The brick shown in drawing the is glued to the floor. A 3500-N force is applied to the top surface of the brick as shown. If the brick has a shear modulus of 5.4 109 N/m2, how far to the right does the top face move relative to the stationary bottom face?
2.6E-6
I tried to use Youngs Moduleust B = (F/A)/(dL/l) to get 1.3x10^-6
but the answer is 1.1x10^-6
To find out how far the top face of the brick moves relative to the stationary bottom face, we can use Hooke's Law and the formula for shear strain.
Hooke's Law states that the shear stress (τ) is directly proportional to the shear strain (γ), and the constant of proportionality is the shear modulus (G):
τ = G * γ
In this case, we are given the shear modulus (G = 5.4 * 10^9 N/m^2) and the applied force (F = 3500 N). To find the shear stress, we need to determine the area over which the force is applied.
Let's assume the top face of the brick has a length (L) and a width (W). The area (A) over which the force is applied is given by A = L * W.
Next, we can calculate the shear stress (τ) using the equation:
τ = F / A
Calculate the area (A) and substitute the values into the equation to find the shear stress (τ).
Once we have the shear stress (τ), we can use Hooke's Law to calculate the shear strain (γ) using the equation:
γ = τ / G
Finally, to find how far the top face of the brick moves to the right relative to the stationary bottom face, we multiply the shear strain by the height (H) of the brick's thickness:
Δx = γ * H
Substitute the values into the equation to find the displacement (Δx).
Please provide the dimensions (L, W, H) of the brick to proceed with the calculation.