# Spring Displacement Confusion

#### snowcrystal42

Hi,

I'm confused as to the difference between the spring stretch displacements in these two problems:

1. "In .75 s, a 7kg block is pulled through a distance of 4.0 m on a frictionless horizontal surface, starting from rest. The block has a constant acceleration and is pulled by means of a horizontal spring that is attached to the block. The spring constant of the spring is 415 N/m. By how much does the spring stretch?"

Mathematically, I understand how to solve this, but why is the stretch distance not the same as the distance the block was pulled? This sounds sort of stupid, but if the box was pulled 4 m, shouldn't the spring be pulled the same distance with it?

2. "A spring is resting vertically on a table. A small box is dropped onto the top of the spring and compresses it. Suppose the spring has a spring constant of 450 N/m and the box has a mass of 1.5 kg. The speed of the box just before it makes contact with the spring is 0.49 m/s. What is the magnitude of the spring's displacement when the spring is fully compressed?"

Why is the magnitude of the spring's displacement here equal to the vertical displacement of the box, but not in the previous case?

Thanks!

#### Pmb

PHF Hall of Fame
... why is the stretch distance not the same as the distance the block was pulled?
Because the spring will elongate a distance different than the block will move. Think of a slinky pulling a large mass. If a constant force is exerted on the other end of the slinky the slinky will elongate by a large amount ut the block will hardly have moved.

This sounds sort of stupid, ...
Now now, tut tut. We'll have none of that kind of talk here. No question is stupid if your motivation is an honest attempt to learn. In science we say that no question is stupid.

2. "A spring is resting vertically on a table. A small box is dropped onto the top of the spring and compresses it. Suppose the spring has a spring constant of 450 N/m and the box has a mass of 1.5 kg. The speed of the box just before it makes contact with the spring is 0.49 m/s. What is the magnitude of the spring's displacement when the spring is fully compressed?"

Why is the magnitude of the spring's displacement here equal to the vertical displacement of the box, but not in the previous case?
Because now we're looking at a totally different scenario. Here, once the box contacts the spring the distance of compression is identical to the displacement of the box because the box is causing the spring to compress.

That last part may not be clear. If not then please let me know and I'll try to do better.

If I were you I'd draw a diagram of these things. Seeing them outside your head in the real world is quite different than seeing them in your head. Trust me! I'm certain there's a reason for this. After all, when you're only thinking about something by picturing it in your minds eye you're using a different part of your brain then when you're actually seeing it. After all when you're actually seeing something you're using your visual cortext whereas before you weren't.

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#### studiot

In 1) The spring moves with the block, not adjacent to it. So its total movement is partly extension and partly diplacement (translation). IOW both ends move.

But in 2 the spring rests on an immobile foundation so one end doesn't go anywhere. So its total movement is only due to compression.