Drag equation and d(kinetic energy)/d(displacement)

In summary, the conversation discusses using the drag equation to find the distance a projectile will travel based on its initial kinetic energy and mass. The solution involves rearranging the equation and using the natural logarithm function.
  • #1
Tiiba
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Homework Statement



Given the drag equation and a projectile's initial kinetic energy and mass, find the distance in which it will come to rest (or at least, become absurdly slow).

Homework Equations



https://en.wikipedia.org/wiki/Drag_equation

The Attempt at a Solution



Force = .5 * fluid density * drag coefficient * area * velocity^2.
Velocity = sqrt(2 * energy / mass)
Force = fluid density * drag coefficient * area * energy / mass.

When the bullet emits dE energy, it travels dE/F.

Thus, position delta = dE/dP = dE/F = dE / (fluid density * drag coefficient * area * energy at step / mass)

dE/dP = (mass / (fluid density * drag coefficient * area)) 1/E dE

Everything in front of 1/E is a constant, so it isn't integrated. The integral of 1/E is ln(E), so the solution is

displacement = (mass / (fluid density * drag coefficient * area)) (log(E0) - log(1 eV))

4. ?

WTF is ln(E)?
 
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  • #3
What in particular? I just took the drag equation and rearranged it. I want to figure out how far the projectile moves based on its mass and speed. How would you do it?
 

Related to Drag equation and d(kinetic energy)/d(displacement)

1. What is the drag equation and how is it used in science?

The drag equation is a mathematical formula used to calculate the force of drag on an object moving through a fluid, such as air or water. It takes into account various factors such as the object's shape, size, and velocity to determine the force of drag acting on it. This equation is commonly used in aerodynamics and fluid mechanics to understand and predict the behavior of objects in motion.

2. How is the drag equation derived?

The drag equation is derived from the principles of fluid mechanics and Newton's second law of motion, which states that the force acting on an object is equal to the product of its mass and acceleration. By considering the forces acting on an object moving through a fluid, such as pressure and friction, the drag equation is derived to calculate the force of drag on the object.

3. What is the significance of d(kinetic energy)/d(displacement) in the drag equation?

This term in the drag equation represents the rate of change of kinetic energy with respect to displacement. It takes into account the change in the object's kinetic energy as it moves through the fluid, which is affected by the force of drag acting on it. This term is important in understanding the overall effect of drag on an object's motion.

4. How does the drag coefficient affect the drag equation?

The drag coefficient is a dimensionless quantity that represents the shape and size of an object and how it affects the force of drag. It is included in the drag equation to calculate the force of drag more accurately. Objects with a higher drag coefficient will experience a greater force of drag than those with a lower drag coefficient.

5. Can the drag equation be applied to all types of objects and fluids?

The drag equation is applicable to a wide range of objects moving through various types of fluids, as long as certain assumptions are met. These include the object moving at a constant velocity, a laminar flow of the fluid, and a steady-state motion. However, it may not accurately predict the drag force for complex objects or in non-ideal fluid conditions.

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