F=ma proof and understanding force

In summary: This force can be caused by a push or pull, and is equal to mass multiplied by acceleration. In the example given, a ball is released from rest and after 1 second it has an acceleration of 9.81m/s^2, meaning the force acting on it is 9.81N (newtons). This force is due to gravity, and will continue to act on the ball as it falls. In terms of statics and dynamics, the distinction depends on whether the net force on an object is zero or not. Finally, it is not possible to talk about force without considering time, as it is a factor in calculating force and understanding its effects.
  • #1
chandran
139
1
general
force is a push or pull.

how this push or pull is equal to mass x acceleration.

one more doubt.

a ball is released from rest from the top of a building. initial velocity=0.after 1sec velocity is 9.81m/sec. so acceleration is 9.81m/sqs. so force
that caused the ball to fall from 0 to 1sec is 9.81N considering the mass to be 1kg. from 1second to 2seconds the net force is another 9.81N.
am i correct in the above statements.

Can anybody clarity on force on statics theory and the force referred in dynamics theory.
 
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  • #2
Let me put in my dear terms.Technical ones.

In the Newtonian formulation of classical mechanics,the second postulate (which is valid in inertial reference frames) says that,for a mechanical system undergoing translation movement (a system of point masses):

[tex] \frac{d\vec{p}}{dt}=\sum_{k}\vec{F}_{k} [/tex]

,where [itex] \vec{p} [/itex] is the total momentum of the system and [itex] \vec{F}_{k} [/itex] are the internal & external forces...

So u can "prove" that
[tex] \vec{F}=m\vec{a} [/tex]

,starting with the II-nd axiom & simplifying hypothesis...

Daniel.

P.S.That acceleration is [itex] \left|\vec{g}\right|=9.80665 \ \mbox{ms}^{-2} [/itex]
 
  • #3
chandran said:
a ball is released from rest from the top of a building. initial velocity=0.after 1sec velocity is 9.81m/sec. so acceleration is 9.81m/sqs. so force
that caused the ball to fall from 0 to 1sec is 9.81N considering the mass to be 1kg. from 1second to 2seconds the net force is another 9.81N.
am i correct in the above statements.
All correct. Ignoring air resistance, the only force on a falling body is that due to gravity, its weight.

Can anybody clarity on force on statics theory and the force referred in dynamics theory.
Can you restate your question? Whether or not a problem is one of statics or dynamics depends on whether the net force on an object is zero. Zero or not, forces are treated the same way.
 
  • #4
Well,

I too want to understand the concept of "force".
I find it a bit hard to understand.

1> I don't need proofs. I just need the understanding. :cool:
2> Is 'time' a part of 'force' ?? . Can we talk about force ignoring time ?
 
  • #5
A force is anything that causes a body to change it's velocity. One can talk about a force acting without reference, however, one cannot define force without reference to time. Essentially unless a body is in equilibrium (no net force), it is not meaningful to talk about force without reference to time.

See this; http://en.wikipedia.org/wiki/Force

~H
 
  • #6
if a body changes its velocity (momentum), a force has been exerted
 

1. What is the equation F=ma used for?

The equation F=ma is used to calculate the force exerted on an object. It relates the mass of an object (m) to its acceleration (a) when a force (F) is applied to it.

2. How is the equation F=ma derived?

The equation F=ma is derived from Newton's Second Law of Motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. By rearranging the equation, we get F=ma.

3. Can you give an example of how F=ma is used in real life?

One example of how F=ma is used in real life is in car crashes. When a car crashes into an object, the force exerted on the car is equal to the mass of the car multiplied by its acceleration. This helps us understand why cars with heavier mass experience more force in a crash.

4. What units are used in the F=ma equation?

The unit for force (F) is Newtons (N), the unit for mass (m) is kilograms (kg), and the unit for acceleration (a) is meters per second squared (m/s²).

5. Why is it important to understand the concept of force and the F=ma equation?

Understanding the concept of force and the F=ma equation is important in many fields of science and engineering. It helps us understand how objects move and interact with each other, and allows us to make accurate predictions and calculations in various situations. It is also crucial for understanding more complex principles such as work, energy, and momentum.

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