A spherical particle of mass m� is shot horizontally with initial speed v0 into a viscous fluid. Use Stokes’ law to find an expression for vx(t), the horizontal velocity as a function of time. Vertical motion due to gravity can be ignored. Express your answer in terms of the variables v0, η, r, t, m, and appropriate constants. A 4.8-cm-diameter, 55 g ball is shot horizontally into a tank of 40∘C∘C honey. How long will it take for the horizontal speed to decrease to 10%% of its initial value?

A spherical particle of mass m� is shot horizontally with initial speed v0 into a viscous fluid. Use Stokes’ law to find an expression for vx(t), the horizontal velocity as a function of time. Vertical motion due to gravity can be ignored. Express your answer in terms of the variables v0, η, r, t, m, and appropriate constants. A 4.8-cm-diameter, 55 g ball is shot horizontally into a tank of 40∘C∘C honey. How long will it take for the horizontal speed to decrease to 10%% of its initial value?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter15: Fluids

Section: Chapter Questions

Problem 46PQ

See similar textbooks

Similar questions

Show that the Reynolds number NRis unitless by substituting units for all the quantities in its definition and cancelling.
A rock with a mass of 540 g in air is found to have an apparent mass of 342 g when submerged in water. (a) What mass of water is displaced? (b) What is the volume of the rock? (c) What is its average density? Is this consistent with the value for granite?
A rain gauge consists of a funnel with a diameter D = 10 cm that collects rain and deposits liquid water of density ρ = 1 × 103 kg / m^3 inside a cylinder of diameter d = 1 cm. The column of collected liquid rises at the rate of one centimeter per minute. a) If the raindrops fall into the funnel with a velocity of 10 m / s, calculate the mass of water liquid in a cubic meter of the atmosphere. b) Assuming that the raindrops have a radius of 1 mm, determine the number of drops in a cubic meter of the atmosphere. Justify your calculation method.
For the flow of an incompressible viscous fluid and an axial flow in cylindrical pipe v = v(p)ê,, one side of the Navier-Stokes equation gives v:(7 x v) = 0. Show that the displayed equation, i.e. V²(V × v) = 0, leads to the differential equation 1 d d?v° 1 dv = 0. p dp dp2 p² dp
A balloon filled with helium gas has an average density of ρb = 0.31 kg/m3. The density of the air is about ρa = 1.23 kg/m3. The volume of the balloon is Vb = 0.075 m3. The balloon is floating upward with acceleration a. Express the weight of the balloon, W, in terms of ρb and Vb.
The differential change in pressure p close to the surface of a static fluid is given by the following expression: dp/dy = -3Ap2,where A is a constant, with units of 1/(atm•m), and p is the pressure in atm. The pressure at the surface of the fluid is p(0) = 1 atm, and the coordinate y here is positive upwards with origin at the surface. Write an expression for the absolute pressure as a function of y.
What is the approximate mass of the air in our 10 m × 12 m × 4 m physics lab? The density of air is 1000 g/cm3. Convert density to kg/m^3
Drag Force: A spherical particle of radius 5.9 cm and a mass of 226 g is moving through a fluid of the same density. (This means you can ignore the effects of gravity.) The position of the particle is given by x (t) 1 In (1+ bvot), where x is its position and t is the elapsed time. The initial speed vo is 27.8 m/s, and the constant b is 0.3 m-1. (b) What is the velocity of the particle after 3.3 seconds? (c) What is the acceleration of the particle after 3.3 seconds?
A balloon filled with helium gas has an average density of ρb = 0.31 kg/m3. The density of the air is about ρa = 1.23 kg/m3. The volume of the balloon is Vb = 0.075 m3. The balloon is floating upward with acceleration a. Calculate the numerical value of Fb in N.
On a perfect fall day, you are hovering at a low altitude in a hot-air balloon, accelerated neither upward nor downward. The total weight of the balloon, including its load and the hot air in it, is 12000 N. What is the volume of the displaced air in units of m'? (Use 1.2 kg for the density of air) m HINT: Use g = 10 to convert the weight of the ballon in N to a mass in kg.
A spherical particle falling at a terminal speed in a liquid must have the gravitational force balanced by the drag force and the buoyant force. The buoyant force is equal to the weight of the displaced fluid, while the drag force is assumed to be given by Stokes Law, Fs = 6πrηv. Show that the terminal speed is given by v = (2R2 g/9η) . (ρs − ρ1) , where R is the radius of the sphere, ρs is its density, and ρ1 is the density of the fluid, and η the coefficient of viscosity.
A fluid that occupies a volume of A Liter weighs B N at a location where the gravitational acceleration is 9.80 m/s2 A = 4.5 liters B = 15 N Mass of this fluid (kg) is _________. Density (kg/L) of fluid is ________.