PURPOSE:
To expose the student to new equipment and lab procedures. And to calculate the spring constant and period of a simple harmonic motion.

INTRODUCTION:
You have noticed many objects have a tendency to return to their original location after they have been moved slightly. You have probably also noticed most objects not only return to their original position but continue too far, so that they may swing back and forth several times before they come to rest. A playground swing is a convenient example for a discussion of this kind of motion, because we have all ridden one, and more importantly, pushed one. Now there are many objects that behave like swings in their motion (In classical physics this behavior is termed SIMPLE HARMONIC MOTION). In this lab we will use two opposing springs holding a central cart on an air track. The air track allows us to almost eliminate friction so our oscillating (swinging) cart will not slow down. If the cart is pushed to the right or left, it will rebound and swing to the other side of center because one spring has been stretched. Once passing center, the opposite spring is stretched and slows down the cart and then starts it on its opposite journey. The time it takes to travel from the far left to the far right and back to the far left (one cycle) is called the period. The distance the cart traveled on each side of center is its amplitude.

You will observe the period of a cart with a known mass as it oscillates on an air track and compare this value to a calculated one.

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A standard air track with opposing springs will provide the platform for our simple harmonic motion. The central cart is equipped with an indicator to show its position on the track.

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A mass can be attached to our air cart by a line and pulley located on the left end of the air track.

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An adjustable photogate will radio a computer monitor the time it takes for one full cycle of our cart during its harmonic motion.

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If you get into trouble and perform some procedure that causes the lab to fail(lab equipment will no longer operate), you can press the "Reset" button and the simulation will return to the starting position.

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PROCEDURE:

1) You can adjust the background shading by clicking on the "Special" button to the right and selecting "Background". Click on the "Special" button and select "Print Blank Report" to obtain a web page that can be printed and used as a lab report. (the program will not be interrupted)

2) Drag the central cart, on the air track, and at the same time press the "p" key. This will release the cart from the air track. Place the cart on the electronic balance and record its mass in kilograms. Place the cart back on the center of the air track. Drag the red weight, just to the right of the balance, and place it on the balance. Record its mass.

3) Grasp the right end of the left spring and drag it to the left side of the cart and release. If you lined up the end of the spring and the left side of the cart the spring will attach to the cart. Drag the left end of the right spring and attach it to the right side of the cart in the same manner. Move the cart back and fourth on the air track. CAUTION: if you drag the spring too far it may distort and you will have to reset.

Calculating the spring constant:

4) Notice that a string has been looped over the pulley located at the left end of the air cart. Pick up the right end loop and pull it toward the cart. If the cart is too far away, slide the cart over to the left just past center. Attach the loop to the cart in the same manner that you attached the springs.

5) Once the cart has been attached to both springs and the string, turn on the air to the air track by pushing on the green button on the air blower located on the table. Because of the string, the cart will return to center and the cart pointer should indicate 50 cm on the meter stick. Pick up one of the 25 g (0.025 kg) weights and hang it on the left end of the string. The cart will move to the left and come to rest. Record the distance traveled by the cart (example: 50 cm to 42 cm = 8 cm or 0.08 meters). Add the second weight and record the total distance from 50 cm. Finally add the third weight and record the total distance.

Observing the period:

6) Turn off the air to the air track. Grab the left end of the string where it attaches to the cart and move it away from the cart and finally drop it. Drag the cart so its pointer indicates 10 cm to the right of the center point.(60 cm) Turn on the air to the air track. The cart should oscillate back and fourth. Turn on the photogate monitor by clicking on its front button. Notice that the sensor starts to glow on the photogate. Drag the sensor down until it is blocked by the passing black card on the cart. The period will then be timed and be displayed on the monitor. The photogate monitor has been set to time 2 passings of the black card and thus one period. Record this observed period.

7) Turn off the air and set the cart to 20 cm to the right of center and then turn the air back on. Record the period. Repeat this for 30 cm to the right and record.

8) Turn off the air and pick up the red extra weight that you originally massed. Place it on the center of the cart by dropping it over the black card. You have now increased the total mass of the cart. Drag the cart to 10 cm to the right of center and turn on the air. Record the period.

9) Calculate the requested values asked for on the lab sheet and any given by your teacher. For help on these values click on the "Special" button and select "View Data & Hints". Select "File Report" to send a copy to be viewed by your teacher.