Relation between acceleration, mass, and net force.

In summary, the equation ##a = \frac{F}{m}## describes the relationship between acceleration, net force, and mass. It does not prove anything, but rather expresses this relationship mathematically. It is also important to note that this equation only holds true if acceleration is constant and all other forces are negligible.
  • #1
avito009
184
4
As we know [tex]\ a= \frac {F} {m} [/tex]
So does this equation prove that acceleration is directly proportional to the net force and inversely proportional to the mass of the object?
 
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  • #3
avito009 said:
As we know [tex]\ a= \frac {F} {m} [/tex]
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.
 
  • #4
DaleSpam said:
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.
 
  • #5
Raptor said:
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.
 
  • #6
MohammedRady97 said:
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.
 
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  • #7
Raptor said:
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?
 
  • #8
Raptor said:
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.
 
  • #9
MohammedRady97 said:
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.
 
  • #10
MohammedRady97 said:
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.
 
  • #11
Raptor said:
Force causes acceleration. You should avoid saying acceleration causes force.
The formula says nothing about what causes what.
 
  • #12
Raptor said:
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.
 
  • #13
Raptor said:
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.
 
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  • #14
Raptor said:
It is better to say acceleration is dependent on force than the inverse.
Which is exactly what the original post describes!

Raptor said:
You should avoid saying acceleration causes force.
Who said that?
 
  • #15
Raptor said:
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.
 
  • #16
Raptor said:
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.
 

1. How are acceleration, mass, and net force related?

The relationship between acceleration, mass, and net force is described by Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that as the net force increases, the acceleration of the object also increases, and as the mass increases, the acceleration decreases.

2. What is the formula for calculating acceleration?

The formula for acceleration is a = F/m, where "a" represents acceleration, "F" represents net force, and "m" represents mass. This formula shows the direct relationship between acceleration and net force, and the inverse relationship between acceleration and mass.

3. How does an object's mass affect its acceleration?

An object's mass has an inverse relationship with its acceleration, meaning that as the mass increases, the acceleration decreases. This is because a larger mass requires a greater force to accelerate it, according to Newton's second law of motion.

4. What is the role of net force in determining an object's acceleration?

The net force acting on an object is the total of all the forces acting on the object. According to Newton's second law of motion, the net force determines the acceleration of the object. If the net force is greater, the acceleration will also be greater, and if the net force is smaller, the acceleration will also be smaller.

5. How do these concepts apply to real-life situations?

The relationship between acceleration, mass, and net force is present in many real-life situations, such as when a car accelerates or when a person jumps off a diving board. In both cases, the net force applied to the object determines its acceleration. Additionally, the mass of the object also plays a role in determining its acceleration, as seen in the difference between how quickly a small car and a large truck can accelerate.

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