- #1

Woopa

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How can Force=0 if there is acceleration? (This is the first time I have encountered the product rule so this may be part of my misunderstanding)

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- Thread starter Woopa
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- #1

Woopa

- 21

- 4

How can Force=0 if there is acceleration? (This is the first time I have encountered the product rule so this may be part of my misunderstanding)

- #2

Filip Larsen

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- #3

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Note that the "new form" of Newton's second law given here is not valid in general. There are several threads on here analysing this question.

In fact it's not really Newton's second law, but an equation that is only valid in this specific case.

PS the author has confusingly used the same letter ##v## for the velocity of the rocket and the velocity of the expellant. A simpler way to look at this is to use conservation of momentum:

$$m_r\Delta v_r + \Delta m_e v_e = 0$$Where we need the assumption that ##\Delta m_e## is small compared to ##m_r##. Otherwise, we would need to be more explicit that the mass of the rocket is changing from ##m_r + m_e## to ##m_r## after the expellent is fired out.

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- #4

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E.g. this recent discussion.There are several threads on here analysing this question.

- #5

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1) Wrongly stating Newton's second law as ##F = m\frac{\Delta v}{\Delta t} + v\frac{\Delta m}{\Delta t}##.

2) Mistakingly using the change in velocity of the rocket as ##\Delta v## and the velocity of the expellant as ##v## in this equation.

- #6

Mister T

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There is no acceleration. The rocket accelerates in one direction and the propellant accelerates in the opposite direction. The acceleration of the system (the system consisting of the rocket and the propellant) is zero.How can Force=0 if there is acceleration?

- #7

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https://www.physicsforums.com/threa...ed-about-newtons-2nd-law.1050482/post-6861805

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