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Force Position Chart

In the chart above, you can see the force (N) on the y axis and the horizontal position (m) on the x axis.

How would you visualize this in your head? I'm trying to imagine the movement of a 1 kg box, but I just can't. Does anyone have any method or tips on visualizing the movement of a box following this force position chart?

I'm trying to study physics and I can't get past this small thing which is supposedly super easy. I'm pulling my hair out on such a simple bit of physics! I would really appreciate any help I can get, even if it's just another question that would redirect me in the right path. I'm definitely doing something wrong here.

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  • $\begingroup$ Not all physics concepts are easy to visualize directly. This is an example. There aren't many real world examples of this specific curve. (Flip it upside down, however, and you have a very common and intuitive relationship - the force applied by a spring.) You've got an object that's pushed forward more the more it moves forward. The immediate conclusion is that we will see an ever-increasing acceleration. Precisely how fast, one needs to do the math. An object in free-fall would be subject to a constant force - a horizontal curve - so we know that this box will accelerate more radically. $\endgroup$ – Kristoffer Sjöö May 8 at 19:29
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You might be an intuitive thinker. You need an image, a film, in your head to properly understand and visualise the scenario. I have it the same way. You can visualise a scenario like this by finding a proper example. Eventually with training you will be able to make up an example and see the scenario before you on the spot.

Here, the force grows when the position grows. We might be dealing with a spring - when you elongate it (position change of one end of the spring), the spring force increases linearly according to Hooke's law. Meaning, when you elongate it it gradually becomes harder to elongate it further.

Does anyone have any method or tips on visualizing the movement of a box following this force position chart?

Note that we do not know the movement, the motion, from this graph. You can elongate your spring fast or slow. It doesn't matter. You can elongate it to $3\,\mathrm m$ on the x-axis with a corresponding force on the y-axis, and then keep it there; maybe you tie the spring end to something so it just stays at this setup. In other words, where you are on this graph says nothing about the movement or motion.

When the axes do not involve speeds, accelerations or most importantly time, then you might not have enough info from the chart to determine a unique motion. The graph here just shows us the relationship between force and position of something, but says nothing about any motion parameters.

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    $\begingroup$ Thanks! The spring example helped and I kind of get it now. $\endgroup$ – BrianZhang May 8 at 22:18

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