# Momentum and Pressure and Forces

• Pawnag3
In summary, the conversation discusses the relationship between force and velocity, with two different formulas being compared. The first formula shows that force is proportional to velocity squared, while the second formula shows that force is directly proportional to velocity. The contradiction between these two relationships is explained by considering the dot product and using latex formatting.
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.

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

Pawnag3 said:
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.

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!

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)

Pawnag3 said:
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

Last edited by a moderator:
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.

## 1. What is momentum and how is it calculated?

Momentum is a measure of an object's motion. It is calculated by multiplying the object's mass by its velocity.

## 2. How is momentum related to force?

Momentum is related to force through Newton's second law of motion, which states that the force applied to an object is equal to the rate of change of its momentum.

## 3. What is pressure and how is it measured?

Pressure is defined as the force applied per unit area. It is measured in units of pascals (Pa) or newtons per square meter (N/m^2).

## 4. How does pressure affect the motion of objects?

Pressure can affect the motion of objects by exerting a force on them. For example, high pressure areas can cause objects to move towards them, while low pressure areas can cause objects to move away from them.

## 5. Can pressure and momentum be transferred between objects?

Yes, pressure and momentum can be transferred between objects through collisions or interactions. For example, when two objects collide, momentum can be transferred from one to the other. Similarly, pressure can be transferred through fluids or gases through the process of convection.

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