# How does one calculate the energy used depending on the velocity and air resistance of an object [closed]

I'm in need of a equation that can tell me how much energy/work I need to move an object inside a low air-pressure tube. The equation should (if possible) include drag, object velocity and mass. If there isn't such a equation i would also be happy if you could show me a way how to get to the calculate the work/energy needed.

Thank you for you're time. If you have any questions about my issue please do ask.

## closed as unclear what you're asking by Aaron Stevens, Gert, ZeroTheHero, Buzz, Kyle KanosJan 24 at 11:04

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• At high Reynolds number, the drag force is usually modeled as: $F_D=\frac12 \rho v^2 C_A A$ – Gert Jan 22 at 17:03

Assume that the object is moving in the opposite direction to that of the drag force.

If you know the magnitude of the drag force $$F_{\rm drag}(t)$$ and the speed of the object $$v(t)$$ then rate at which energy is being dissipated at a particular time $$t$$ is $$F_{\rm drag}(t) \,v(t)$$.

To evaluate the total energy dissipation from time $$t_{\rm start}$$ to time $$t_{\rm finish}$$ you will need to do an integration $$\displaystyle \int_{t_{\rm start}}^{t_{\rm finish}} F_{\rm drag}(t) \,v(t) \, dt$$

• Assume that the object is moving in the opposite direction to that of the drag force. Assume? Friction (here air drag) is ALWAYS in the opposite direction of motion. – Gert Jan 22 at 16:58
• @Gert I do not know why I wrote that sentence but on reflection you can have a moving fluid applying a frictional force on an object in the direction of motion of the object when the object is moving slower than the fluid. – Farcher Jan 22 at 23:56