Answer:
Sure, I can help you with that. Here are the steps involved in solving the problem:
1. **Define the variables.**
The following variables are used in the problem:
* **h:** The height of the plate, which is 2 mm = 0.002 m
* **L:** The length of the plate, which is 1.25 m
* **W:** The width of the plate, which is 1.25 m
* **v:** The velocity of the plate, which is 0.18 m/s
* $\mu$: The dynamic viscosity of the oil, which is 2.5 N.s/m²
* $\rho$: The density of the oil, which is 0.85 * 1000 kg/m³ = 850 kg/m³
* g: The acceleration due to gravity, which is 9.8 m/s²
* F: The force required to lift the plate
2. **Determine the area of the plate.**
The area of the plate is calculated as follows:
```
A = L * W = 1.25 m * 1.25 m = 1.5625 m²
```
3. **Determine the volume of the oil displaced by the plate.**
The volume of the oil displaced by the plate is calculated as follows:
```
V = A * h = 1.5625 m² * 0.002 m = 0.00390625 m³
```
4. **Determine the weight of the oil displaced by the plate.**
The weight of the oil displaced by the plate is calculated as follows:
```
W_o = \rho * V * g = 850 kg/m³ * 0.00390625 m³ * 9.8 m/s² = 3.37 N
```
5. **Determine the force required to overcome the viscous drag on the plate.**
The force required to overcome the viscous drag on the plate is calculated as follows:
```
F_v = \mu * L * v = 2.5 N.s/m² * 1.25 m * 0.18 m/s = 0.46 N
```
6. **Determine the total force required to lift the plate.**
The total force required to lift the plate is calculated as follows:
```
F = F_o + F_v = 3.37 N + 0.46 N = 3.83 N
```
Therefore, the force required to lift the plate with a constant velocity of 0.18 m/s is 3.83 N.
Step-by-step explanation: