A question about conservation of momentum

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Discussion Overview

The discussion revolves around the conservation of momentum as it applies to a hypothetical scenario involving a boat and frogs. Participants explore how the timing of the frogs' jumps affects the resulting velocity of the boat, considering both simultaneous and sequential jumps. The conversation touches on concepts of impulse and relative velocities.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant describes a scenario where frogs jump from a boat simultaneously, leading to a certain velocity of the boat (v1) in the opposite direction, and questions why a different velocity (v2) results when the frogs jump sequentially.
  • Another participant suggests that the impulse concept may clarify the situation, noting that simultaneous jumps create a large force over a short time, while sequential jumps produce smaller forces over a longer duration.
  • There is a discussion about the relative velocities of the frogs and the boat, with one participant clarifying that the frogs' velocity (v) is relative to the boat, while the resulting velocities (v1 and v2) are relative to the water.
  • Questions arise regarding the ambiguity of the term "velocity" in the context of the frogs' jumps, specifically whether it refers to pre-leap, post-leap, or mid-leap conditions.

Areas of Agreement / Disagreement

Participants express differing views on the implications of simultaneous versus sequential jumps and how they affect the boat's velocity. The discussion remains unresolved, with no consensus on the intuitive understanding of the scenario.

Contextual Notes

Participants acknowledge the complexity of the problem, particularly regarding the definitions of velocity and the timing of the frogs' jumps, which may influence the interpretation of the results.

papercace
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Let's say you've got a boat filled with n frogs of mass m each. Let's also say that all the frogs jump simultaneously out of the boat in the same direction with velocity v, then the boat will get a velocity v1 in the opposite direction because of conservation of momentum.

Now if we instead let each frog jump separately with velocity v, the boat will get a velocity v2 that is bigger than v1.

I did see the formula and the derivation for why the boat gets a different velocity, but I'm still not getting it intuitively. If the same mass is leaving the boat at the same velocity, why does the boats velocity differ depending upon when the mass leaves the boat?
 
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papercace said:
Let's say you've got a boat filled with n frogs of mass m each. Let's also say that all the frogs jump simultaneously out of the boat in the same direction with velocity v, then the boat will get a velocity v1 in the opposite direction because of conservation of momentum.

Now if we instead let each frog jump separately with velocity v, the boat will get a velocity v2 that is bigger than v1.

I did see the formula and the derivation for why the boat gets a different velocity, but I'm still not getting it intuitively. If the same mass is leaving the boat at the same velocity, why does the boats velocity differ depending upon when the mass leaves the boat?

What happens if all the frogs do an identical jump (it terms of the mechanics of their jump)?
 
papercace said:
If the same mass is leaving the boat at the same velocity, why does the boats velocity differ...
Those two velocities are relative to what?
 
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Buzz Bloom said:
Hi papercace:

Perhaps the following will be helpful.

Regard,
Buzz

Yes I know what impulse is. If the frogs jump simultaneously, then the impulse time will be short but the force impacted on the boat will be large. If they jump one after the other, the force of each jump will be small but they will do it over a longer time. In the end they should add up to be the same impulse, I think.

PeroK said:
What happens if all the frogs do an identical jump (it terms of the mechanics of their jump)?

Sorry I don't understand your question.

A.T. said:
Those two velocities are relative to what?

Yeah I should have stated that. v is relative to the boat while v1 and v2 are relative to the water.
 
papercace said:
Yeah I should have stated that. v is relative to the boat while v1 and v2 are relative to the water.
So what is the velocity of the frogs with respect to the water in the two cases?
 
papercace said:
Yeah I should have stated that. v is relative to the boat while v1 and v2 are relative to the water.
That still leaves v ambiguous -- relative to the boat pre-leap, post-leap or mid-leap?
 

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