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 slide, we can use the concept of viscosity and the formula for viscous drag:
F = ηAv
Where:
F is the force,
η is the viscosity of the fluid (glycerine),
A is the cross-sectional area of the fluid,
and v is the relative velocity between the two slides.
First, let's calculate the cross-sectional area. Since the glycerine has been placed in between the slides, the cross-sectional area is the same as the area of one slide.
A = width x length
A = 1.0 cm x 4.0 cm
A = 4.0 cm^2
Next, we need to convert the given velocity from m/s to cm/s to match the unit of the cross-sectional area.
v = 0.35 m/s * 100 cm/m
v = 35 cm/s
Now, we need to look up the viscosity of glycerine. The viscosity of glycerine varies with temperature, but for this calculation, we'll assume it is 1.49 kg/m·s (at 20°C).
We can convert the viscosity to the appropriate unit:
η = 1.49 kg/m·s * 100 g/kg * 1 cm/m
η = 149 g/cm·s
Finally, we can substitute the values into the formula:
F = ηAv
F = 149 g/cm·s * 4.0 cm^2 * 35 cm/s
Now, let's convert the grams to Newtons by dividing by 1000:
F = 149 g/cm·s * 4.0 cm^2 * 35 cm/s / 1000
F = 2.614 N
Therefore, the force required to pull one of the microscope slides at a constant speed of 0.35 m/s relative to the other slide is approximately 2.614 N.
To find the force required to pull one microscope slide at a constant speed of 0.35 m/s relative to the other slide, we can use the concept of viscosity.
Viscosity is a measure of a fluid's resistance to flow. It determines how easily a fluid can be deformed or flows. The force required to pull the microscope slides can be determined using the formula:
F = η * A * v / d
where:
F is the force required to pull the microscope slides,
η (eta) is the dynamic viscosity of the fluid (glycerine in this case),
A is the area of the sliding surfaces,
v is the relative velocity between the slides (0.35 m/s in this case),
and d is the distance between the slides (1.8 mm or 0.0018 m).
First, let's calculate the area of the sliding surfaces. We have two microscope slides, each with a width of 1.0 cm and a length of 4.0 cm. Hence, the area of each slide is:
A = width * length = (1.0 cm * 4.0 cm) = 4.0 cm² = 4.0 * 10^-4 m²
Next, we need to determine the dynamic viscosity of glycerine. The dynamic viscosity of glycerine at room temperature is typically around 1.4 Pa⋅s (Pascal-seconds). However, the actual value may vary slightly depending on the specific type of glycerine and the temperature.
Now, we can substitute the given values into the formula to calculate the force:
F = (1.4 Pa⋅s) * (4.0 * 10^-4 m²) * (0.35 m/s) / (0.0018 m)
Simplifying the equation:
F = 0.014 N
Therefore, the force required to pull one microscope slide at a constant speed of 0.35 m/s relative to the other slide is approximately 0.014 Newtons (N).