Modeling Object Motion in a Viscous Liquid: mg - kv = m(dv/dt)?

[Pseudo Statistic]

Hey,
I have this homework thing where I have to model an object's motion through a viscous liquid.
I'm to assume that the resistive force directed upward is kv.
Now, I'm going to take the downward direction as positive and the up as negative..
Should my force equation be mg - kv = m(dv/dt) or mg - kv = m(-dv/dt)?
This is confusing me because I know that the acceleration opposes the direction of motion, so should it be dv/dt or -dv/dt?
Thanks.

 

[andrevdh]

Well you know that the objecj is going to fall downwards, so the downwards acceleration will decrease as the drag increases up to the point where the drag is equal to the weight of the object. At which point the acceleration will be zero and the object has reached it's terminal velocity. So the acceleration will be >= 0. Usually when one solves such equations analytically, for say the acceleration, the sign of the obtained value will indicate in which direction the object is accelerating. If you put it in as -a in the equation and the solution gives a positve answer, then we know that the object is in the minus direction. If on the other hand the solution gives the acceleration a negative value, then we know that the acceleration is actually in the positive direction. So it doesn't matter which sign you give it (as long as you do not get the directions of the other quantities wrong thought, in which case you will be analysing a different physical situation!).

 

[kyle8921]

I would first like to commend you for taking the initiative to understand and clarify your homework assignment. It shows a strong understanding of the scientific process and a desire for accuracy.

To answer your question, the correct force equation in this scenario would be mg - kv = m(-dv/dt). This is because the resistive force, represented by kv, is acting in the opposite direction of the object's motion, which is represented by -dv/dt. This is consistent with the concept of acceleration opposing the direction of motion.

It is also important to note that in this equation, the acceleration is represented by dv/dt, not just dv. This is because acceleration is the rate of change of velocity over time, and therefore must be represented as a derivative with respect to time (dt).

I hope this helps clarify any confusion and I encourage you to continue exploring and questioning scientific concepts. Keep up the good work!