Investigation 6D: Graphing motion on an inclined plane

Essential questions

What is the acceleration of an object down an inclined plane?
What do the motion graphs of an object down an inclined plane look like?

Graphs of position versus time and velocity versus time show the nature of the motion of an object, such as a block sliding down a frictionless ramp. Unaccelerated motion (i.e., with constant velocity) will have one set of shapes for those graphs, whereas accelerated motion will show different graphical relationships. Physicists often use properties of a graph to measure fundamental physical quantities.
In this investigation you will answer this question: How can you use motion down a ramp graphically to measure the acceleration due to gravity g?

Part 1: Position–time and velocity–time graphs

Set the initial height h_{0} to 200 m.

Set the inclination angle θ to 30°.

Check the boxes to graph both position and velocity versus time.

Run the simulation.

Describe the shapes of the position–time and velocity–time graphs.

Using the equations of motion, explain why each graph has that shape.

In this interactive simulation, you will study motion along an inclined plane. The block slides faster or slower down the plane depending on its steepness. You can plot the position and/or velocity as a function of time in a rotated reference frame along the plane.

Part 2: Measuring the acceleration due to gravity

Devise a procedure to measure g using the simulation, a table, a graph, and a = (h/x)g.

Your procedure should use at least five different values of θ.

Your procedure should include graphing your data, drawing a trend line through the data points, measuring the slope of the line, and using that slope as part of calculating g.

For your written report, write down your procedure, noting the steps required for collecting data, graphing data, making calculations, and arriving at the answer.

What is the value of the slope of a line through your data? (Remember to include units!)

What is the physical meaning of the graph’s slope? Use velocity, time, and acceleration in your answer.

In your written report, note your conclusion for the value of the acceleration due to gravity and explain any discrepancies from the commonly accepted value.