The slope of a kinetic energy vs. potential energy graph

[niteeks]

Homework Statement

I have plotted a graph of Gravitational potential energy (y-axis) vs. kinetic energy (x-axis), and I have found the value of the slope to equal -1.4. The thing is I don't know what the -1.4 equals to? Since I have to find the percentage error, I need to know the theorectical value of the experiment, to put into the equation of % error. I have tried several ways to determine what the value would be like but I don't think they make sense:

The Attempt at a Solution

(kg(m/s^2)m)/((kg(m^2/s^2))/2) which equals finally 2 (theo value)

and when I put into percentage error formula:

(|theo-exp|/|theo|)x100→(2-(-1.4)/2)x100→1.7x100=170% (which is impossible)

or something I found on the internet:

For a freely falling body,
P.E. + K.E. = cosntant
=> x + y = constant, where x = P.E. and y = K.E.
=> P.E. vs. K.E. graph is a line with slope = - 1

I don't understand how -1 should be the theo value of the slope... But it works perfectly in my equation for percentage error!

(|theo-exp|/|theo|)x100→(-1-(-1.4)/-1)x100→0.4x100=40% (which makes more sense)

Could someone help me understand this? And tell me my mistakes? It doesn't make any sense to me! Thanks!

Homework Equations

em=ek+pe

 

[LawrenceC]

Hint:

Write the equation as

PE + KE = C, where C is a constant.

Then put it in the form of y = mx + b

What is m?

 

[niteeks]

Uh well "m" equals -1 right?

 

[LawrenceC]

That's correct.

 

[asteriatic]

The slope of a kinetic energy vs. potential energy graph is determined by the relationship between the two variables. In this case, the slope of -1.4 indicates that for every unit increase in kinetic energy, there is a decrease of 1.4 units in potential energy. This slope can also be interpreted as the change in potential energy over the change in kinetic energy.

In terms of the percentage error calculation, the theoretical value of the slope would be -1, as stated in the second attempt at a solution. This is because the theoretical relationship between kinetic energy and potential energy is a straight line with a slope of -1, as shown in the equation PE + KE = constant.

The first attempt at a solution is incorrect because it does not take into account the units of the variables. The units of the slope should be in J/m or m/s^2, not just a number.

In conclusion, the theoretical value of the slope should be -1 and the percentage error calculation should be (|-1.4-(-1)|/|-1|)x100 = 40%. This indicates that there is a 40% difference between the experimental and theoretical values, which could be due to experimental error or other factors. It is important to carefully consider the units and equations when interpreting data and calculating errors in scientific experiments.