AIR TRACK WITH ACCESSORIES 

1.   INTRODUCTION 

The Sci-Supply SS1701 Air Track is a complete set of experimental apparatus for the study of linear motion.  The main component of the set, the air track, is a closed hollow channel, the top surfaces of which form an inverted “V”.  These finely-machined surfaces are very straight and smooth, and have a series of small holes drilled through to the inside of the channel.  With positive air pressure supplied to the channel, a stream of air spills out of each hole.  A glider with mating inverted “V” bottom surfaces, when placed on the air track, will then be supported by a cushion of air, and glide along the track with negligible friction.  A full compliment of accessories is included in the set, to facilitate the study of such physical phenomena as: 

·       Constant velocity under zero external force, 

·       Acceleration under the influence of gravity or an external force, 

·       Exchange and conservation of momentum, 

·       Elastic and inelastic collision, 

·       Exchange and conservation of energy, 

·       Simple harmonic motion. 

 The assembled apparatus is shown in Figure 1.1.  Accessories are shown in Figure 1.2.  A photogate digital timer (Sci-Supply SS20120) and a blower /
air supply (Sci-Supply SS1702) are also required to use the apparatus. A complete set with air track, blower / air supply and photogate digital timer is also available (Sci-Supply SS1700) 

 2.   TECHNICAL CHARACTERISTICS 

• Track length: 120cm
• Overall straightness: <0.10mm
• 400mm straightness: <0.05mm
• Working plane angle: 90° ±0.1°
• Surface roughness: Ra 3.2
• Diameter of air holes: 0.8mm
• Air feed fitting diameter: 30mm
• Working air pressure: >5.8kPa
• Operating conditions: 0°C to +40°C, RH <85%
• Glider length: 121mm
• Glider mass: ~155g
• Operating air gap: >0.10mm (glider loaded <465g, air pressure >5.8kPa)

 Figure 1.1: Assembled Apparatus 

Figure 1.2: Accessories in Storage Tray 

3.   OPERATION AND MAINTENANCE 

A wide variety of experiments may be performed with the airtrack.  The air track set includes an array of accessories to support these experiments.  It is recommended that this manual be read thoroughly to gain familiarity with the track and its accessories, so that the full flexibility of the set may be realized. 

3.1  Assemble the level adjusting stand to the bottom of the track with two M40-20 machine screws and bolts. Place the accessory plastic soles under the feet of the apparatus, so that the tips of the feet rest in the center holes of the soles.  Position the air track on a flat, level, hard surface.  Use a spirit level to adjust the leveling screws on the level-adjusting stand so that the stand is horizontal. Inclination of the track may be adjusted by placing a rise block under the single support.  Inclination can be fine-adjusted by partially unscrewing the single support; the screw pitch on the support is 1mm.  Leave the apparatus in place for the duration of the session; it will have to be re–leveled if it is moved. 

3.2  Attach the flexible air hose between the air feed fitting and the blower / air supply.  Turn on the air supply and verify that all holes on the track are clear.  If a hole is obstructed, it may be cleared with a 0.5mm pin or wire.  The rubber end caps of the track can be removed to clean the inside of the track as necessary. 

3.3  To level the air track: With the air supply turned on, place a glider on the track.  Release the glider gently so that your hand does not impart even a slight force to the glider once it is floating on its air cushion.  Verify that the glider remains stationary on the air track, not drifting to one side or the other.  If the glider drifts, adjust the height of the single track support by screwing or unscrewing the support. 

3.4  Optimum glider speed is ~50cm/s.  Best results will be obtained if experimental conditions result in glider speeds in this vicinity. 

3.5  To avoid influencing the motion of the glider, care must be exercised that the track and glider are not touched, jarred, or otherwise interfered with while the glider is in motion. Also, to avoid marring the surface of the track, never place a glider on the track, or let a glider rest on the track, unless the air supply is turned on. 

3.6  After each session, the track surface should be wiped gently with a clean, dry, soft, lint-free cloth.  The track should be stored hanging vertically, in a cool, dry location. 

4.   EXPERIMENTS 

4.1  Average and Instantaneous Velocity 

Velocity may defined as distance traversed divided by time taken to traverse that distance, or   .  If Δs is finite, v as defined will be the average velocity over that distance.  As the time Δt approaches zero, v approaches the instantaneous velocity at s; in other words .  In this experiment, an accelerated motion will be set up.  Average velocity will then be determined from a fixed point over a series of successively shorter Δs, hence, shorter Δt.  Average velocity will be seen to
approach an instantaneous velocity as Δt is decreased.  

Step 1:   Set up the apparatus as shown in Figure 4.1.  Level the track as described in paragraph 3.3.  Incline the track by placing the short rise block under the single support.  Install the starting position bracket at a convenient position on the high end of the track, and a spring bumper on the low end.  Install one photogate at about the 70cm position. 

Step 2:   Turn on the air supply.  Put the timer in the “S2” mode. 

Step 3:   Install a 10cm U-flag on the glider.  Place the glider on the high end of the track, in contact with the starting position bracket.  

Step 4:   Release the glider gently but sharply.  The glider will accelerate down the track, pass the photogate, and rebound off the spring bumper. 

Step 5:   Press the [Memory] button on the counter.  Record time “C1”. 

Step 6: Repeat steps 3 through 5 with the 5cm, 3cm, and 1cm U-flags on the glider, recording the time “C1” corresponding to each U-flag. 

Step 7:   Calculate  for each flag, using the distance between flag leading edges as Δs, and the corresponding C1 as Δt. 

Step 8:   Observe that v approaches an instantaneous value as Δs decreases.  You may wish to plot v as a function of Δs. 

Figure 4.1: Velocity 

4.2  Acceleration 

Acceleration is defined as the time rate change of velocity, or  , where v₁ and v₂ are the instantaneous velocities corresponding to times t₁ and t₂, and _t1-2
is the time elapsed between t₁ and t₂.  In this experiment, an accelerated motion will be set up.  Velocities will be determined at two well-separated photogate positions; as well the time elapsed between photogate passings.  From these data, acceleration can be calculated. 

Step 1:   Set up the apparatus as shown in Figure 4.2.  Level the track as described in paragraph 3.3.  Incline the track by placing the short rise block under the single support.  Install the starting position bracket at a convenient position on the high end of the track, and a spring bumper on the low end.  Install two photogate at about the 30cm and 90cm positions. 

Step 2:   Turn on the air supply.  Put the timer in the “a” mode. 

Step 3:   Install a 1cm U-flag on the glider.  Place the glider on the high end of the track, in contact with the starting position bracket. 

Step 4:   Release the glider gently but sharply.  The glider will accelerate down the track, pass the photogates, and rebound off the spring bumper. 

Step 5:   Record times “1”, “1 – 2”, and “2” from the timer. 

Step 6:   Calculate , using 1cm (the distance between flag leading edges) as Δs, and the time “1” as Δt₁.� Calculate v₂ similarly. 

Step 7:   Calculate acceleration as .  You may wish to repeat the experiment a number of times to evaluate average deviation and possible error. 

Step 8:   Optional.  The short rise block is 5mm tall, and the distance between track supports is 600mm.  This gives the track a slope of .  You may wish to verify that the acceleration of the glider equals the acceleration of gravity () times the slope of the track. 

Figure 4.2: Acceleration 

4.3  Newton’s Second Law of Motion 

Newton’s Second Law states the equivalence of force with the time rate change of momentum.  This is equivalently expressed as mass times acceleration, or.  In this experiment, the track will be level, but the glider will be accelerated by a constant force.  This force will be the weight of a hanging weight bucket, attached to the glider by a cord passing over a pulley. �The acceleration of the glider will be equal to the hanging weight, divided by the combined masses of the glider and hanging weight. 

The experiment can be performed either by holding glider mass constant and varying the hanging weight, or by holding hanging weight constant and varying the glider mass.  Both methods are described below. 

4.3.1   Method 1: Constant Glider Mass, Varying Hanging Weight 

Step 1:   Set up the apparatus as shown in Figure 4.3.  Position the track so that the end opposite the air supply extends slightly beyond the edge of the table.  Level the track as described in paragraph 3.3.  Install the starting position bracket at a convenient position at the air-supply end stop.  Install a spring bumper on the bracket on the opposite end stop.  Install two photogates at about the 30cm and 90cm positions. 

Step 2:   Install the pulley between the two bearing screws on the end stop opposite the air supply.  Run the bearing screws in far enough that they hold the needle
bearings of the pulley captive, but that the pulley spins freely.  Apply a drop of light oil to each bearing. 

Step 3.   Install a 1cm U-flag and a glider hook on the glider.  Weigh the glider and the empty weight pail on a beam scale.  Record these weights. 

Step 4:   Run a length of light cord over the pulley.  Secure the hanging end to the weight pail, and the other end to the glider using a glider hook.  Adjust the length of the cord and the position of the starting position bracket, such that the pail does not touch the floor with the glider at the pulley end of the track, and so the pail does not climb over the pulley with the glider at the starting bracket. 

Step 5:   Turn on the air supply.  Put the timer in the “a” mode. 

Step 6:   Place the glider at the end of the track, in contact with the starting position bracket.  Verify that the cord is in the sheave of the pulley.  Make the initial run with an empty pail. 

Step 7:   Release the glider gently but sharply.  The glider will accelerate down the track, pass the photogates, and rebound off the spring bumper. 

Step 8:   Record times “1”, “1 – 2”, and “2” from the timer. 

Step 9:   Calculate , using 1cm (the distance between flag leading edges) as Δs, and the time “1” as Δt₁. �Calculate v₂ similarly. 

Step 10:         Calculate acceleration as .  You may wish to repeat the experiment a number of times to evaluate average deviation and possible error. 

Step 11:         Add about 5g to the pail, press the [Clear] button on the timer, and repeat steps 6 through 10.  Repeat with 10g added to the pail. 

Step 12:         Verify that for each case, acceleration of the glider is equal to the weight of the pail, divided by the combined masses of the glider and pail. 

4.3.2   Method 2: Constant Hanging Weight, Varying Glider Mass 

Step 1:   Set up the apparatus per steps 1 through 5 of paragraph 4.3.1 above.  Put 10g in the pail. 

Step 2:   Place the glider at the end of the track, in contact with the starting position bracket.  Verify that the cord is in the sheave of the pulley.  Make the initial run with an unweighted glider. 

Step 3:   Release the glider gently but sharply.  The glider will accelerate down the track, pass the photogates, and rebound off the spring bumper. 

Step 4:   Record times “1”, “1 – 2”, and “2” from the timer. 

Step 5:   Calculate , using 1cm (the distance between flag leading edges) as Δs, and the time “1” as Δt₁. � Calculate v₂ similarly. 

Step 6:   Calculate acceleration as .  You may wish to repeat the experiment a number of times to evaluate average deviation and possible error. 

Step 7:   Add a 50g weight to the glider, press the [Clear] button on the timer, and repeat steps 2 through 6.  Repeat with 100g added to the glider. 

Step 8:   Verify that for each case, acceleration of the glider is equal to the weight of the pail, divided by the combined masses of the glider and pail. 

Figure 4.3: Newton’s Second Law of Motion 

4.4  Conservation of Momentum 

Momentum is defined as the product of mass and velocity. �The total momentum of a system remains constant (or is conserved) through any lossless process.  In these experiments, the momentum of two gliders is determined before and after impact.  Two photogates are mounted at fixed positions along the test track.  The gliders are fitted with double flags of known distance between leading edges.  The gliders are then placed on the track, outside the photogates, and put in motion toward each other so that they collide between the two photogates.  Interval time is measured at each photogate passing.  The velocity at either photogate may be calculated by the formula .  

Both elastic and inelastic collision can be investigated.  In the case of elastic collision, the gliders rebound off each other at impact, exchanging momentum according to .  In the case of inelastic collision, the gliders remain coupled at impact and combine momentum according to . 

4.4.1   Elastic Collision 

Step 1:   Set up the apparatus as shown in Figure 4.4.1.  Level the track as described in paragraph 3.3.  Install spring bumpers at both ends of the track.  Install two photogate at about the 30cm and 90cm positions. 

Step 2:   Install 1cm U-flags on the gliders.  Install a spring bumper on one of the gliders.  Weigh the gliders on a beam scale.  Record these masses. 

Step 3:   Turn on the air supply.  Put the timer in the “Col” mode. 

Step 4:   Place the gliders at their initial positions outside the photogates.� Place the glider with the spring bumper on the track so that the bumper faces
the other glider. 

Step 5:   Set both gliders into motion toward each other.  The gliders pass their respective photogates, collide, and make final photogate passes.  Interval times for each photogate will be displayed on the timer. 

Step 6:   Calculate initial and final velocities for each glider by the formula , using 1cm (the flag leading edge distance) as Δs, and interval times as Δt. 

Step 7:   Calculate the total momentum of both gliders, before and after collision.  Total momentum before collision should equal total momentum after collision according to
. 

Figure 4.4.1: Elastic Collision 

4.4.2   Inelastic Collision 

Step 1:   Set up the apparatus as shown in Figure 4.4.2.  Level the track as described in paragraph 3.3.  Install spring bumpers at both ends of the track.  Install two photogate at about the 30cm and 90cm positions. 

Step 2:   Install 1cm U-flags on the gliders.  Install a velcro joiner on each of the gliders.  Weigh the gliders on a beam scale.  Record these masses. 

Step 3:   Turn on the air supply.  Put the timer in the “Col” mode. 

Step 4:   Place the gliders at their initial positions outside the photogates.� Place the gliders on the track so that the velcro joiners face each other. 

Step 5:   Set both gliders into motion toward each other.  The gliders pass their respective photogates, collide, and make final photogate passes.  Interval times for each photogate will be displayed on the timer. 

Step 6:   Calculate initial and final velocities for each glider by the formula , using 1cm (the flag leading edge distance) as Δs, and interval times as Δt. 

Step 7:   Calculate the total momentum of both gliders, before and after collision.  Total momentum before collision should equal total momentum after collision according to  . 

Figure 4.4.2: Inelastic Collision  

4.5  Simple Harmonic Motion 

A mass constrained by a linear spring, set in motion about its equilibrium position, will exhibit simple harmonic motion.  The period of vibration is given by the equation , where m is mass, and K is the spring stiffness. 

In this experiment, a glider will be attached between two springs, which in turn are attached to the air track end stops.  The glider oscillates, with a single flag passing through a photogate as it passes its equilibrium position. 

Step 1:   Set up the
apparatus as shown in Figure 4.5.  Level the track as described in paragraph 3.3.  Install a spring on each of the end stop brackets.  Install a photogate at the 60cm position. 

Step 2:   Install a single flag and two glider hooks on the glider.  Weigh the glider on a beam scale.  Record this mass. 

Step 3.   Turn on the air supply.  Put the timer in the “T” mode. 

Step 4:   Connect the glider hooks to the free ends of the two springs. 

Step 5:   Place the glider on the track, about 30cm to one side of the photogate. �Release the glider gently but sharply.  The glider will oscillate about the photogate. 

Step 6:   After several cycles, record the period times from the timer. Average these times. 

Step 7:   Calculate the ratio
. 

Step 8:   Attach one 50g weight to the glider.  Repeat steps 2 through 7.  Verify that the ratio is equal to that previously calculated in step 7. 

Figure 4.5: Simple Harmonic Motion

Planck’s
Constant

Measuring
Instrument

SS20802

The Purpose of this Instrument

This device can be used to experimentally derive Planck’s constant by demonstrating the photoelectric effect of visible light.

How It Works

The energy of an electromagnetic wave (in this case visible light) is absorbed by a vacuum phototube causing it to emit electrons.  This device will measure the induced current allowing the user to determine Planck’s constant.

Configuration

The instrument contains a light source (12 V/35 W halogen tungsten lamp), a dark-box which contains a vacuum phototube (sensitive component), a DC amplifier, and five color filters.

Accuracy of this Device

- The dark current is less than 0.003 µA.

- The power supply is 110±11 V / 50±1 Hz

- The error of the accelerate voltage is less than ±2%.

- Planck’s constant is found to vary less than ±15% of accepted value (h=6.62619×10³⁴ Js).

Figure 1 Planck’s Constant Measuring Instrument

1. The cover of the receiving dark-box

2. Drawtube

3. Light Source

4. Guide (used to change the distance of the light source from the phototube)

5. Scale (measures the distance of the light source from the center of the phototube)

6. Digital meter (displays the voltage and Photocurrent)

7. Current multiplier

8. Light intensity adjuster

9. Accelerate voltage adjuster

10. Voltage direction switch

11. Power indicator

12. Display mode switch (used to change display from voltage to photocurrent

13. Power switch

14. Color filters (can be inserted in the drawtube to change the wavelength of the light)

15. Vacuum phototube

16. Focus lens

17. Dark-box (houses the vacuum phototube)

Figure 2 Inside the dark-box

Calibration

Loosen the screws on the cover of the dark-box and remove the plate.  Increase the voltage to ±15 V and turn on the light.  The light should shine on the middle area of the phototube’s cathode plate adjust the direction of the light to create the greatest current possible while other conditions remain unchanged.  Then replace the cover and tighten the screws.

Experiment Procedures: Finding the Relationship between Photocurrent and Light Intensity

Turn on the instrument and allow it to heat for five minutes. Then insert the red filter into the drawtube, position the light source in the 25 cm position, set the current multiplier to ‘×1’ or ‘×0.1’ and current direction to ‘+’.  Now gradually adjust the accelerate voltage to increase the photocurrent to saturation.  Record the voltage and the photocurrent, using the display mode switch to change from voltage to current.  Change the distance (r) between the light source and the vacuum phototube by sliding the light source along the guide.  Record the photocurrent for several values of r.  Plot the
relationship between photocurrent and the distance r.

Cover the drawtube with your hand, and the photocurrent will drop to zero almost instantaneously.  When you remove your hand the photocurrent will be restored just as quickly; this should not take more than 10^-9s, demonstrating that there is very little delay with the photoelectric effect.

Experiment Procedures: Measuring Planck’s Constant

Turn on the instrument and allow it to heat for five minutes. Then insert the red color filter into the drawtube, turn light intensity up to high, set the current multiplier to ‘×0.001’ and change current direction to ‘-’. Adjust the accelerate voltage until the photocurrent is zero, switch the display mode to view the voltage and record the voltage.  Repeat this process for each of the filters, recording the voltage value for each wavelength.  Plotting the energy vs. light frequency will give the value of Planck’s constant.

Maintenance

The instrument should be operated in a dry, temperature controlled (0 to 40°C), indoor area to prevent corrosion.  For the most accurate results prevent stray light from entering the dark-box directly.  When experiments are complete, insert the black cover into the drawtube to protect the vacuum phototube.  The phototube may need to be replaced if sensitivity is
reduced by age.

Store the instrument in a dust and moisture proof place.  If dust accumulates on the phototube, collection mirror, or color filters they should be cleaned with a miscible liquid, such as alcohol, and absorbent cotton.

Introduction:

The Sci-Supply SS20121 Free-Fall Apparatus is an instrument designed to measure the acceleration of a free-falling steel ball.  The main component of the device is a vertical stand.  The stand is constructed of extruded aluminum, is fitted with a graduated scale for measuring the positions of various attachments, and includes two full-length T-slots for securing the attachments using hex-head machine bolts and thumb-nuts.  The stand is supported by a cast-iron base, the legs of which are equipped with leveling screws, and includes a muslin pouch for catching the falling ball.  Two 18mm steel balls are included.  The apparatus also includes an electromagnetic ball release and two photogates, all of which are wired through an electrical harness to a four-pin DIN jack.  The jack interfaces directly with an SS20120 Photogate Digital Timer (not included), but can be adapted to many other timers.  Finally, the apparatus includes a plumb-bob to assist in adjusting the leveling screws so that the apparatus stands perfectly vertical.

A steel ball is suspended at the top of the stand by the electromagnetic release.  When the electromagnet is de–energized, the ball drops from the electromagnet, falls through the photogates, and is caught in the pouch.  The photogate signals are processed by the timer for display.

The assembled apparatus and timer are shown in Figure 1.

Assembly:

Step1 – Assemble the Base:  Secure the legs to the base with the included six (two per leg) allen-head cap screws.  Run the cap-screws through the base from the top so that their heads are recessed in the counter-bores in the base, and into the threaded holes in the legs.  Tighten the screws with the included allen key.  Run the leveling screws into the feet of the legs (one screw per foot) from the top.  The assembled base is shown in Figure 2.

Step 2 – Assemble the Expansion Sleeve to the Base:  Assemble the flat washer onto the 12cm–long hex–head machine bolt so that the washer is under the head of the bolt.  From the bottom of the base, assemble the bolt and washer through the center hole of the base.  From the top, position the hollow expansion sleeve over the bolt so that the slotted end of the sleeve is at the top.  Thread the conical plug, tapered side first, onto the bolt, so that the tapered side of the plug will be pulled into the slotted end of the expansion sleeve when the bolt is tightened.  See Figures 3 and 4.

Step 3 – Secure the Vertical Stand to the Base:  Slide the heads of three small hex-head machine screws into each of the two T-slots in the vertical stand, one slot on either side of the stand.  Run a thumb-nut loosely onto each of the screws.  Lay the vertical stand on a table (scale-side up) so that its bottom end extends slightly beyond the edge of the table.  Assemble the base to the vertical stand by fully inserting the expansion sleeve into the bottom end of the stand.  Rotate the stand so that the pouch is at the top and the rear leg is positioned vertically downward.  Tighten the machine bolt at the center of the base with a 14mm socket wrench.  See Figure 5.  Stand the entire assembly on the floor.

Fig. 2: Assembled Base Fig. 3: Expansion Sleeve Hardware Fig. 4: Expansion Sleeve on Base

Step 4 – Mount the Attachments:  Slide the two top machine screws and thumb-nuts toward the top of the stand and snug them temporarily.  Position the electromagnetic ball release at the top of the scale, so that the bottom edge of its mount plate is at 0mm as read on the graduated scale.  Loosen the thumbnuts, slide the screws into the slots of the mount plate, and tighten the thumbnuts.  Adjust position as necessary.  Mount the two photogates similarly: one at the bottom of the stand, the other at an intermediate position.  The frame of each photogate has a square notch through which its position may be read on the graduated scale, at the bottom edge of the notch.

Set–Up:

Step 1 – Level the Base:  Place the Free-Fall Apparatus on a flat, level, hard–surfaced floor.  Run the drilled screw at the top end of the plumb–bob line into the threaded hole in the bottom of the electromagnet.  Pay out the line and let the bob hang free; it should hang inside the gap of the bottom photogate.  Adjust the leveling screws in the base legs so that the plumb–bob is exactly centered in the gap of the photogate, as shown in Figure 6.  Leave the apparatus in place for the duration of the session; it will have to be re–plumbed if it is moved.

Step 2 – Set Up the SS20120 Photogate Digital Timer:  Plug the DIN plug into the mating receptacle on the rear panel of the timer.  Plug the power cord of the timer into a 120vac outlet.  Turn the timer’s power switch to the ‘ON’ position.  The timer will execute a brief self–test.  Press the ‘FUNCTION’ button repeatedly until the LED indicating the ‘g’ function is illuminated.

Points to Consider Before Using the Apparatus:

The SS20120 Photogate Timer drives the electromagnetic ball release.  When the ‘Electromagnet’ button is pressed and released, the electromagnet is energized.  Note that a button’s function is always initiated upon release of the button, not on the initial press.  Pressing (and releasing) the button again de–energizes the electromagnet and simultaneously triggers the timer.

It must be noted however, that even though the timer starts running immediately when the ‘Electromagnet’ button is released, the electromagnetic field takes approximately 10 milliseconds to collapse to the point at which the ball drops away.  This time can (and should) be measured by positioning the upper photogate so that, with ball suspended in the electromagnet, the bottom of the ball’s shadow just touches the top of the photogate’s sensor window; and measuring the drop time.  As always, it is good experimental technique to take the average of multiple measurements.  This delay time must be subtracted from all raw measured times before they are entered into subsequent calculations.  The apparatus’ 150cm maximum drop distance is not great; and earth’s gravitational acceleration is a brisk 9.8 m/s².  Failure to account for this seemingly tiny 10 millisecond delay will foul the results of acceleration calculations by 3% to over 15%, depending on the distance of the drop.  The shorter the drop, the greater the error.

As an unrelated practical matter, you may wish to wrap a rubber band around the outside of the pouch, to prevent the ball from rebounding out of the pouch after a drop.  Also, to avoid surface damage to the balls, drop a ball only into an empty pouch.

Figure 6: Plumb-Bob in Photogate

Performing the Experiment:

Step 1:  Position the bottom photogate near the bottom of the scale (1485mm for example).  Position the top photogate at some intermediate position (360mm for example). Verify that the electromagnetic release is positioned at 0mm as described above.  Record these positions on your data sheet.

Step 2: With the SS20120 Photogate Timer turned on and in ‘g’ mode, press and release the ‘Electromagnet’ button.

Step 3: Place a steel ball on the electromagnet.  The ball should hang suspended by the electromagnet.

Step 4: Press and release the ‘Electromagnet’ button.  The ball will drop from the electromagnet, fall through the photogates, and be caught in the pouch.  The photogate timer will alternately display C1 (the time for the ball to fall from the release to the top photogate) and C2 (the time for the ball to fall from the release to the bottom photogate.)  Record C1 and C2 on your data sheet.

Step 5:  Repeat steps 2 through 4 at least five times, so that the average times, average deviations, and Possible Errors of the data may be calculated.

Step 6:  Subtract the average electromagnet release time from all average times C1 and C2, to obtain the correct average drop times.  Record these times on your data sheet.

Step 7:  Calculate the acceleration of the ball using the formula

a = 2s / t²

where

a = acceleration in m/s²

s = distance of drop in meters

t = time of drop in seconds (t = (C – 10)/1000 for data taken with the photogate timer)

For example, a drop distance of 1485mm yields a C2 drop time of about 560 msec, or 0.560 seconds. (A complete experiment would include multiple measurements and a calculated average, average deviation, and Possible Error.)

s = 1485 / 1000 = 1.485 meters

t = (560 – 10) / 1000 = 0.550 seconds

a = 2 x 1.485 / (0.550)² = 9.82 m/s².

This yields an Actual Error of

[(9.82 – 9.80) / 9.80] x 100% = 0.2%

Use the local gravitational acceleration for your latitude and elevation in the Actual Error calculation.   Is your Actual Error less than your Possible Error?  If so, your method is sound.

Take data at multiple drop distances to test the hypothesis that gravitational acceleration is constant.