How to calculate the energy lost in a projectile from drag?

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Discussion Overview

The discussion revolves around calculating the energy lost in a projectile due to drag, specifically when the projectile is shot straight upwards. Participants explore both theoretical and experimental approaches to understanding the impact of drag on the projectile's energy loss.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions how to calculate energy lost due to drag, noting that the force of drag is proportional to velocity, which is not constant for a projectile.
  • Another participant asks whether the scenario is based on an actual experiment with measured values or a theoretical exercise with given quantities.
  • A different participant suggests that energy lost can be calculated as force times distance, mentioning that the force of drag is a square function of velocity and should be combined with gravitational effects.
  • Another contribution proposes using the potential energy difference between the maximum height without drag and the maximum height with drag to determine energy loss.
  • One participant describes a simulation approach where calculations are performed in small time steps, allowing for the determination of velocity and drag force at each step, and notes the need to account for aerodynamic rotational forces if the projectile is not spherical.

Areas of Agreement / Disagreement

Participants express various methods and considerations for calculating energy loss due to drag, but there is no consensus on a single approach or resolution of the problem. Multiple competing views and methods remain present in the discussion.

Contextual Notes

There are limitations regarding the assumptions made about the projectile's motion, the dependence on specific definitions of drag, and the unresolved nature of the mathematical steps involved in the proposed calculations.

Necm
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The force of drag is proportional to velocity, but with a projectile velocity isn't constant, so how could i calculate the energy lost due to drag?
The projectile in question is being shot straight upwards, so that may make this problem much more simple.
 
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Is this an actual experiment, where you will be measuring things like velocity, or is it a theoretical exercise where you will be given values for certain quantities?
 
Necm said:
The force of drag is proportional to velocity, but with a projectile velocity isn't constant, so how could i calculate the energy lost due to drag?
The projectile in question is being shot straight upwards, so that may make this problem much more simple.
Well, the energy lost is force times distance and the force of drag is a square function of velocity. You should be able to put that together (with, in this case, gravity) to find the energy loss due to drag.
 
You could use the potential energy difference corresponding to the maximum height you'd expect without drag and the maximum height with drag.
 
These problems are usually simulated in small time steps. At each time step, the object velocity and orientation is known and the resultant drag force is calculated. If the object is a sphere, you don't have to worry about its orientation. Otherwise, you need to also calculate aerodynamic rotational forces and keep track at each step of its orientation and resultant coefficient of drag.
 

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