Hi there, quick question:
How would you find the shear modulus of a ruler (plastic 12 in)? I don't exactly get it. You have to bend it which will help you...???
-Thanks!
Bending it like a beam, or measuring its vibrational frequency when clamped at one end, will tell you the bulk modulus E, not the shear modulus G. For a shear modulus determination, you would have to twist it in torsional loading. Then look up the equation for twist angle vs torsional stress. The section moment of inertia and the shear modulus will be involved.
To find the shear modulus of a ruler, you need to apply torsional loading by twisting it. Here's a step-by-step guide to help you:
1. Set up the experiment: Clamp one end of the ruler securely so that it does not move. Make sure the ruler is positioned horizontally and can freely rotate around its clamped end.
2. Apply torsional force: At the other end of the ruler, apply a twisting force gradually. You can use a torsion device or simply grip the ruler and twist it manually. Keep in mind to apply the force gradually to avoid damaging the ruler.
3. Measure the twist angle: As you apply the torsional force, carefully measure the twist angle of the ruler. You can use a protractor or any other measuring device that allows you to accurately determine the angle of rotation.
4. Calculate torsional stress: Torsional stress is the stress created within the ruler as a result of twisting. You can calculate it using the equation:
Torsional Stress = (Torque * Distance) / Moment of Inertia
Torque refers to the twisting force you applied, distance is the distance from the clamped end where the torque is applied, and the moment of inertia is a property specific to the ruler's cross-sectional shape.
5. Plot twist angle vs. torsional stress: With the measured twist angles and calculated torsional stresses, plot a graph of twist angle against torsional stress.
6. Determine the slope of the graph: The shear modulus, denoted by "G," can be determined from the slope of the graph. The equation relating the twist angle and torsional stress is:
Twist Angle = (G * Torsional Stress * Length) / (Moment of Inertia * Shear Modulus)
By rearranging the equation, you can solve for the value of the shear modulus.
It is important to note that this method assumes that the ruler behaves linearly within the applied range of torsional stress. For accurate results, it is recommended to repeat the experiment with different torque values and calculate an average shear modulus value.