![]() The angle between this gravitational force and the y-axis (which I set as perpendicular to the plane) is the same angle (θ) that the track is inclined. But only a component of the gravitational force accelerates the cart. Since the cart can only accelerate in the direction of the incline, there is only one force that pushes in this direction-the gravitational force. Here is a force diagram for a cart (with no friction) rolling down an inclined plane. If you want to stay I am going to connect the acceleration of the cart to something else-the local gravitational field. If you only care about finding the acceleration, you may be excused. I've gone over this before, so let me just leave you with this older post that goes over some of the details of finding the slope for a linear function.įinding the Slope of the Incline (and Friction) Honestly, this pops up in so many labs and students commonly struggle with this idea. Further, it is important that you find the slope and realize that this slope has some meaning. You should also understand that a linear graph is nice because you can easily estimate a best fit line if you use graph paper (just by using a straight edge). You should make a graph because it's probably the best way to analyze your data. Allain likes graphs"-but that's not true (well, it's true I like graphs). I know students often think "I have to make a graph because Dr. So there are some actual reasons for making a graph. But if you calculate the acceleration without the graph, you are explicitly stating that the y-intercept is zero-which it might not be. This is pretty close to zero, so that's good. Second, what about the y-intercept? In the linear fit above, I get a y-intercept of -0.00399 meters. How do you know your initial model (the kinematic equation) is legitimate if you don't plot your data? You need to see that it sort of fits a linear function. You might get a similar value for the acceleration, but treating each point individually isn't the same as looking at all the data at once. Isn't this the same thing as making a graph? Well, no. For the horizontal axis, we will plot t 2 instead of just time since the distance should be proportional to time squared. So let's compare our expected model with the generic equation for a line.Īs you can see, we will have to plot distance on the vertical axis to make it look like our expected linear function. Second, I want to make a graph that is linear. Yes, I know that this should be on the horizontal axis since it's the independent variable, but the graph will look better this way. First, I am going to put distance on the vertical axis. According to our kinematic equation, distance should be proportional to time squared. In this case, what do we expect? Should this be a linear function? No, our model for the acceleration does not predict that the distance should be proportional to the time. In most cases it is to show that there is a relationship between the variables being plotted on the two axes. We have a graph, but what do we do with it? Why should we ever make a graph? Should we just make a graph because a lab report has to have a graph? No, there is a reason to make a graph. ![]()
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