Homework Problem Regarding Linearization

[student23561235]

Homework Statement

Hey Guys, I don't really want to have to post this in of all places due to how advanced everyone else is compared to me, but I went to my second physics class and I have a huge problem. My teacher gave me my homework, but I have no idea on Earth how to do it because she rushed the lesson because of a pep rally. I'm sure I'm not the only one in my class with this same problem, but I'd rather not give up on my first day of physics class.

The problem is: mgh = 1/2kx^2
and she simply asks: Find the slope, Write down what the slope means/represents, then find k.

g is gravity (9.8 m/s^2)
k is spring constant (what she wants us to solve for)
m is mass of marble (.2 kg)
h is maximum height achieved
x is distance the spring has been compressed.

It also comes with a table,
Distance Spring is Compressed (m) | Max Height Achieved (m)
.05 | .219
.1 | .875
.2 | 3.5
.3 | 7.88
.4 | 14
.5 | 21.9 but there's a catch. You have to graph it in excel and linearize the data to be allowed to find the slope,
instead of simply solving for it algebraically (at least I think she didn't want us to do that.)

simple as that. At least I think this is simple. This was my first day of physics after all.

Homework Equations

The Attempt at a Solution

My attempt was creating a scatterplot of x(distance compressed) vs. h(max height) to the square root in order to try to linearize it. When done, it does create a linear graph with a solvable slope of 10.

However, whenever you place 10 into the spring constant and check to see if they are equal by inputting a corresponding x and h, they aren't equal. Where am I messing up here? I know the answer will probably be painfully obvious to you, and honestly, I don't mind if you come off rude. I'm here to learn, any replies would be amazing.

 

[TomHart]

If I have time later, I will try to take a look at it, but there are a lot of smart guys on here. Someone will probably help you out before I get back to you.

This is just meant as a little encouragement: When I was taking my first semester physics (long ago and far away), I went into my professor, frustrated, and said something like, "I just don't know how to do these problems." This is what he said to me: "You are probably used to being able to look at a problem and know immediately how to solve it. In physics, it won't always be that way. You just have to start working with what you have." That was very comforting to me. I stuck it out and got through it. Hang in there. And don't feel bad about not knowing as much as the people here. In that regard, here's a twist on a cute little story I heard.

A man came into a town he had never been to before and saw an old man sitting in front of the drug store. So he walked up to the old man and said, "Were any famous physicists born here?" The old man responded, "No, only babies."

 

[TSny]

Hello, and welcome to PF!

When plotting a linear relation Y = mX + b between two variables (Y vs. X), note that the slope, m, is the coefficient of X (the variable plotted on the horizontal axis).

If you plot x vs h^1/2, what is the coefficient of h^1/2 in the linear relation between x and h^1/2?

Instead of plotting x vs h^1/2, you might consider a different plot with h plotted on the vertical axis. Then what would you plot on the horizontal axis to get a linear relation? How would the spring constant be related to the slope of this graph?

 

[TSny]

A man came into a town he had never been to before and saw an old man sitting in front of the drug store. So he walked up to the old man and said, "Were any famous physicists born here?" The old man responded, "No, only babies."