FREE FALL APPARATUS: Measuring the acceleration of a free-falling steel ball.
SS20121 Free-Fall Apparatus
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.
Figure 1: The Assembled Apparatus with Timer
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. 4: Expansion Sleeve on Base
|Fig. 5: Base Installed on Vert. Stand|
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.
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|
|Figure 7: Stand, Photogate, and Timer|
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
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.