A Engine $E$ is hinged on a Wooden block which is placed on a perfectly smooth surface:

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Now the block is given an initial velocity $V$ (by some external agent) and the Engine is started.

The Engine has some sort of fuel and is capable of producing constant $10\ \mathrm W$ power.

The Engine applies some force on the Block (as a result of the generated power). We know , Power = Force x Velocity.

Again, the velocity of the block, engine $V$ system can't alter (because of absence of external forces).

So, can we say the force applied by the Engine $E$ on the block depends on the initial velocity $V$ of the block?


closed as unclear what you're asking by John Rennie, sammy gerbil, Jon Custer, Kyle Kanos, Gert Jan 8 '17 at 18:53

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  • $\begingroup$ can't alter velocity due to absence of external forces - then how do cars move? What exactly does the engine do in your system? Just sits on top of the block? $\endgroup$ – Gallifreyan Jan 6 '17 at 11:29
  • $\begingroup$ Cars move due to Friction $\endgroup$ – Programmer Jan 6 '17 at 11:49
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    $\begingroup$ I'm not saying there's change in momentum here, just a side note. What I don't understand is, what sort of force does the engine apply to the block? $\endgroup$ – Gallifreyan Jan 6 '17 at 12:37
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    $\begingroup$ to answer generally the title: F=dp/dt, and as p=mv force is proportonal to the change in time of velocity times mass. I applies to all forces so you cannot maket the last statement, generally $\endgroup$ – anna v Jan 6 '17 at 13:11
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    $\begingroup$ This really isn't such a bad question. It doesn't deserve all the down votes. It might be clearer if the engine was a rocket. The question might be rephrased like this. "A rocket burns fuel at a constant rate, and therefore has constant power. It applies a constant force to the block. Velocity continually increases. But $P = F \cdot V$. What gives?" $\endgroup$ – mmesser314 Jan 6 '17 at 14:37

Your setup makes no sense. It is unclear what happens with the power your engine generates. What is clear is that since there is no relative motion between the engine and the block (at least that's how I interpret what you are saying), that power is completely unrelated to either the force between the engine and the block or the velocity of the block. You can't just take an equation like $P=\mathbf F\cdot\mathbf V$ and plug in some random quantities. You would have to separate a (sub-)system that the power is being transferred to, and analyze forces and velocities on that subsystem.

So, no, there is no relation between the force between engine and block versus the velocity of the arrangement. They have nothing to do with each other.

  • $\begingroup$ This is a comment, not an answer (IMO). $\endgroup$ – sammy gerbil Jan 6 '17 at 13:40
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    $\begingroup$ @sammy gerbil Better now? $\endgroup$ – Pirx Jan 6 '17 at 13:43

If there is an "absence of external forces", then your engine must be doing work on the block; in that case, the relative velocity between engine and block changes, but the velocity of the system doesn't matter. If, on the other hand, the engine is a "rocket motor", then it is expelling matter - and conservation of momentum says that there must be an equal and opposite change of momentum of the engine-block system.


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