Graphing question with Springs and Energy?

In summary, there is some debate about the correct convention for graphing the results of a lab where weights are hung off a spring to find the spring constant. Some argue that the independent variable, weight, should be on the x axis and the dependent variable, length, on the y axis. Others suggest that it would be easier if the graph was flipped and F was plotted against x, as the slope would then equal k. However, it ultimately does not matter which convention is used as long as the relationship between the variables is accurately represented.
  • #1
Let's say there's a lab where one hangs weights off a spring, and graphs the length and weight to find the spring constant.

Graphs have the independent variable--weight in this case--on the x axis, and the dependent variable--length--on the y axis. So, by that method, the graph should be Length vs Weight

But when I learned about Hooke's law and whatnot, I saw that the graphs were Weight vs Length, because of F = kx

Which way is the correct convention?
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  • #2
I think it would be easier if you plotted F versus x. That way the slope of the line would equal k. But it doesn't really matter. If you plotted x versus F, the equation of the line would be x = (1/k)F, so the slope would equal 1/k.
  • #3

it is important to understand that there are different conventions and approaches to graphing data. In the case of a spring experiment, it is common to see both types of graphs, with either weight or length as the independent variable. Ultimately, the choice of which variable to place on the x axis depends on the purpose of the graph and the research question being addressed.

If the goal is to determine the relationship between weight and length and find the spring constant, it may be more appropriate to have weight as the independent variable and length as the dependent variable, as this aligns with Hooke's law. However, if the focus is on the physical properties of the spring itself, such as its elasticity or stiffness, it may be more useful to have length as the independent variable and weight as the dependent variable.

Ultimately, the most important aspect is to clearly label and explain the variables on the graph and the purpose of the experiment. This will ensure that the results are accurately represented and can be interpreted correctly.

1. How do you graph a spring's energy?

To graph a spring's energy, you first need to measure the displacement of the spring from its equilibrium position. This can be done by stretching or compressing the spring and measuring the distance. Next, you need to calculate the potential energy of the spring using the formula PE = 1/2 * k * x^2, where k is the spring constant and x is the displacement. Finally, plot the displacement on the x-axis and the potential energy on the y-axis to create a graph.

2. What is the relationship between a spring's energy and its displacement?

The relationship between a spring's energy and its displacement is directly proportional. This means that as the displacement of the spring increases, so does its potential energy. The graph of this relationship is a parabola, with the energy increasing as the displacement increases.

3. How do you determine the spring constant from a graph of spring energy?

To determine the spring constant from a graph of spring energy, you need to find the slope of the graph. The slope represents the change in potential energy over the change in displacement. The spring constant is equal to the slope of the graph, so you can calculate it by dividing the change in potential energy by the change in displacement.

4. Can a spring's energy be negative?

Yes, a spring's energy can be negative. This occurs when the spring is compressed and its displacement is negative. In this case, the potential energy of the spring is negative, indicating that work has been done on the spring to compress it. It is important to note that the total energy of the spring (potential energy + kinetic energy) will always be positive.

5. How does the mass of an object affect the spring's energy?

The mass of an object does not directly affect the spring's energy. The potential energy of a spring is determined by its displacement and spring constant, which are independent of the mass of the object attached to the spring. However, the mass of the object can affect the displacement of the spring, which in turn affects its potential energy. In general, a heavier object will cause a larger displacement and thus result in a higher potential energy for the spring.

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