Momentum and Pressure and Forces

[Pawnag3]

This is a theoretical question that I have, it might be somewhat elementary, or I might be missing something. Basically, we have two formulas:
1) We know that
P = F/A
By multiplying by d/d, we get:
P = Work/Volume
P = Energy/Volume
P = 1/2 mv² / V
Therefore
F/A = 1/2 mv² / V
And therefore, the force is equal to the velocity squared.
2) However, according to F*t = mv
We say that Force is directly proportional to velocity.

Do you see the contradiction?
Please Help

Note: I'm basically comparing the relationship of force with respect to velocity

 

[The legend]

F/A = 1/2 mv² / V
And therefore, the force is equal to the velocity squared.
2) However, according to F*t = mv
We say that Force is directly proportional to velocity.

Do you see the contradiction?

in the first sentence
$$\frac{F}{A}=\frac{1}{2}\frac{mv^2}{V}$$
Now when you bring the area on the other side A/V becomes 1/length or 1/distance and cancels with one (length)² of velocity ... hence there is only one velocity term left and hence F proportional to v.

Another mistake is you have considered F*d=Work but actually its the dot product between them.

Rem: F/A is proportional to v² not force!

 

[Pawnag3]

Umm, thanks, that clarifies everything :D
But I have one question:
1) How did you make the formatting look so nice? :D
I couldn't figure it out (but then again, I didn't spend too much time, under which heading is it? :P)

 

[The legend]

Umm, thanks, that clarifies everything :D
But I have one question:
1) How did you make the formatting look so nice? :D
I couldn't figure it out (but then again, I didn't spend too much time, under which heading is it? :P)

I used latex or tex as its called ... you can learn it here
https://www.physicsforums.com/showthread.php?t=386951

 

[rwisz]

in the two formulas.

Thank you for your question. It is important to understand that both formulas are correct and are not contradictory. The first formula, P = F/A, represents the pressure exerted by a force on a given area. This formula is often used in fluid mechanics to calculate the pressure at a specific point. In this case, the force and area are constant, so the pressure is directly proportional to the force.

The second formula, F*t = mv, represents Newton's second law of motion. It states that the force applied to an object is equal to its mass multiplied by its acceleration. In this case, the force and time are constant, so the velocity is directly proportional to the force.

Both formulas are valid in their respective contexts and do not contradict each other. The first formula is used to calculate pressure, while the second formula is used to calculate the force necessary to accelerate an object. It is important to understand the context in which each formula is used to avoid confusion. I hope this helps clarify any misconceptions you may have had.