Final answer:
To determine the vertical displacement of plate A due to shear strains in the symmetrically placed rubber pads when a vertical force is applied, we use the shear modulus and the dimensions of the rubber pads to calculate the shear strain and deformation. The original height of the rubber pads is needed to find the exact displacement. Without it, the problem cannot be solved.
Step-by-step explanation:
The student's problem involves the concept of shear strain in materials, specifically rubber pads used as part of a support consists of rigid plates. In the situation described, two symmetrically placed rubber pads connect three rigid plates, and a vertical force of 5N is applied to one of the plates, known as plate A. To calculate the vertical displacement of plate A due to the shear strain in the rubber pads, we need to use the relationship between shear stress, shear strain, and the shear modulus (Gr), which is given in the problem as 0.20 MPa or 200,000 N/m2
Shear strain (γ) can be computed using the equation γ = τ / G, where τ is the shear stress and G is the shear modulus of the material. Shear stress is calculated as the force F applied perpendicular to the area A (τ = F/A). Given the dimensions of the rubber pads and the force applied, we can compute the area as A = 30mm x 20mm = 600mm2 or 600 x 10-6 m2. By calculating the shear stress and using the given shear modulus, we can find the shear strain. The shear deformation or displacement (Δx) is shear strain times the original height (Lo) of the rubber pads, where Lo can be estimated based on the provided information or an additional detail the student might have.
It is important to note that if the original height (Lo) of the rubber pads is not given, the problem may not be solvable without additional data. For the student to proceed, they will need to find the height of the rubber pads or similar experimental setups to predict the vertical displacement accurately.