mehaha said:
i am in a sumular situation. and i am having trouble with the relationship with x and y and i have the independent variable as Distance and the dependent variable as the weight of the coin. is this corect
You did not explain in detail how you carried out your measurements, i.e. what you kept fixed (if anything) and what you varied, because that will determine the choice of dependent and independent variable. Let's assume that you have mass ##m_L## (representing the cyclist in the original problem) on the left side of the fulcrum at distance ##x_L## from it and mass ##m_R## on the right side of the fulcrum at distance ##x_R## from it. At the tipping point, the relevant equation is $$m_L*x_L=m_R*x_R~.$$Here is where I differ philosophically with
@haruspex. In a given trial, the independent variable is the quantity that is set
before performing the measurement and the dependent variable is the value that that is obtained
as a result of the measurement.
Cause precedes effect.
Keeping that in mind, I mention here three possibilities that might describe how you conducted your experiment. In all cases, the measurements can be summarized in a plot where you have a straight line passing through the origin in the form ##y=ax## where ##x## is the independent variable, ##y## is the dependent variable and ##a## is the constant slope.
You fix ##m_L## representing the mass of the cyclist, you put a certain number of coins on the other side at a fixed position and you find the value of ##x_L## at which tipping occurs. Then, ##x_L## is the dependent variable that goes on the left-hand side and the rest of the stuff goes on the right-hand side. $$x_L=\frac{m_R*x_R}{m_L}.$$ That's one trial. An important question is "what do you do next for the rest of trials?" Here are three possibilities when mass ##m_L## does not change from one trial to the next:
(a) Keep ##x_R## fixed and change ##m_R## to new values. Then the independent variable is ##m_R## whilst the constant slope is ##a=\dfrac{x_R}{m_L}##.
(b) Keep ##m_R## fixed and change ##x_R## to new values. Then the independent variable is ##x_R## whilst the constant slope is ##a=\dfrac{m_R}{m_L}##.
(c) Change both ##m_R## and ##x_R##. Then the independent variable is the product ##\cancel{m_R*x_R}## whilst the constant slope is ##\cancel{a=\dfrac{1}{m_L}}##.
There are other combinations of variables, which I am not going to list. However, the fact remains that, in all possibilities above, ##x_R## is determined last after the other three have been set. Being determined last in all trails is what makes ##x_R## the dependent variable. The independent variable is the variable (or combination of variables) that changes from one trial to the next and the slope is what remains the same in all trials. You can see how that idea is applied in the three possibilities above.
I am including what follows for completion. What if you varied all 4 variables from one trial to the next? Suppose that for each trial you start with a random choice of two masses and two positions. If you do that, the probability will be very high that the system
will not be at the tipping point. Now suppose that from one trial to the next you randomly select which three to set and which to determine last in order to get to the tipping point. How do you include the results from all your trials in a single plot when there is no clearly identifiable variable that was determined last?
Answer: Your dependent variable is the ratio ##y=\dfrac{m_R*x_R}{m_L*x_L}## and the independent variable is the number of the trial ##n=1,2,3,~\dots~## A plot of ##y## vs. ##n## will give you a straight line with zero slope at value ##y=1##.
As you see from the above rather lengthy exposition
only you can determine which of the four variables is your dependent variable because
only you know what you did, how you did it and which of the 4 variables you consistently determined last. If none of them was consistently determined last, then I have already explained how to deal with it.
