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An object moving in a liquid experiences a linear drag
Chapter 6, Problem 75CP(choose chapter or problem)
An object moving in a liquid experiences a linear drag force: \(\vec{D}=(b v\), direction opposite the motion ), where \(b\) is a constant called the drag coefficient. For a sphere of radius \(R\), the drag constant can be computed as \(b=6 \pi \eta R\), where \(\eta\) is the viscosity of the liquid.
a. Find an algebraic expression for \(v_{x}(t)\), the \(x\)-component of velocity as a function of time, for a spherical particle of radius \(R\) and mass \(m\) that is shot horizontally with initial speed \(v_{0}\) through a liquid of viscosity \(\eta\).
b. Water at \(20^{\circ} \mathrm{C}\) has viscosity \(\eta=1.0 \times 10^{-3} \mathrm{~N} \mathrm{~s} / \mathrm{m}^{2}\). Suppose a 4.0-cm-diameter, 33 g ball is shot horizontally into a tank of \(20^{\circ} \mathrm{C}\) water. How long will it take for the horizontal speed to decrease to \(50 \%\) of its initial value?
Equation Transcription:
Text Transcription:
^vec D=(bv, direction opposite the motion)
b
b=6 pi eta R
eta
v_x(t)
x-component
R
m
20^circC
eta=1.0 x 10^-3Ns/m^2
20^circC
50%
Questions & Answers
QUESTION:
An object moving in a liquid experiences a linear drag force: \(\vec{D}=(b v\), direction opposite the motion ), where \(b\) is a constant called the drag coefficient. For a sphere of radius \(R\), the drag constant can be computed as \(b=6 \pi \eta R\), where \(\eta\) is the viscosity of the liquid.
a. Find an algebraic expression for \(v_{x}(t)\), the \(x\)-component of velocity as a function of time, for a spherical particle of radius \(R\) and mass \(m\) that is shot horizontally with initial speed \(v_{0}\) through a liquid of viscosity \(\eta\).
b. Water at \(20^{\circ} \mathrm{C}\) has viscosity \(\eta=1.0 \times 10^{-3} \mathrm{~N} \mathrm{~s} / \mathrm{m}^{2}\). Suppose a 4.0-cm-diameter, 33 g ball is shot horizontally into a tank of \(20^{\circ} \mathrm{C}\) water. How long will it take for the horizontal speed to decrease to \(50 \%\) of its initial value?
Equation Transcription:
Text Transcription:
^vec D=(bv, direction opposite the motion)
b
b=6 pi eta R
eta
v_x(t)
x-component
R
m
20^circC
eta=1.0 x 10^-3Ns/m^2
20^circC
50%
ANSWER:
Step 1 of 4
In this problem, we have to find an algebraic expression for \(v x(t)\) in the \(x\)-components of velocity and also find the horizontal speed to decrease 50% of its initial value.