Determine the mass of an unknown object using an inertial balance.

1. This will count as a MAJOR grade.
2. Teams will work together to collect & analyze data and practice fine tuning their equation.
3. Each team member will determine the mass of an unknown object - it's an individual assessment.
4. The team member may have the following items during the assessment:

• page 37 and 38 from their unit packet
• a calculator (class or personal calculator)
• an electronic device (laptop, tablet or phone for Graphical Analysis)
• team members may share calculators and electronic devices
• each member will have 10 minutes to collect & analyze their data and and submit the mass of their unknown.

1. Inertial Balance
2. C-Clamp
3. Spacer
4. Rubber Pad
5. Mass Set
6. Motion Detector
7. Meterstick (optional)

The NUMBER in your Inertial Balance's tray MUST match your Team Number.

🛑 Each inertial balance is different so you must ALWAYS work at the same table with the same inertial balance. 🛑

The inertial balance is clamped to the table with the spacer between the balance and table. The spacer allows the balance to oscillate freely above the surface of the table.

A rubber pad is placed in the balance's tray. The pad will prevent the mass from sliding in the tray when collecting data.

NOTE - Your rubber pad may be a different color.

A meterstick may be placed along side the balance. The meterstick must not touch the balance.

Place a motion detector 30-40 cm from the inertial balance.

Open Graphical Analysis and pair your motion detector.

Practice setting the tray in motion. Pull the tray 1 cm to the side and release it. The tray will oscillate back and forth.

DO NOT pull the tray more than 1 to 1.5 centimeters. Doing so will give you faulty data and may damage your balance.

Practice Collecting Data.

1. Place 200 grams in the tray.

2. Set the tray oscillating.

3. Click "Collect" on Graphical Analysis.

4. After the data is collected, click on the zoom button.

5. A sinusoidal graph should appear on your screen.

Troubleshooting - How to produce a smooth and continuous sinusoidal graph.

• Adjust the motion detector's position (aim and distance).
• Lessen the amplitude of oscillation if the mass slides in the tray.

Measure and record the time for AT LEAST 5 complete oscillations.

Identify the left most crest as "zero". From this crest count over and identify the 5th crest.

Clicking/Touching the screen will bring up a vertical line. Values will appear giving the position and time of the line's intersection with the graph. Move the line to obtain time values.

• Record the time of the zeroth crest.
• Record the time of the 5th crest.

Subtracting the two values will give the time for 5 complete oscillations.

Dividing the difference by 5 gives the time for one wave or one complete oscillation.

For better results, collect the time for as many complete waves as possible. The more waves you collect time over the more any error is spread out over the waves.

For Example

Let's assume you have a 0.5 second error in your ability to measure time.

1. If you collect the time for 5 complete waves, the error of 0.5 seconds is shared equally between the 5 waves. Each wave has an error of +/- 0.1 seconds.
   
   
2. If you collect the time for 10 complete waves, the error of 0.5 seconds is shared equally between the 10 waves. Each wave has an error of +/- 0.05 seconds.

The smaller the error the more accurately you'll be able to make a prediction from your lab data.

It may be necessary to adjust to collection time to increase the number of oscillations.

Collect data for the following masses: 50, 100, 150, 200, 250, 300. 350, 400, 450 and 500 grams.

DO NOT put a mass greater than 500 gram on the balance.

• For each mass, measure the time for "N" complete oscillations.
• For each mass, calculate the time for one complete oscillation

Record your data on page 37 in your Newton's Laws Unit Packet.

Graph mass vs period on the graph paper on page 38 in your Newton's Laws Unit Packet.

NOTE - The graph will NOT be a linear relationship (a straight line).

You will need to linearize your data.

Manipulate either the x or y variable variable to produce a linear graph. The units of the manipulated variable should be reasonable. Enter your manipulated data into Desmos, Excel, Google Sheet or Graphing Calculator and determine the equation for the line of best fit.

Record your linearized equation to determine the mass of an unknown object on page 38 in your Newton's Laws Unit Packet.

🛑 Pages 37 & 38 will be turned in on the day of your performance assessment. 🛑

Test your linearized equation by determining the mass of unknown objects: keys, phone, wallet, etc.

1. Place an unknown mass in the inertial balance and determine the time for one complete oscillation.
2. Enter the oscillation time into your linearized equation to determine the unknown mass.
3. Mass the unknown using the balance at the front of room.
4. Calculate the percent difference to determine your score. Your grade is determined by how much your predicted mass is off from the actual mass.