Newton's Second Law Confusion [closed]

I don't quite understand the relationship between an object's mass, acceleration and net force. For example, if a car was going to the right at a constant velocity or with no acceleration, does that mean that it would have no net force?

From my understanding, net force is directly related to acceleration, as where ever the force is applied, the acceleration follows. Can someone please explain it using a better example and answer my question?

I tried to do some research on this but can't find information pertaining to the situation I have laid out.

closed as off-topic by sammy gerbil, ACuriousMind♦, garyp, Diracology, GertJul 27 '16 at 2:16

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• I'm actually not sure what you need explained. You seem to understand it quite well. A net force causes an acceleration and an acceleration must imply a net force causing it. And mass is the "resistance" against acceleration - inertia. – Steeven Jul 26 '16 at 8:07
• I agree with @Steeven You seem to have it spot on. What is making you feel uncertain? (If you want to clarify your question, it might be better to edit the question rather than post a comment which might be missed.) – garyp Jul 26 '16 at 11:01
• I'm voting to close this question as off-topic because there is no confusion here, there is nothing to explain. – sammy gerbil Jul 26 '16 at 11:08
• @Steeven Whenever I question myself I just can't seem to recall fast enough- I keep having to think of scenarios like these but that leads to even more confusion. – Imagine Dragons Jul 27 '16 at 2:25

You are correct. The car has no net force on its environment, and the environment has no net force on the car. This is true of any object traveling with a constant velocity.

This is even true in the vertical direction. There is a force of gravity pulling down on the car, and there is a force caused by the road pushing up on the car. If the car is not accelerating up nor down, then these forces must be equal and opposite such that the net force is zero.

The one minor tweak I would make to what you are saying is in the second paragraph. You say "Wherever the force is applied, the acceleration follows," but its also valid to think of its as "wherever there is an acceleration, there must be a corresponding force." The two properties do not so much "follow" each other as they are directly linked to each other. In most cases, your intuition will lead you to correct results. However, sometimes a problem will be posed where you know the acceleration and not the forces. In solving such problems, its nice to remember that you can use the equations in either direction.

If a body is moving, this doesn't mean that a net force certainly must be exerted on it. It can move without any net force (First Law of Newton). You might say "How that body has started its motion without any net fore?" The answer is: "Equations of motion are moment equations, i.e. they are stated for moments not for a time interval ($F(t_0)=ma(t_0)$). So when we say a body is moving without any net force, we mean at that instance ($t$), net force acting on it is zero and it is moving with constant velocity at that instance.(It is obvious that net force can be zero for a time interval ($t_1 \le t \le t_2$). Then, $F(t)=ma(t)=0\;,\;t_1 \le t \le t_2$)"

If a body is moving with constant velocity, this doesn't mean that no force is exerted on it. It is possible that some forces are exerted on it but net (resultant) force is equal to zero.

You are correct in your definition of force. A car, not accelerating, has zero net force associated with it. However, if the car were to hit something--let's say it's me standing in the middle of the street--it would exert a net force on me, and by Newton's Third Law experience a net force equal in magnitude and opposite in direction.

So how can an object that is not accelerating exert a force on another object? First, consider what happens: the car hits me in this scenario, which causes it to slow down and me to speed up. If the car is slowing down, it is undergoing negative acceleration. I mentioned Newton's Third Law earlier; the forces experienced by myself and the car are equal in magnitude due to the Third Law, so adding them up using the Second Law, the system consisting of myself and the car has experienced zero net force, as we expect.

To bring math into this, let a force $F$ be equal to mass $m$ times acceleration $a$: $F=ma$. We know from basic calculus that acceleration can be defined using velocity $v$ as $a=\frac{\mathrm dv}{\mathrm dt}$. Substituting, we get $F=m\frac{\mathrm dv}{\mathrm dt}$. $m\frac{\mathrm dv}{\mathrm dt}$ represents a change in momentum, where a momentum $p$ is defined as $p=mv$, so if we want to deal with changes in mechanical force, such as when I am hit by a car, we will inevitably need to consider momentum. It follows that $F=\frac {\mathrm dp}{\mathrm dt}$.