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First of all, I am really sorry if this question is bad. I was thinking about the second law of motion, the famous $F=ma$. I was trying to get the idea behind this equation, I got some ideas but I am not able to use them to make this equation. I don't know advanced math, because I am in 9th grade. I can't just accept this equation until I make it on my own, so that I can understand each thing behind this.

Some information that I got :

1) As applied Force increases, the object accelerates faster, which means that Force is directly proportional to acceleration.

2) If I keep on increasing the mass of the body, and apply the same force, then the body accelerates less.

Now, can someone please help me to form the equation, so that I can think intuitively of what is actually happening?

One observation of mine: The ratio between the force and acceleration is the mass of the body, by this equation, why does this happen?

I would be really happy if I can imagine the meaning of this and move on.

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closed as unclear what you're asking by John Rennie, ACuriousMind, Hritik Narayan, user36790, Gert Dec 24 '15 at 3:47

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Newton's second law is an experimental fact that cannot be justified, as all the other first principles: it might have been anything else, only the empirical results confirm the above. $\endgroup$ – gented Dec 23 '15 at 14:03
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Your point number 1) is precisely the answer to your question. As to why the constant of proportionality is the mass m that is because that is how mass is defined. Specifically, that is the definition of inertial mass. We have another concept of mass that comes from gravitational attraction. These two concepts could have different numerical values, but it has been demonstrated to a high level of accuracy that they are identical.

You may still be wondering why the second law has this form. The only answer to that question is that experiments consistently support this form. Physics does not answer the question why. Why is a question for philosophy.

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1 Newton, the SI unit of force, is defined as the force needed to accelerate a 1 kg object at 1 meter per second squared ($N=kg*\frac{m}{s^2}$). Therefore, force is derived as mass (kilograms) $*$ acceleration (meters per second squared).

If a body is accelerating, then there is a external force being exerted on the object (Netwon's First Law: An object at rest stays at rest and an object in motion stays in uniform linear motion unless acted upon by an external, unbalanced force). The force exerted is directly proportional to the acceleration. The force exerted is also proportional to the rate of change of momentum of the object ($p=mv \Rightarrow p/s=mv/s=ma=F$)

Hope that helps, Kaien Yang

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