Because of their light weight and flat bottoms, basket coffee filters are good ways of probing the resistive forces exerted by the air on objects moving in it. (A stack of them are shown at the right.) If the filter is falling straight down and smoothly, the inertial drag that the air exerts on it is given by Fdrag=0.5 C p A v² where C is a dimensionless constant, p is the density of the air, A is the area the filter presents to the air (~the area of the bottom circle of the filter), and vis the velocity of the filter moving through the air. A.As the filter falls, it speeds up until the resistive force pointing up is equal to the force of gravity moving down. It then moves with a constant terminal velocity, VT. A.1 If the filter has a mass of m, find an equation that expresses the velocity with which the filter is moving once these forces balance. Show your work. A.2 Suppose you have measured the mass of the filter to be 1 gram, its radius to be 8 cm, and its terminal velocity to be 1 m/s. If you take the density of air to be 1 kg/m³ and the gravitational field to be 10 N/kg, find the value of the constant C. B. The Reynold's number, Re, for an object moving in a fluid is the inertial drag force given above divided by the viscous force, where u is the viscosity of the fluid, Fviscous fluid-sphere=-6uRv R is the radius of the object and vis its velocity through the fluid. (This is actually correct up to a dimensionless factor. For this problem take Re to be the ratio of the magnitudes of these two forces.) B.1 Write an equation for the Reynolds number for this example, simplifying the equation as much as possible (e.g., cancelling factors that are both in the numerator and denominator).
Because of their light weight and flat bottoms, basket coffee filters are good ways of probing the resistive forces exerted by the air on objects moving in it. (A stack of them are shown at the right.) If the filter is falling straight down and smoothly, the inertial drag that the air exerts on it is given by Fdrag=0.5 C p A v² where C is a dimensionless constant, p is the density of the air, A is the area the filter presents to the air (~the area of the bottom circle of the filter), and vis the velocity of the filter moving through the air. A.As the filter falls, it speeds up until the resistive force pointing up is equal to the force of gravity moving down. It then moves with a constant terminal velocity, VT. A.1 If the filter has a mass of m, find an equation that expresses the velocity with which the filter is moving once these forces balance. Show your work. A.2 Suppose you have measured the mass of the filter to be 1 gram, its radius to be 8 cm, and its terminal velocity to be 1 m/s. If you take the density of air to be 1 kg/m³ and the gravitational field to be 10 N/kg, find the value of the constant C. B. The Reynold's number, Re, for an object moving in a fluid is the inertial drag force given above divided by the viscous force, where u is the viscosity of the fluid, Fviscous fluid-sphere=-6uRv R is the radius of the object and vis its velocity through the fluid. (This is actually correct up to a dimensionless factor. For this problem take Re to be the ratio of the magnitudes of these two forces.) B.1 Write an equation for the Reynolds number for this example, simplifying the equation as much as possible (e.g., cancelling factors that are both in the numerator and denominator).
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Please answer parts A-B. For B3, the two forces to compare are intertial drag and viscous drag force.
Transcribed Image Text:Because of their light weight and flat bottoms, basket coffee filters are good ways of probing the resistive forces exerted by the air on objects
moving in it. (A stack of them are shown at the right.) If the filter is falling straight down and smoothly, the inertial drag that the air exerts on it is
given by
Fdrag =0.5 C p A v²
where C is a dimensionless constant, p is the density of the air, A is the area the filter presents to the air (~the area of the bottom circle of the filter),
and vis the velocity of the filter moving through the air.
A.As the filter falls, it speeds up until the resistive force pointing up is equal to the force of gravity moving down. It then moves with a constant terminal velocity, VT.
A.1 If the filter has a mass of m, find an equation that expresses the velocity with which the filter is moving once these forces balance. Show your work.
A.2 Suppose you have measured the mass of the filter to be 1 gram, its radius to be 8 cm, and its terminal velocity to be 1 m/s. If you take the density of air to
be 1 kg/m³ and the gravitational field to be 10 N/kg, find the value of the constant C.
B. The Reynold's number, Re, for an object moving in a fluid is the inertial drag force given above divided by the viscous force, where μ is the viscosity of the fluid,
viscous
fluid-sphere =-6лμRv
R is the radius of the object and v is its velocity through the fluid. (This is actually correct up to a dimensionless factor. For this problem take Re to be the ratio of the
magnitudes of these two forces.)
B.1 Write an equation for the Reynolds number for this example, simplifying the equation as much as possible (e.g., cancelling factors that are both in the
numerator and denominator).
B.2 If the viscosity of air is about 10-3 kg/m-s, find the value of the Reynolds number for the coffee filter falling in air.
B.3 From your calculation, which force do you expect to dominate for a falling coffee filter? Mark both if they are about the same.
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