AH-16B: Newton’s Second Law and Third Law – (using Smart Cart)
(Rev: 03-10-2021)

OBJECTIVE
The purpose of this activity is to study Newton’s Second and Third Laws.

EQUIPMENT
ME-6960 PASTrack

ME-8979 Mass and Hanger Set (ME-8967)

ME-1240 Smart Cart

ME-1241 Smart Cart

Capstone Software

ME-8999 IDS Spring Kit

String (SE-8050)

ME-9448B Super Pulley with Clamp

THEORY
Newton described the relationship between acceleration, force, and mass as follows: The acceleration of an object is directly proportional to and in the same direction as the net force, and inversely proportional to the mass of the object:

(1)

Where a is acceleration, Fnet is net force, and m is mass.

We will apply Newson’s 2nd law to find the acceleration of the system shown in Fig. 1. We can see that the system consists of two masses: and . We have to use a special method — “isolation”, we isolate one mass from another.

For , there is only one force, tension in the string that pulls to the right (assuming no friction between the cart and the track contacting surface, as the wheels are very good).

For , there are two forces, weight , going down and tension force going up. The Pulley is rotating to the right (clockwise), and the acceleration of and are always the same.

Apply Newton’s 2nd Law to and separately:

Add these 2 equations and cancel the tension

This is the theoretical or calculated value of acceleration of & system. For example:

, and ,

We can calculate tension by substituting and to eq. 3:

In this experiment we will compare the calculated values with the measured values of the acceleration and force.

Newton’s Third Law states that for every force there is an equal and opposite Reaction Force.

PROCEDURE FOR SECOND LAW
Equipment Setup
1. Assemble the PASTrack and place it on a horizontal surface. Level the Track by placing the Smart Cart on it. If the cart rolls one way or the other, use the Adjustable Feet at one end of the Track until the Track is level and the cart does not roll one way or the other. Also adjust the middle adjustable feet so that the weight of the track is on all six feet.

2. Attach the End Stop on the left end and the Super Pulley at the right end of the Track. (If your table is such that you cannot do this, reverse the two directions).

3. Remove the Magnetic Bumper from the Smart Cart, and attach the hook to measure force. Place the Smart Cart on the track with the hook towards the pulley.

4. Tie one end of a string to the hook on the Smart Cart, and its other end to the mass hanger. To fasten the string to the mass hanger, wrap the string four or five turns around the notched area of the mass hanger. Use enough length of string so that the mass hanger hangs a few cm under the pulley when the Smart Cart is at the far end of the Track.

5. Put the string in the pulley’s groove. Adjust the height of the pulley so the string is parallel to the Track.

6. The final setup should look like shown in Fig. 1.

C:Userskhalid.bukhariOneDrive – Houston Community Collegecourse materialLAB REVISIONRev-Take Home Labsimagestrack-2.jpg

Figure 1: Setup for Newton’s Second Law.

Computer Setup
1. Open Capstone Software. Click the Hardware Setup icon. The Hardware Panel opens. Select Bluetooth.

2. Press the power button on the Smart Cart for a few seconds, till the red light turns on, and the small red light starts blinking. The Smart Cart is now in Bluetooth mode, and should be detected by Capstone.

3. Confirm the Smart Cart ID on Capstone, and click it. Select to use the Force Sensor and Position Sensor in the Smart Cart.

4. Close the Hardware Panel by clicking the Hardware Setup Icon again.

5. Select Sensor Data.

Data Collection
1. Set Recording Conditions to Start recording at position about 5 cm, and Stop Condition at about 65 cm. Actual values depend on the size of your track.

2. Select Velocity on Y-axis and Time on X-axis. Attach about 20 to 30 grams to the weight hanger. Hold the cart near the left end of the track.

3. Start Recording, and then release the cart.

4. Stop the cart before it collides with the pulley. Data recording should stop automatically when the cart reaches the Stop Condition.

5. Find the slope of the line on the Y-T graph. This is the measured acceleration of the Cart. You may have to ignore the data at the end points if it deviates from the straight line. (see Fig. 3)

6. Select Force on the Y-axis, and time on the X-axis. You will now see the force as a function of time for the same case that you had just run. Find the average value of the force for the same range of data that you used for finding the acceleration. (see Fig 4)

7. Fill up the data in the Data Table.

8. Repeat with 250 g and 500 g on the cart. (You may need to use more mass in the hanger to get a good acceleration).

PROCEDURE FOR THIRD LAW
1. Remove the string and the Pulley. Attach the second End Stop on the right side of the Track.

2. Remove the magnetic bumper and attach the hook to the second Smart Cart. Turn it on, and put it on the track so that the hooks face each other.

3. Attach a spring from the Spring Kit with one end on each hook.

4. In Capstone, select both Smart Carts. In each cart select Force Sensor only.

5. In the graph, select Force (Blue) on the Y axis and Time on the X-axis. Click the tool that shows a vertical arrow with a green flower to its right. This will open a new Y–axis on the right side. Select the Force (Red) on this right side Y axis.

6. Now hold one cart with one hand and pull the other away with your other hand. Apply different amounts of force. (See figure 2) You should get two graphs, one for each cart.

7. Click the Coordinates Tool, and select the “Coordinates Tool”. Use this tool to get the value o=f the force as measured by both Smart Carts for at the same instant of time. Repeat for some other values of time. Enter the forces in the Data Table for Third Law. (see Fig. 5)

8. Find the percent difference between the two forces.

Extra Credit: Attach the magnetic bumpers to both carts and do the measurements (as you did for the spring). Make required data table.

EXTRA CREDIT:

Set up the equipment and verify the answer to the last question in the Pre-Lab Quiz. Show the relevant graphs, and picture of the setup.

C:Userskhalid.bukhariOneDrive – Houston Community Collegecourse materialLAB REVISIONRev-Take Home Labsimagesthird-law.jpg

Figure 2: Arrangement for Third Law.

Note: In your report, you must:

· Attach pictures of your setup for all cases.

· Attach graphs from Capstone for all cases.

You may have to re-submit if these are missing.

Video upload showing the experiment being performed will be Extra Credit.