrect conversion factor: 43 cm^2 = 4300mm^2. Beyond that, with my limited understanding of shear deformation (I used to understand it once 40 years ago), and my disdain for Pascals (we use psi in the States!), the Shear Modulus seems very low, even for a sponge.. Are you sure of the magnitude of the deformation angle? You should probably repost in the Engineering forum, if no further help is forthcoming here.

As a scientist, it is important to double check your calculations and units to ensure accuracy. In this case, the units for stress should be N/cm^2 instead of N/mm^2. This would result in a shear modulus of 28 Pa, which is the correct answer. Additionally, it is important to note that the deformation angle should be converted to radians (8.4° = 0.1464 radians) for accurate calculations. Overall, it is important to pay attention to units and conversions in order to obtain accurate results in scientific calculations.

## What is shear modulus?

The shear modulus is a measure of a material's resistance to deformation under shear stress. It is a measure of how easily a material can be sheared or twisted.

## How is shear modulus measured?

Shear modulus is typically measured using a shear test, where a force is applied parallel to the surface of a material causing it to deform. The resulting deformation and applied force are used to calculate the shear modulus.

## What factors affect the shear modulus of a sponge?

The material properties of the sponge, such as its density and porosity, can affect its shear modulus. The moisture content and temperature of the sponge can also impact its shear modulus.

## Why is the shear modulus of a sponge important?

The shear modulus of a sponge can affect its ability to absorb and hold water, as well as its overall strength and elasticity. It is an important factor to consider in the design of sponges for various applications.

## How does the shear modulus of a sponge compare to other materials?

The shear modulus of a sponge is typically lower than that of other solid materials, such as metals and plastics. This is due to the porous nature of sponges, which allows for more deformation under shear stress.

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