Comparing Aluminum & Copper Deflection Angles

[Loligo]

Homework Statement

The Shear modulus for aluminum and copper are 25GPa and 35GPa, respectively. An aluminum and copper pole, both the same length are subjected to the same shear force at the top of each pole, bending each pole a different angle y. Which pole has a higher angle of deflection and by how much?

Homework Equations

Formulas I am using are Shear Modulus = Shear Stress/Shear Strain
S = σ/ε = (F/A)/(Δx/L_o)
angle y = ε = Δx/L_o

The Attempt at a Solution

Since the forces are equal and area should be equal (under assumption the poles are the same dimensions the shear stress (σ) is equal for both poles.
Rearranging the formulas I get σ=S*y
σ_A=σ_C so 25GPa*y_A=38GPa*y_C
I get that the angle the deflection for the aluminum pole will be 1.52 times that of the copper pole.

 

[PhanthomJay]

is it 35 or 38 GPa? Insert correct value and round off to one decimal point, and your result will be OK. Shear stress is usually designated as $$\tau$$, and shear modulus is usually referred to as $$G$$. This distinguishes it from normal stress ($$\sigma$$) and elastic modulus ($$E$$) used for normal strains.

 

[Loligo]

The aluminum pole has a shear modulus of 25 GPa and the copper pole 35GPa.
Is it correct to say that the shear stress will stay the same with the poles are identical in proportions and are subjected to the same force

 

[PhanthomJay]

The aluminum pole has a shear modulus of 25 GPa and the copper pole 35GPa.
Is it correct to say that the shear stress will stay the same with the poles are identical in proportions and are subjected to the same force

Yes. The problem does not specifically state that both poles are similar in cross section, so it must be assumed that they are identically proportioned..

 

[rdl]

This means that the aluminum pole will have a higher angle of deflection than the copper pole by 52%.

I would like to clarify that the units for shear modulus are in Pa (Pascals), not GPa (Gigapascals). Therefore, the correct values for aluminum and copper would be 25,000,000 Pa and 35,000,000 Pa, respectively.

With this correction, I agree with your solution that the aluminum pole will have a higher angle of deflection than the copper pole. This is because aluminum has a lower shear modulus, making it more flexible and easier to bend compared to copper. This also means that for the same applied force, the aluminum pole will experience a greater amount of shear strain compared to the copper pole, resulting in a higher deflection angle.

It's important to note that the exact deflection angle will also depend on other factors such as the dimensions and shape of the poles, as well as the type of force being applied. However, based on the given information, we can conclude that the aluminum pole will have a higher angle of deflection than the copper pole.