# 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

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 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

## 1 Answer

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