Background:

If an unbalanced force (F) is applied to an object of mass (m) over a distance (d), there is work done on the object. The work done is equal to the unbalanced force multiplied by the distance:

Suppose the work is done vertically, that is, let us say that the force applied to the object is gravitational force. As the object is acted upon by gravity, it speeds up travelling downward, and gains kinetic energy. Stated mathematically, the work done by gravity is equal to the change in kinetic energy of the object:

The purpose of this laboratory activity is to compare the work done on an object and the change in kinetic energy of the object. If the two values are close, we can safely assume that the work done on an object is transformed into kinetic energy.

The Question:

Is the kinetic energy gained by an object equal to the work done on it?

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:

• force sensor
• photogate/pulley system
• photogate port
• small masses with hanger
• manual or electronic balance
• string
• table clamp
• dynamics cart and track

Procedure:

Step 1:

Step 2:

Plug the photogate/pulley system into the first port of the photogate port.

Obtain a dynamics track and single cart. Move the end stop on the track to the very end of the track. Attach the force sensor to the dynamics cart:

Step 3:

Attach the photogate/pulley system to the end of the dynamics track (behind the end stop) using the table clamp. Connect a mass hanger to one end of a string, and the other end to the hook on the force sensor attached to the cart. Hang the string over the pulley so that the mass hanger dangles from the end of the track. When the set up is complete, it should look as follows:

Step 4:

Press the tare button on the force sensor. Attach an object of known mass to the end of the string so that the bottom of the object is just above the floor when the end of the cart is against the end-stop. Record the value of the hanging mass in a data table such as the following:

Step 5:

Open the DataStudio file "P19WorkEnergy.DS" in your DataStudio experiment library folder. If you do not have the experiment library installed, you can download it:

Step 6:

To record a trial of data, follow these steps:

• Pull the cart away from the photogate so the object on the end of the string is just below the pulley.
• Turn the pulley so the beam of the photogate is not blocked (the light-emitting diode or LED on top of the photogate is not lit).
• Start data recording.
• Release the cart so that it can move toward the photogate.
• End data recording just before the cart reaches the end stop.

Analyzing and Interpreting:

Step 7:

Run #1 will appear in the data list in the experiment setup window. To analyze the data, follow these steps:

• Click on the table display to make it active. Click the "Statistics" button.
• Record the value of the maximum velocity (at the bottom of the table) for Run #1 in the data table. Use the maximum velocity and total mass of the cart, force sensor and hanging mass to calculate the maximum kinetic energy:

• Click in the graph display to make it the active window.
• In the force vs. position graph display, click and drag the cursor to highlight the region of data that corresponds to the motion.
• Integrate to find the area under the curve of the force vs. position graph. Do this by selecting "area" in the statistics menu. The value reported by the integration is equal to the total work done by the falling mass. Record this value in your data table.

Step 8:

Repeat steps 6 and 7 with different amounts of mass added to the hanging mass.

Forming Conclusions:

1.	How does the maximum kinetic energy and the total work done by the falling mass compare? Explain any significant difference.
2.	Write a summary sentence or two that answers the question: "Is the kinetic energy gained by an object equal to the work done on it?"