Background:

The amount of potential energy of an object changes as its vertical position changes. When a juggler throws a ball into the air, the ball reaches maximum potential energy at its maximum height.

As the ball falls back to the hand, the potential energy is converted to kinetic energy. It is this conversion from potential to kinetic energy that will be replicated in this lab. Falling occurs very quickly and is difficult to measure, so in this activity a cart on an inclined ramp will be used.

The Question:

What is the relationship between potential and kinetic energy for a falling object?

Variables:

Identify the type of data you will collect to support your hypothesis and state the manipulated, responding and controlled variables in this investigation.

Materials:

• motion sensor
• USB Link
• base and support rod
• meter stick
• triple beam balance or electronic scale
• dynamics system (if you do not have a dynamics system, you can substitute any smooth ramp and low-friction rolling cart or toy)

Procedure:

Step 1:

Make sure that the motion sensor is set to "cart":

Attach one end of the track to the rod stand. Raise this end 5.0 to 8.0 cm higher than the other end. Attach the motion sensor to the raised end of the track as shown below.

Step 2:

Upon opening the DataStudio file, you will be presented with a energy-time graph that looks something like this:

The graph represents the kinetic and potential energies of the system. These are calculated by the DataStudio software, based on the data collected by the motion sensor.

Step 3:

Before beginning data collection, the potential and kinetic energy calculations must be tailored to your experimental conditions. Do this by performing the following steps:

Click to open the KE calculation in the Data Summary window:

Find the mass of the cart you will be using, and enter the kilogram value in the KE calculation window ("m" variable), then close the window by pressing "Accept":

Click to open the PE calculation in the Data Summary window. Enter the mass of the cart you will be using ("m" variable), along with the vertical distance in metres the cart will travel ("h" variable). Also enter the length of track the cart will travel ("l" variable), then close the window by pressing "Accept":

You are now ready to proceed with the trail and collect data.

Step 4:

1. Hold the cart 15 cm from the sensor
2. Press the start button in DataStudio, simultaneously allowing the cart to roll down the incline.
3. The computer will automatically stop collecting data.
4. If the release of the cart and the collection of data by the motion sensor are not synchronized, click the "Experiment" menu and select "Delete all data runs."
5. Repeat 1-4 until the procedure is mastered.

Analyzing and Interpreting:

1.	Describe the changes in the different energies as the cart rolls down the track.
2.	Double click on the "KE & PE & TE" graph in the DataStudio displays window. This graph represents the kinetic, potential, and total energies of the system. Based on the shape of the TE (total energy) line, what is your explanation of what happened to the total energy of the system?
3.	How would the KE, GPE, and TE graphs change if the cart was half of its original mass?
4.	How would the KE, GPE, and TE graphs change if the height of the incline doubled?
5.	How can you account for the small amount of "lost" energy as the cart rolls down the incline?

Forming Conclusions:

Based on the data you have collected, write a summary statement for the following question:

6.	What is the relationship between potential and kinetic energy for a falling object?

Extending:

• Describe the changes in energy if the cart ran into a compressible spring at the bottom of the track. If possible, design and conduct an experiment to test your theory.