Lab Report Constant Accleration

Purpose The intent of this laboratory procedure is to use linear regression and statistical mathematics to calculate the initial velocity of a moving object, calculate the acceleration while factoring in the angle of inclination, and to use that information to verify the equation V 2f =V 2i 2a x 

Laboratory Equipment •

Photogate with timer

•

Air track with compressor

•

Air track glider with 100mm wide flag

•

Vernier Calipers

•

Wooden Block

•

Standard issue meter stick.

Laboratory Procedure 1. Set up the air track by connecting the air compressor to the track using the hose. Place a glider on the track and turn on the compressor. Adjust the support legs so that the track is level. When the track is level the glider should be able to remain stationary. If you are going to angle the air track, then why is it important to first level the track? A level starting position ensures that the angle that is introduced per the laboratory procedure is the only change in angle. 2. Elevate one end of the track with the wooden block. Measure the height, h, of the block and the distance, d , between the support legs. 3. You will be using of the large black “flags” to measure the velocity of the glider. The photogate timer will measure how long it takes this flag to pass through. Use the vernier calipers to measure the width, w, of the flag. Attach the flag to the top of the glider — making sure the flag’s width is parallel to the length of glider. Why might this be important? If the flag were to pass at an angle, the photogate wouldn't record the accurate time the full

length of the flag takes to pass through the point of reference. 4. Set up the photogate timer by setting the timer to GATE mode — which means that it will measure the time that the photogate is blocked. Set the time scale to 0.1 ms. Adjust the height of the photogate so that the flag on the glider trips the timer. The red LED on top of the photogate shows when the gate is blocked. You will need to re-adjust the gate as you move the photogate timer along the track. Make sure the gate is perpendicular to the air track. Why might this be important? If perpendicular, the distance the flag on the glider travels under the photogate is its exact width, while an angle results in a longer width being recorded. 5. Place the glider at the top of the air track, up against one end. Record the position of the leading edge of the glider as x0. You will be using the position of the leading edge to track the position of the glider. 6. Place the photogate approximately 25 cm from x0 by using the glider to see when the flag on the glider trips the photogate (i.e. when the LED turns red). Move the glider back and forth and record the exact position of the glider’s leading edge when the LED is just barely turned on. You need not have the photogate at exactly x0 + 25.0 cm — but you do need to know the exact location. 7. Release the glider from the top and record the time for the glider to pass through the timer. Record three times for this distance. The glider must be released from rest each time. Why might this be important? Vi at rest: V i=0

mm , which eliminates one variable of the equation, reducing the sec

complexity of the lab. 8. Repeat steps 6 & 7, moving the timer approximately 25 cm each time, until you reach the lower end of the track.

Data h Block =20 mm

d Legs=1000 mm

w Glider =100 mm

x 0=14.5 mm

Table 1: Experimental data

x

 x= x−x 0

 t in sec Trial 1

Trial 2

Trial 3

Average

V in

mm sec

2

V in

mm2 sec 2

411 mm

266.5 mm

0.2903

0.2902

0.2903

0.2903

344.53

118700.9

658 mm

513.5 mm

0.2180

0.2173

0.2172

0.2175

459.7

211324.09

916 mm

766.5 mm

0.1807

0.1804

0.1801

0.1804

554.26

307204.14

1156 mm 1011.5 mm

0.1580

0.1583

0.1583

0.1583

631.83

399209.14

1408 mm 1363.5 mm

0.1423

0.1425

0.1425

0.1424

702.03

492846.12

Calculations •

a=

m 2 mm 2

s a=375.763 2 a=187.88 •

mm s2

h a theoretical = g sintan−1  d mm 20mm a theoretical =9800 2 sin tan−1  1000mm s a theoretical =195.96

mm s2

Conclusions •

How well does your data verify the theory? Note that you are comparing how both velocity is related to distance under constant acceleration and that the acceleration itself was constant. In addition, it is possible to predict what the value of the acceleration should be given how the air track was inclined. What was your percent error, using the theoretical value for acceleration as the accepted value? The experimental data verifies the theory well, as the graph shows a nearly linear trend in the points, demonstrating that a was constant throughout the experiment. Percent Error = ∣Value Experimental −Value Theoretical∣ Value Actual =

∣

187.88

mm s

2

−195.96

195.96 =

mm s2

4.12%

mm s2

∣

•

Based on your data, did your experiment have any systematic or random uncertainties? Identify any observed sources of each type of uncertainty and how they affected your results. Do these observed uncertainties affect your answer to the first question? Do not list hypothetical possibilities or excessively minor effects. Never list “human errors!” The only systematic uncertainties were in the precision of the instruments. The meter stick had an uncertainty value far greater than the uncertainty value presented by either the Vernier calipers or the photogate. The meter stick would have had contributed the greatest uncertainty to the procedure. The random uncertainties would have included any friction induced by the air track and slight levelling errors at the beginning of the procedure, thereby affecting the velocity calculations.

•

What was the value for the y-intercept for your linear regression line? What is the physical interpretation of this number? In principle, what should it be? If it wasn’t what it should be, how can you explain the difference? The value of the Y-intercept was 18730.3 mm2/sec2, which would translate to the initial squared velocity of the glider. Theoretically, the value should be 0, which means that the glider starts off with zero velocity. More trials would bring the value of the Y intercept toward zero as the initial velocity is divided among more trials, but due to the limitations of physical world, the value would never really become zero.

•

We used a fairly wide flag to measure the instantaneous velocity of the glider at each position of the photogate. Should we have used a narrower flag to get a better measurement of the instantaneous velocity? Recall the definitions of instantaneous vs. average velocity. A narrower flag would allow for the calculation of values closer to the true instantaneous velocity, but the precision of the photogate becomes a limiting factor as the width of the flag becomes smaller. The current width seems like a good compromise to allow for an acceptable calculation of velocity.

MEASUREMENT OF CONSTANT ACCELERATION AP PHYSICS C

Hasith V. Oct 14th 2009