My 1st problem

Classical Mechanics Level 3

Let's assume that in a special case μ \mu , the kinetic friction coefficient of a surface is proportional to an object's instantaneous velocity v ( t ) v(t)

In our case the proportionality constant is 1 or μ = v ( t ) \mu=v(t) .

If a block of mass 1 kg 1\text{ kg} is given an initial velocity of 3 m/s 3\text{ m/s} and is pushed onto a plane surface (not inclined or frictionless).

What will be the amount of time that the block takes to come to a complete stop?

3 years None of the above 8.33 second 2 second

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Tahmid Ranon by Tahmid Ranon , 22, Bangladesh

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1 solution

Steven Chase
Oct 24, 2016

F = m a = m d v d t = − μ W = − v W F = ma = m \frac{dv}{dt} = -\mu W = -vW

d v d t = − W m v \frac{dv}{dt} = -\frac{W}{m}v

v = A e − W m t v = Ae^{-\frac{W}{m} t}

Therefore, the block will never actually come to a stop.

7 Helpful 1 Interesting 1 Brilliant 1 Confused

Thank you for your time... :)

Tahmid Ranon - 4 years, 7 months ago

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