Relation between acceleration, mass, and net force.

[avito009]

As we know $$\ a= \frac {F} {m}$$
So does this equation prove that acceleration is directly proportional to the net force and inversely proportional to the mass of the object?

 

[Dale]

Yes.

 

[nasu]

As we know $$\ a= \frac {F} {m}$$
So does this equation prove that acceleration is directly proportional to the net force and inversely proportional to the mass of the object?

It does not "prove" anything.
It just expresses mathematically a relationship between quantities, as suggested by observation and experiments.

 

[Raptor]

Yes.

No.
F=ma says heavy objects need more force to move, and more force means more acceleration.
a=F/m is just a vector relation saying that acceleration is co linear with net vector F. Decrease In mass decreases the force acting on it which in turn reduces magnitude of acceleration. This is more meaningful.

 

[PFuser1232]

No.
F=ma says heavy objects need more force to move, and more force means more acceleration.
a=F/m is just a vector relation saying that acceleration is co linear with net vector F. Decrease In mass decreases the force acting on it which in turn reduces magnitude of acceleration. This is more meaningful.

I fail to see the difference. One could also argue that the first equation is a vector relation.

 

[Raptor]

I fail to see the difference. One could also argue that the first equation is a vector relation.

Let's say you are rolling down from a mountain. Let's also assume you ate a lot of food on your way down. This increases net acceleration. But how?
The answer is FORCE. We explain this with force.

 

[PFuser1232]

Let's say you are falling down from a mountain. Let's also assume you ate a lot of food on your way down. This increases acceleration. But how?
The answer is FORCE. We explain this with force.

I still can't understand why you disagreed with DaleSpam. Could you please elaborate on your original statement?

 

[PFuser1232]

Let's say you are falling down from a mountain. Let's also assume you ate a lot of food on your way down. This increases acceleration. But how?
The answer is FORCE. We explain this with force.

And by the way, acceleration of free fall is independent of mass.

 

[Raptor]

I still can't understand why you disagreed with DaleSpam. Could you please elaborate on your original statement?

Dale was not wrong at all. I just wanted to give a more meaningful statement.
It is better to say acceleration is dependent on force than the inverse.
Force causes acceleration. You should avoid saying acceleration causes force.

 

[Raptor]

And by the way, acceleration of free fall is independent of mass.

Who said you are in free fall?? Mountains are triangular. You can roll on it instead of just falling.i was just giving a hypothetical example.now mg's sine component is greater for heavier object. So acceleration in the frame of reference of mountain surface is more.

 

[A.T.]

Force causes acceleration. You should avoid saying acceleration causes force.

The formula says nothing about what causes what.

 

[PFuser1232]

Who said you are in free fall?? Mountains are triangular. You can roll on it instead of just falling.i was just giving a hypothetical example.now mg's sine component is greater for heavier object. So acceleration in the frame of reference of mountain surface is more.

A body of mass $m$ placed on a smooth slope with an angle of inclination $θ$ has an acceleration of $gsinθ$. Mass doesn't show up.

 

[Doc Al]

No.
F=ma says heavy objects need more force to move, and more force means more acceleration.
a=F/m is just a vector relation saying that acceleration is co linear with net vector F. Decrease In mass decreases the force acting on it which in turn reduces magnitude of acceleration. This is more meaningful.

No, not more meaningful.

If you want to find the acceleration of something, you need the net force and the mass, just like the first post stated. Saying that decreasing mass decreases the force is only true if you hold the acceleration constant.

 

[Doc Al]

It is better to say acceleration is dependent on force than the inverse.

Which is exactly what the original post describes!

You should avoid saying acceleration causes force.

Who said that?

 

[AdityaDev]

Who said you are in free fall?? Mountains are triangular. You can roll on it instead of just falling.i was just giving a hypothetical example.now mg's sine component is greater for heavier object. So acceleration in the frame of reference of mountain surface is more.

Even the,
$mgsinx$ - $kN$ =$ma$
$a = gsinx - kN$
$a = gsinx - kcosx$
As $N = mgcosx$ for equilibrium along perpendicular direction of plane.
N is the normal reaction.

 

[Dale]

No.
F=ma says heavy objects need more force to move, and more force means more acceleration.
a=F/m is just a vector relation saying that acceleration is co linear with net vector F. Decrease In mass decreases the force acting on it which in turn reduces magnitude of acceleration. This is more meaningful.

You are making a distinction without a difference. They are the same thing.