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Instruction Manual

012-10242A

Dynamics Cart Magnetic Damping

ME-6828

For other recommended equipment, see experiments starting on page 3.

Introduction

Use the Magnetic Damping Accessory to add drag to a PASCO dynamics cart. When the cart moves on an alumi-

num track, the accessory’s magnets generate eddy currents in the track, which cause an opposing magnetic field.

The resulting drag force is proportional to the cart’s velocity. The amount of damping can be varied by changing

the size of the gap between the magnets and the track.

This manual includes set-up instructions, three experiments (starting on page 3), and sample data (page 13).

Set-up

The Magnetic Damping Accessory attaches to a cart magnetically using the magnets built into the cart’s bumper.

If your cart does not have bumper magnets, install them before using the Magnetic Damping Accessory. (See

instructions included with your cart for bumper magnet installation.)

1. Remove the keeper plate from the Magnetic Damping Accessory and put it aside.

Included Equipment Part Number

1. Magnetic Damping Accessory ME-6828

2. Keeper plate 648-10173

Required Equipment Part Number

PAScar, Plunger Cart, or Collision Cart ME-6950, ME-9430,

ME-9454

Aluminum Dynamics Track ME-6953

or similar

Summary of content (15 pages)

PAGE 1
In s t r u c ti on M an u a l ® 0 1 2 - 1 0 2 4 2A Dynamics Cart Magnetic Damping ME-6828 1 2 Included Equipment Part Number 1. Magnetic Damping Accessory ME-6828 2. Keeper plate 648-10173 Required Equipment Part Number PAScar, Plunger Cart, or Collision Cart ME-6950, ME-9430, or ME-9454 Aluminum Dynamics Track ME-6953 or similar For other recommended equipment, see experiments starting on page 3. Introduction Use the Magnetic Damping Accessory to add drag to a PASCO dynamics cart.
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D y n a mi c s C a r t M a g n e t ic D a m p i n g 2. Place the Magnetic Damping Accessory on the magnet-equipped end of the cart as illustrated. 3. Place the cart on an aluminum track. 4. Slide the Magnetic Damping Accessory up or down to adjust the amount of damping. The magnets should not touch the track. To set a gap size that can be measured or reproduced, use a stack of cards as a gauge. Place the cards between the magnets and track as illustrated.
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ME-6828 E x p e r im e n t 1 : D a m p e d O s c i ll a t io n Experiment 1: Damped Oscillation Equipment Part Number Dynamics Cart Magnetic Damping ME-6828 Motion Sensor (optional for Method II) PS-2103A or similar Cart1 ME-6950, ME-9430, or ME-9454 Aluminum Track1 ME-6953 or similar Harmonic Springs1, 2 ME-9803A or similar Adjustable End Stop1 ME-8971 or similar IDS Pivot Clamp1 ME-9810 Large Table Clamp ME-9472 90 cm Rod ME-8738 or similar 1These 2 items are components of many PASC
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D y n a mi c s C a r t M a g n e t ic D a m p i n g E x p e r im e n t 1 : D a mp e d O s c i ll a t io n 4. Release the cart. 5. Allow the cart to oscillate. Count (and write down) the number of down-up cycles that the cart completes before stopping. 6. Repeat steps 3 through 5 with the gap set to 8 mm, 6 mm, 4 mm, and 2 mm, and with the magnets as close as possible to the track without touching. Skip to the Questions section on page 4.
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ME-6828 E x p e r im e n t 2 : C r it ic a l D a m p in g Experiment 2: Critical Damping Equipment Part Number Dynamics Cart Magnetic Damping ME-6828 Stopwatch (for Method I) or Motion Sensor (for Method II) ME-1234 or similar Cart1, 2 ME-6950, ME-9430, or ME-9454 Aluminum Track1 ME-6953 or similar Harmonic Springs1, 3 ME-9803A or similar Adjustable End Stop1 ME-8971 or similar IDS Pivot Clamp1 ME-9810 Large Table Clamp ME-9472 90 cm Rod ME-8738 or similar 1These PS-2103A or similar
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D y n a mi c s C a r t M a g n e t ic D a m p i n g E x p e r im e n t 2 : C r i ti c a l D a m p in g 3. Use tape or a pencil to mark the track about 50 cm above equilibrium. 4. Pull the cart up the track to the mark. 5. Let the cart go and carefully observe it’s movement as it comes to a stop. If the cart overshoots equilibrium and comes back up the track, it is under-damped. If it comes to a stop without overshooting, it is either over-damped or critically damped. 6.
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ME-6828 E x p e r im e n t 2 : C r it ic a l D a m p in g Data Collection 1. Pull the cart up the track exactly to the mark. 2. Release the cart and start data recording at the same time. 3. Wait until the cart stops. 4. Stop data recording. 5. Move the magnets up by about 1 mm to make the system under-damped. 6. Repeat steps 1 through 4. 7. Move the magnets down as close to the track as you can get them (without touching) to make the system over-damped. 8. Repeat steps 1 through 4.
PAGE 8
D y n a mi c s C a r t M a g n e t ic D a m p i n g E x p e r im e n t 2 : C r i ti c a l D a m p in g b, the damping constant ( F damping = – bv ) determined by the height of the magnets ω0 = k ⁄ m , the natural frequency of the system in the absence of damping γ = b ⁄ m , a quantity with units of frequency If m and k are held constant, then the damping behavior of the system (whether it is under-, over-, or critically damped) depends on the value of b.
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ME-6828 E x p e r im e n t 3 : P r e d i c ti n g T e r m i n a l Ve lo c it y Experiment 3: Predicting Terminal Velocity Equipment Part Number Dynamics Cart Magnetic Damping ME-6828 Motion Sensor PS-2103A or similar Cart1 ME-6950, ME-9430, or ME-9454 Aluminum Track1 ME-6953 or similar IDS Pivot Clamp1 ME-9810 Large Table Clamp ME-9472 90 cm Rod ME-8738 or similar Angle Indicator2 ME-9495 1These 2Or items are components of many PASCO dynamics systems.
PAGE 10
D y n a mi c s C a r t M a g n e t ic D a m p i n g E x p e r im e n t 3 : P r e d ic t in g Te r mi n a l Ve lo c it y Equation 3 assumes that magnetic drag is the only source of friction. A real cart is also affected by friction that is not proportional velocity, but is constant as long as the cart is moving. If this additional frictional force is f 0, then the net force on the cart is F net = ma = – bv – f0 (eq. 4) ( for v > 0 ) and f m v = – ----- a – ---0b b (eq.
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ME-6828 E x p e r im e n t 3 : P r e d i c ti n g T e r m i n a l Ve lo c it y Data Collection You may need to try several times to complete the following steps successfully. If you do not get it right, delete your data and try again. The recorded data should show the motion of the cart only after you release it and before it comes to a complete stop. There should be about 1 s of recorded data. Use one hand to push the cart and the other hand to start and stop data recording. 1.
PAGE 12
D y n a mi c s C a r t M a g n e t ic D a m p i n g E x p e r im e n t 3 : P r e d ic t in g Te r mi n a l Ve lo c it y Part III: Measuring Terminal Velocity Set-up 1. Take the cart off the track and set it aside. (Be careful not to let the Magnetic Damping Accessory shift on the cart.) 2. Use a table clamp, rod and pivot clamp to raise the left end of the track (with the motion sensor attached). Adjust the incline to 3.0°. Experiment set-up for Terminal Velocity, Part III Data Collection 1.
PAGE 13
ME-6828 S a m p le D a ta Sample Data Experiment 1: Damped Oscillation Damping increases as the magnets are moved closer to the track. Experiment 2: Critical Damping Critical damping makes the cart stop in the shortest time. Note that, due to static friction, the under-damped cart stops at a slightly different position.
PAGE 14
D y n a mi c s C a r t M a g n e t ic D a m p i n g S a mp le D a ta Experiment 3: Predicting Terminal Velocity The graph below shows position versus time as the cart is coming to a stop on a level track. The graph below shows velocity versus acceleration for the cart on the level track. From the slope and intercept of the best-fit line: – m ⁄ b = – 0.52 s and – f 0 ⁄ b = – 0.033 m/s . From these values and equation 7, the predicted terminal velocity is v T = 0.23 m/s .
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ME-6828 T e c h n ic a l S u p p o r t Technical Support For assistance with any PASCO product, contact PASCO at: Address: PASCO scientific 10101 Foothills Blvd. Roseville, CA 95747-7100 Phone: 916-786-3800 (worldwide) 800-772-8700 (U.S.) Fax: (916) 786-7565 Web: www.pasco.com Email: support@pasco.com Limited Warranty For a description of the product warranty, see the PASCO catalog.