# Drag force = Mass * deacceleration?

Xenekaro
For the motion of a spherical ball under water, can its drag force be calculated by knowing only its mass and deceleration?

## Answers and Replies

jetwaterluffy
Yes. F=ma. Deceleration and acceleration are essentially the same thing.
F=Force
m=mass
a=acceleration.

PhysicsChode
Yes. Deceleration is just a negative acceleration, so it will make F negative, and thus will be the opposing, unbalanced force (in this case the drag).

Mentor
Realize that whenever you calculate mass*acceleration for an object, you are calculating the net force on the object.

Xenekaro
ok awesome. I thought F=ma was only valid for terminal velocity so I was wondering about the drag equation.Thanks again guys!

Gold Member
No. The mass times the acceleration in this case will give you drag minus weight (draw a free body diagram). You will have to add the weight to the net force to get the drag.

Gold Member
ok awesome. I thought F=ma was only valid for terminal velocity so I was wondering about the drag equation.Thanks again guys!

Accceleration will be zero at terminal velocity (it has reached a steady velocity)
The drag force will be equal to the weight force under that condition.

Xenekaro
No. The mass times the acceleration in this case will give you drag minus weight (draw a free body diagram). You will have to add the weight to the net force to get the drag.

Ya, I was worried about this. So supposing I know that the (mass*deceleration) value is x and the weight of the object is y. Would the drag force be x+y? Or are there other factors to be considered?

I find the drag force calculations to be too simple to actually warrant the need to formulate the more complex drag equation. I mean why worry about drag coefficient if you can calculate the drag just by knowing the object's mass and deceleration rate.

Gold Member
You have the weight acting downward, which is $-mg$ and the drag acting upward opposing the motion, which is $F_d$ If you sum the forces, you get:
$$\sum F = F_d - mg = ma$$
Solving that for $F_d$ gives you:
$$F_d = m(a+g)$$

Xenekaro said:
I find the drag force calculations to be too simple to actually warrant the need to formulate the more complex drag equation. I mean why worry about drag coefficient if you can calculate the drag just by knowing the object's mass and deceleration rate.

Probably because you almost never know the deceleration of a given object. That deceleration will also change depending on how long an object has been falling since the drag is dependent on the velocity of the object. It also isn't simple when you are talking about something with more forces acting on it like an aircraft or a car.

Xenekaro
Ok thanks for the explanations! I just have 1 more question. Say if I want to compare:
Fd=m(a+g) and
Fd = 0.5pv2acd

Would the velocity in the second equation have to be the average or instantaneous velocity? Average velocity refers to the mean of initial and final velocity which I used to calculate acceleration in the first equation.
Instantaneous velocity would probably work better for equation II but I am trying to compare the Fd of the two equations. The second equation refers to the theoretical force of drag in my experiment and the first one is the experimental Fd.

nasu
In both equations you have instantaneous values. Instantaneous acceleration in the first one and instantaneous velocity in the second one. And they provide the instantaneous value of the drag force, which is variable.
An average acceleration won't be too useful, in my opinion. anyway, averaged over what? The whole motion or just the portion before reaching terminal velocity?

potatoecannon
I would suggest you likely have 3 forces equate to the deceleration, not 2.

Depending on the ball material (density), there will likely be a significant buoyancy term as well.