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<h2 class="hd hd-2 unit-title">Intro to Resistive Forces</h2>
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<p> This sequence introduces resistive forces, or drag forces that have some velocity-dependence. The models that we'll explore come from experimental observation and are only applicable to certain materials and velocity ranges. However limited, these techniques have useful applications to problems calculating the effects of air resistance and viscosity.</p><p> As you go through the lesson, you will find this list of reading from the textbook complementary to the videos and exercises, and on many occasions these readings will contain relevant material to the presentation:</p><ul><li> Drag forces in Fluids <a href="/courses/course-v1:MITx+8.01.1x+3T2018/pdfbook/0/chapter/8/27"><i class="it">chapter 8, section 8.6</i></a></li><li> Worked Example: Free Fall with Air Drag <a href="/courses/course-v1:MITx+8.01.1x+3T2018/pdfbook/0/chapter/8/49"><i class="it">chapter 8, example 8.12</i></a></li></ul>
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<h2 class="hd hd-2 unit-title">L14v1: Intro to Resistive forces</h2>
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<h3 class="hd hd-2">L14v1: Intro to Resistive Forces</h3>
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<h2 class="hd hd-2 unit-title">L14v2: Resistive Forces - Low Speed Case</h2>
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<h2 class="hd hd-2 unit-title">L14v3: Resistive Forces - High Speed Case</h2>
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<h2 class="hd hd-2 unit-title">L14Q1: Differential Equations and Drag</h2>
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L14Q1-1: Differential Equation and Drag, Part (A)
</h3>
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<p>
A block of mass \(m\) is moved by a constant horizontal force of magnitude \(F\) along a horizontal surface. The coefficient of kinetic friction between the block and the surface is \(\mu\). In addition to friction, the block experiences the air drag, whose magnitude is given by \(F_d=bv\) where \(b\) is a constant coefficient and \(v\) is the speed of the block.
</p>
<strong>
Part A
</strong>
<p>
What is the differential equation describing the motion of the block?
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\(\displaystyle \frac{dv}{dt}=F-\mu mg &#8211; bv\)
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\(\displaystyle \frac{dv}{dt}=F&#8211; bv\)
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\(\displaystyle \frac{dv}{dt}=F-\mu mg +bv\)
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\(\displaystyle m\frac{da}{dt}=F-\mu mg &#8211; bv\)
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\(\displaystyle m\frac{da}{dt}=F&#8211; bv\)
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\(\displaystyle m\frac{da}{dt}=F-\mu mg +bv\)
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\(\displaystyle \frac{dv}{dt}=\frac{F-\mu mg &#8211; bv}{m}\)
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\(\displaystyle \frac{dv}{dt}=\frac{F&#8211; bv}{m}\)
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\(\displaystyle \frac{dv}{dt}=\frac{F-\mu mg +bv}{m}\)
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<h3 class="hd hd-3 problem-header" id="lore_ls04_23792_checkpoint__differential_equation_and_drag__part__b__randxyzy3lg69k4-problem-title" aria-describedby="block-v1:MITx+8.01.1x+3T2018+type@problem+block@lore_ls04_23792_checkpoint__differential_equation_and_drag__part__b__randxyzy3lg69k4-problem-progress" tabindex="-1">
L14Q1-2: Differential Equation and Drag, Part (B)
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<p>
(Problem Restatement) A block of mass \(m\) is moved by a constant horizontal force of magnitude \(F\) along a horizontal surface. The coefficient of kinetic friction between the block and the surface is \(\mu\). In addition to friction, the block experiences the air drag, whose magnitude is given by \(F_d=bv\) where \(b\) is a constant coefficient and \(v\) is the speed of the block.
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<strong>
Part B
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<p>
After a long period of time, what are the values of the speed and the acceleration of the block? (In other words, what is the terminal velocity?)
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\(\displaystyle v=\frac{F-\mu mg}{bm}\); \(\displaystyle a=0\)
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\(\displaystyle v=\frac{F-\mu mg}{bm}\); \(\displaystyle a=\mu g\)
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\(\displaystyle v=\frac{F-\mu mg}{bm}\); \(\displaystyle a=\frac{F}{m}\mu g\)
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\(\displaystyle v=\frac{F-\mu mg}{b}\); \(\displaystyle a=0\)
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\(\displaystyle v=\frac{F-\mu mg}{b}\); \(\displaystyle a=\mu g\)
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\(\displaystyle v=\frac{F-\mu mg}{b}\); \(\displaystyle a=\frac{F}{m}\mu g\)
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