A thin 1.8-mm coating of glycerine has been placed between two microscope slides of width 1.0 cm and length 4.0 cm. Find the force required to pull one of the microscope slides at a constant speed of 0.35 m/s relative to the other slide.
Answer in N
To find the force required to pull one microscope slide at a constant speed relative to the other, we need to consider the friction force acting between the slides due to the glycerine coating.
The friction force can be calculated using the equation:
Friction force = coefficient of friction × normal force
The coefficient of friction can be determined using the following equation:
Coefficient of friction = shear stress / shear rate
Shear stress is the force per unit area applied parallel to the direction of flow, and shear rate is the rate of deformation per unit length per unit time.
In this case, the shear stress is equal to the force required to pull one slide (Friction force) divided by the contact area between the slides.
The contact area can be calculated by multiplying the width and length of the slides.
Now, let's calculate the force required step by step:
1. Calculate the contact area:
Contact area = width × length = 1.0 cm × 4.0 cm = 4.0 cm^2
2. Convert the contact area to square meters:
1 cm^2 = 1 × 10^(-4) m^2
Contact area = 4.0 cm^2 × (1 × 10^(-4) m^2/cm^2) = 4.0 × 10^(-4) m^2
3. Calculate the shear stress:
Shear stress = Friction force / Contact area
4. Convert the thickness of the glycerine coating to meters:
1.8 mm = 1.8 × 10^(-3) m
5. Calculate the shear rate:
Shear rate = speed / thickness
6. Plug in the given values:
Shear rate = 0.35 m/s / (1.8 × 10^(-3) m) = 194.44 s^(-1)
7. Calculate the coefficient of friction:
Coefficient of friction = Shear stress / Shear rate
8. Calculate the force required:
Force required = Coefficient of friction × Normal force
Since the problem statement doesn't provide the value of the normal force, we cannot determine the exact force required without additional information.