What is the relationship between kinetic energy and gravitational acceleration?

[Makali]

Hello.

I am in a 100 level physics college course and we are learning about conservation of energy. I am working with a program called Logger Pro. I've attached my data in the pictures. Here is a question that I am very much stuck on.

Using the Law of Conservation of Energy, show that the slope of KE/m vs. y is the gravitational acceleration -g

I also need to figure out gravitational acceleration +/- uncertainty.

If more information is needed, please let me know. Thanks in advance for your help! <3

 

[Alloymouse]

Hello.

I am in a 100 level physics college course and we are learning about conservation of energy. I am working with a program called Logger Pro. I've attached my data in the pictures. Here is a question that I am very much stuck on.

Using the Law of Conservation of Energy, show that the slope of KE/m vs. y is the gravitational acceleration -g

I also need to figure out gravitational acceleration +/- uncertainty.

If more information is needed, please let me know. Thanks in advance for your help! <3

Hi, welcome to PF!

From what I can see, your data and graphs plotted have indeed shown that KE/M is -g, so I'm not sure what you are asking for exactly. Are you asking for mathematical proof?

 

[Makali]

I am just confused on what I need to write in my lab report to be honest. Like, is Using the Law of Conservation of Energy, show that the slope of KE/m vs. y is the gravitational acceleration -g, the slope plus the uncertainty in one of the graphs? I'm just confused haha

 

[Makali]

Using the Law of Conservation of Energy, show that the slope of KE/m vs. y is the gravitational acceleration -g: I also need to figure out a mathematical equation for my data analysis section.

 

[Alloymouse]

I am just confused on what I need to write in my lab report to be honest. Like, is Using the Law of Conservation of Energy, show that the slope of KE/m vs. y is the gravitational acceleration -g, the slope plus the uncertainty in one of the graphs? I'm just confused haha

Ah okay

For your lab report i think you need to use mathematical formulae to prove that first, then say it is supported by your data

Consider using: Loss in GPE = gain in KE

 

[Makali]

Using the Law of Conservation of Energy, show that the slope of KE/m vs. y is the gravitational acceleration -g

Is that the slope and uncertainty of one of the graphs?

What mathematical formula can I use to answer
Using the Law of Conservation of Energy, show that the slope of KE/m vs. y is the gravitational acceleration -g:

 

[Alloymouse]

What mathematical formula can I use to answer
:

This:

Consider using: Loss in GPE = gain in KE

I presume you know how KE and GPE are computed (1/2 mv^2, mgh)?

From there you should be able to do some quick algebra and swap the variables around to get KE/m = -g

For uncertainty, I believe you might find googling "fractional uncertainties" and "how to calculate uncertainty in an equation" helpful

 

[Makali]

Thank you.