# Is it possible to convert ρ (density) to Newtons?

1. Feb 14, 2017

### geofix

1. The problem statement, all variables and given/known data
We're given pressure (Which is mass/volume)
and G constant
Looking for minimum r, given pressure, that would produce a certain F value in Newtons...

2. Relevant equations

F=ma
Blanking here* Honestly everyone this is my first physics intense college course and i have no idea where to begin. Yes, we are given reading materials. Nothing I can directly apply with the units... Maybe I need to look again?

3. The attempt at a solution
my attempt is setting up variables and googling.
I d o not know what I'm doing . Bless you physics forum devoteess.

2. Feb 14, 2017

### Staff: Mentor

3. Feb 14, 2017

### geofix

I apologize. I meant density is mass/ volume. Force mass/acceleration.
wait is newton different from force? Pa = 1 newton/ m. I didn't use google for this. I'm using my notes for this.

4. Feb 14, 2017

### Staff: Mentor

So you want to express a density in newtons?

5. Feb 14, 2017

### geofix

Yes but ideally i just want to understand the units...I'm having trouble conceptualizing Pa vs Newtons vs Density even given their definitions.

6. Feb 14, 2017

### Staff: Mentor

I think what you are asking is how do you go from density to the weight of a body (i.e., the force that gravity exerts on the body). If a body is allowed to fall freely, its acceleration is g. So the force that the earth is exerting on the body must be mg in order for ma to equal mg. The mass of a body is equal to its density times its volume: m = ρV. So the force of gravity (its weight) must be ρVg.

7. Feb 14, 2017

### geofix

Thanks chester, but i don't think I'm ready for the solution . i just want to understand f=ma right now. I understand the more force, the faster an object will accelerate but how do mass and acceleration affect the force? Am I dumb for not understanding this ? agh oh well

for example I know that velocity = distance/time
these units are easy to understand but when it comes to force
force = mass * acceleration,
how do I figure out the velocity or acceleration of a still object?
F= MA
A=F/M
Need force and the mass. this seems circular logic.

8. Feb 14, 2017

### haruspex

Whether you are using velocity * time = distance or force = mass * acceleration, you need to know two to find the third.

You also seem a bit confused between dimensions and units. There are some dimensions generally considered fundamental (though there can be debate about this), such as mass, distance, time. Other dimensions can be defined in terms of these: velocity, force, acceleration,pressure, density...
For each dimension we can define units for quantifying it. They are essentially arbitrary, just standards we agree on. In the IS system, we use kg for mass, Pa for pressure, m for distance, Newtons for force. This system has the great benefit that there are no conversion factors. If you have a mass in its standard unit and an acceleration in its standard distance and time units then the numerical product is the force that would produce that acceleration on that mass, in its standard units.
They don't, in any causal sense. Force and mass may be considered causes, with acceleration the consequence. And to be clear, it is ΣF=ma, i.e., the acceleration is the net force divided by the mass. But that doesn't mean you always haveto start with knowledge of the mass and force. If I place a weight on the floor, and it does not fall through, then I can observe that the acceleration is zero and deduce that the normal force equals the weight.

9. Feb 14, 2017

### geofix

Thank you so much Haruspex for your detailed explanation. Context helps tremendously. So if I have pressure, which is a dimension (with units 3.0/cm^3). Do you know how I would go about finding the force(dimension) of 1x 10^9 Pa?
These dimensions don't even seem coorelated. Volume vs force/area?

10. Feb 14, 2017

### haruspex

No, pressure is force per unit area. In dimensions (using L for length, M for mass, T for time) force = mass * acceleration = MLT-2, area = L2, so pressure = force/area = ML-1T-2. In units, 1 Pa = 1 N / m2.

Density = mass/volume = ML-3. In units, kg/m3. (i am not aware of a named SI unit for density.)

Edit: Just noticed that the title of thread says "ρ (pressure)". This might be part of your confusion.
ρ is the Greek letter "rho" and is generally used to represent a density or resistivity. (Not necessarily mass/volume density... could be the density of something else, like charge, and it could be over an area or a line.) This is not to be confused with the Roman letter p, the usual representative of pressure.

Last edited: Feb 14, 2017
11. Feb 14, 2017

### geofix

Ok so the correct title would be using density (mass/volume) to Newtons...I guess im approaching the problem wrong if this is impossible.
<Moderator's note: title changed>

Last edited by a moderator: Feb 15, 2017
12. Feb 14, 2017

### haruspex

As you suspect, that makes no sense. A Newton is a measure of force. Force, pressure and density are all different.
Please state the problem you are trying to solve.

13. Feb 14, 2017

### geofix

ok I'm trying to find the minimum radius of a planet needed to produce a 1 Million Pa in the center of the planet. However, I'm only give the gravity constant value, and the density of the planet. Right now I'm studying every equation in the book. Started with F=ma. i'm on to pressure gradient force. However, I'm still attempting to just get the logic needed to find the right formula.

In problem language:
Find the minimum radius of a planet that's center is 1 million Pa. Given that 1 Pa= 1 N/m^2, and G= 6 x 10^-11 m^3/kg s^2, and the average density is 4 kg/cm^3, find the minimum radius need to produce 1 mil Pa.
Also thanks for your continuous help.

14. Feb 14, 2017

### haruspex

Oh.
Sorry to have to say this, but if I set the level of understanding you have demonstrated so far against the level required by the problem I get a mismatch measured in months, or longer. I hope you do not mind my frankness.
Are there any formulae you have been taught that might be relevant?
If not, do you know how to integrate?

15. Feb 14, 2017

### geofix

Ok. I might drop the course but I'd rather not give up so quickly. I do not know how to integrate but maybe, God willing, I can figure out what I'm doing.

16. Feb 14, 2017

### haruspex

... longer.

Providing you with a crash course on elementary physics and calculus through PhysicsForums would not be a good use of anyone's time. You need to select a less advanced course. Others may have advice you find more palatable.

17. Feb 14, 2017

### geofix

perhaps for fully grasping the problem, you are correct. but for solving it, how could it require months when other students do it?

18. Feb 14, 2017

### haruspex

What were the course prerequisites? Have other students fulfilled more of these?

19. Feb 14, 2017

### geofix

that's the thing. So the only prereq was astro 100 which I took. No recommended courses for it either. the professor turned it into a combination class, with a higher level. but lower level students are supposed to do the same assignments...there are office hours. this is our 3rd week of class.

anyway thanks for all of your input. I'll let you know how it goes.

20. Feb 15, 2017

### haruspex

See of this old thread helps