A force can be a function of position, velocity, or time. Most of the forces we consider in an introduction to dynamics are constant forces, but the text does examine a drag force that is proportional to velocity for a falling object, resulting is a terminal velocity. For this challenge question, imagine a block of mass m sliding across a horizontal surface lubricated with a thick oil, and that the frictional force can be approximated as F, = -bvv If v = vo at time t=0, determine v and x as functions of time. Also show that the maximum distance the block could travel is 2mv3' „3/2 Xmax 3b

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Chapter6: Applications Of Newton's Laws
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A force can be a function of position, velocity, or time. Most of the forces we consider in an
introduction to dynamics are constant forces, but the text does examine a drag force that is
proportional to velocity for a falling object, resulting is a terminal velocity.
For this challenge question, imagine a block of mass m sliding across a horizontal surface
lubricated with a thick oil, and that the frictional force can be approximated as
F, = -byv
If v = vo at time t=0, determine v and x as functions of time.
Also show that the maximum distance the block could travel is
2mv
3b
,3/2
Хтах
Suggestion:
For this problem, begin with the statement:
dv
= -byv
dt
F = ma = m
Transcribed Image Text:A force can be a function of position, velocity, or time. Most of the forces we consider in an introduction to dynamics are constant forces, but the text does examine a drag force that is proportional to velocity for a falling object, resulting is a terminal velocity. For this challenge question, imagine a block of mass m sliding across a horizontal surface lubricated with a thick oil, and that the frictional force can be approximated as F, = -byv If v = vo at time t=0, determine v and x as functions of time. Also show that the maximum distance the block could travel is 2mv 3b ,3/2 Хтах Suggestion: For this problem, begin with the statement: dv = -byv dt F = ma = m
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