4. Certain frictional forces have magnitude proportional to the square of the velocity of the moving object. Thus |Ffriction| = -yv² for some positive constant y. Here there is an annoying sign issue since the frictional force must have sign opposite to the velocity. One can write Felastic = -y|v|v. If an object of mass m is subject to this frictional force and no other forces, and the initial velocity is positive, then the velocity will always be positive and we can just say Ffriction Then the position y of the particle satisfies the equation -yo?. dy dt2 2 dy +y dt = 0. Write out a solution of this equation for the initial conditions y(0) = Yo, (dy/dt)(0) the substitution u = = vo. Hint: The equation reduces to first order. Use dy/dt and solve the first order equation to get u. Then integrate u to get y.

4. Certain frictional forces have magnitude proportional to the square of the velocity of the moving object. Thus |Ffriction| = -yv² for some positive constant y. Here there is an annoying sign issue since the frictional force must have sign opposite to the velocity. One can write Felastic = -y|v|v. If an object of mass m is subject to this frictional force and no other forces, and the initial velocity is positive, then the velocity will always be positive and we can just say Ffriction Then the position y of the particle satisfies the equation -yo?. dy dt2 2 dy +y dt = 0. Write out a solution of this equation for the initial conditions y(0) = Yo, (dy/dt)(0) the substitution u = = vo. Hint: The equation reduces to first order. Use dy/dt and solve the first order equation to get u. Then integrate u to get y.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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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Question

4. Certain frictional forces have magnitude proportional to the square
of the velocity of the moving object. Thus |Ffriction| = -yv² for some
positive constant y. Here there is an annoying sign issue since the
frictional force must have sign opposite to the velocity. One can write
Felastic = -y|v|v. If an object of mass m is subject to this frictional
force and no other forces, and the initial velocity is positive, then the
velocity will always be positive and we can just say Ffriction
Then the position y of the particle satisfies the equation
-yo?.
dy
dt2
2
dy
+y
dt
= 0.
Write out a solution of this equation for the initial conditions y(0) =
Yo, (dy/dt)(0)
the substitution u =
= vo. Hint: The equation reduces to first order. Use
dy/dt and solve the first order equation to get
u. Then integrate u to get y.

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