What Do You Get When You Integrate Force?

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Discussion Overview

The discussion revolves around the integration of force, specifically thrust force, and what physical quantity results from such an integration. Participants explore the implications of integrating force with respect to different variables, including time and distance, and the resulting quantities such as momentum and energy.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that integrating force with respect to time yields linear momentum, as expressed by the relationship F = dp/dt.
  • Others suggest that integrating force over a distance results in energy, indicating that the variable of integration is crucial to determining the outcome.
  • A participant emphasizes the need to specify the quantity being integrated with respect to, noting that different variables lead to different physical interpretations (e.g., momentum from force over time, energy from force over distance).
  • One participant raises a question about the context of integrating thrust force, seeking clarification on the meaning of the variable 'y' in the original problem.

Areas of Agreement / Disagreement

Participants express differing views on the implications of integrating force, with some agreeing on the relationship between force and momentum while others highlight the importance of the integration variable, leading to multiple competing interpretations.

Contextual Notes

The discussion does not resolve the ambiguity regarding the variable of integration and its implications for the resulting physical quantities. There are also unresolved questions about the specific context of the original problem involving thrust force.

Who May Find This Useful

This discussion may be of interest to students and professionals in physics and engineering, particularly those exploring concepts of force, momentum, and energy in relation to integration techniques.

Alcubierre
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Hello,

I came across a problem the other day where the person integrated thrust force from 0 to y in respect to y. And that got me thinking: you integrate jerk to get acceleration and integrate acceleration to get velocity, so what do you get when you integrate a force, namely thrust force? Why would you even do such a thing?
 
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Alcubierre said:
Hello,

I came across a problem the other day where the person integrated thrust force from 0 to y in respect to y. And that got me thinking: you integrate jerk to get acceleration and integrate acceleration to get velocity, so what do you get when you integrate a force, namely thrust force? Why would you even do such a thing?

If we differentiate linear momentum with respect to time , we get force right ?

lim Δt→0 Δp/Δt = dp/dt = F
F = dp/dt

So if we integrate Force with respect to time we get :

∫ F dt = ∫(dp/dt) dt
∫ F dt = p

which is linear momentum.

We use it as it has many uses.

You are given Force as a function of time :
F = t + 5t2 + 6t3.
Now how will you obtain linear momentum of that body at t=5 ?
 
Last edited:
Alcubierre said:
Hello,

I came across a problem the other day where the person integrated thrust force from 0 to y in respect to y. And that got me thinking: you integrate jerk to get acceleration and integrate acceleration to get velocity, so what do you get when you integrate a force, namely thrust force? Why would you even do such a thing?

What is y? A distance? In that case, you integrate force over a length, which gives energy.
 
As you'll have seen from the other replies, it's not enough to say "integrate such-and-such". You have to specify the quantity you're integrating with respect to. For the purpose of understanding the nature of the answer, you can treat it like multiplication by that independent variable. If s, t are distance and time variables respectively, F.dt is force * time = momentum, F.ds is force * distance ('.' being the dot product of vectors) = energy, F[itex]\times[/itex]ds is force-cross-product-distance = torque.
 

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