(published on 10/22/2007)
(published on 06/25/2011)
The F in F = ma is the the total force on an object, often called the "net force." This equation is Newton's second law. (By the way, Newton wasn't made president of the Royal Society until 1703, 16 years after his Principia was published.)
Okay, so we need to consider all the forces on an object for F = ma to be valid. In both of your examples, you only mention one force, where there are actually at least two we need to account for.
In the case of pushing against a wall, there is a so-called normal force equal and opposite to the force you apply, so the acceleration is zero (unless you exceed the breaking strength of the wall). F_total = F_push - F_normal = 0.
In the case of a box being pushed along a floor with friction, there is a friction force opposite the pushing force. The friction force depends on the material (more for rubber, less for ice) and is usually proportional to the weight of the object. F_total = F_push - F_friction = ma (smaller for rubber, larger for ice).
You asked a question which came from curiosity and thinking about physical situations (good). With a little more thinking like that, I bet you would have wondered whether there might be additional forces that would explain your observations. Instead, you cheated yourself of any further understanding.
Rebecca H.
(published on 02/29/2016)
Sure, we can suggest such experiments.
First, let's take proportionality to F. Take some mass and push on it with 1 compressed spring, measuring a. Now use two, then 3, etc. Common sense says that F should be additive. So you can check that a is indeed proportional to F.
Now for fixed a you want to check if F is proportional to m. You can put together 1, 2, 3... nearly identical masses. Check how many of those nearly identical compressed springs you need to get the combined mass accelerating at the fixed a.
Mike W.
(published on 10/03/2016)
I don't usually think of F=ma as "an equation to find the force" although I guess it plays that role in some homework problems. I thnk of it more as a way to predict the acceleration, a, when you have some known forces acting on an object. It turns out not to be quite right. Instead, the rule that makes correct predictions is F=dp/dt, as we said earlier in the thread. p =mv/(1-(v2/c2))1/2. ("m" here means the rest mass.) When v/c << 1, F=dp/dt becomes very close to F=mdv/dt=ma.
Mike W.
(published on 03/04/2018)
As you can see from the preceding answers, F=ma is known not to be generally true, so it can't be the foundation of our current physics. As the discussion above explains, even before it was known to be false, philosophers had noted that the complications you mention make it hard to check whether it holds.
Mike W.
(published on 09/15/2018)