Mass disintegration

Classical Mechanics Level 2

A body of mass $m_{0}$ is placed on a smooth horizontal surface. The mass of the body is decreasing exponentially with disintegration constant $\lambda$ . Assuming that the mass is ejected backward with a relative velocity $u$ . Initially the body was at rest.
Find the velocity of body after time $t$
Answer comes in the form of $\large v=\alpha u^{\beta} \lambda^{\gamma} t^{\delta}$

Type your answer as $\large \alpha+\beta+\gamma+\delta=?$

The answer is 4.

1 solution

Steven Chase
Jul 18, 2020

$m = m_0 e^{-\lambda t} \\ dm = -\lambda m_0 e^{-\lambda t} \, dt$

Conservation of momentum:

$|dm| u = m \, dv \\ \lambda u m_0 e^{-\lambda t} \, dt = m_0 e^{-\lambda t} \, dv \\ dv = u \lambda \, dt \\ v = u \lambda t$

@Steven Chase Very nice solution.

A Former Brilliant Member - 10 months, 4 weeks ago

@Steven Chase can we upgrade this problem
Like A block is going on frictional surface and it's mass is varying, find the work done by friction
Share your views??

A Former Brilliant Member - 10 months, 4 weeks ago

Mass disintegration

The answer is 4.

1 solution

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