The students conducted two experiments to determine the value of the acceleration due to gravity, g. In the first experiment, they measured the time it took a super ball to bounce using a meter stick and digital timer. They calculated g to be approximately 10.5 m/s^2. In their second experiment, they dropped an object from various heights and timed its fall, calculating g to be around 9.5 m/s^2. Their third experiment involved dropping an object from a fixed height of 5.63 meters and timing its fall, determining g to be approximately 10.17 m/s^2.

1. Science AcademyScience Academy
Open Inquiry AssessmentOpen Inquiry Assessment
Objective:Objective:
To determine the value ofTo determine the value of ““gg”” asas
accurately as possible.accurately as possible.
William Liu, Leona Lu, Stella So, Alison WuWilliam Liu, Leona Lu, Stella So, Alison Wu

2. ExperimentExperiment
1. M1. Measure the value of "g" by using aeasure the value of "g" by using a
super ball and meter stick.super ball and meter stick.
2. M2. Measure the value of "g" by droppingeasure the value of "g" by dropping
an objectan object from a high distance to thefrom a high distance to the
ground.ground.
Formula Using:Formula Using:
g = 2d/tg = 2d/t^^22
d=distance (m)d=distance (m)
t=time (s)t=time (s)

3. Experiment 1Experiment 1
Materials:Materials:
 DDigital timerigital timer
 MMeter sticketer stick
 WWhite paper tapehite paper tape
 Whiteboard eraserWhiteboard eraser
 A super ballA super ball
Procedure:Procedure:
 Stabilize the meter stick against theStabilize the meter stick against the
wall to keep it vertical.wall to keep it vertical.
 DDrop the super ball from therop the super ball from the top.top.
 When the ball hits theWhen the ball hits the groundground, the, the
digital timer should be started by thedigital timer should be started by the
partner who is responsible for timing.partner who is responsible for timing.
 Record tRecord the height that the ballhe height that the ball
bounces.bounces.
 When the ball hits theWhen the ball hits the groundground again,again,
the timer must be stopped.the timer must be stopped.
 Make measurements.Make measurements.
 Enter the data into a table.Enter the data into a table.
MMeasure the value of "g" by using aeasure the value of "g" by using a super ballsuper ball
and meter stick.and meter stick.

4. Experiment 1-1Experiment 1-1

5. Experiment 1-1Experiment 1-1
Trials #Trials # 11 22 33 44 55 AveragAverag
ee
Time (s)Time (s) 0.70.7
22
0.700.70 0.80.8
66
0.80.8
22
0.880.88 0.80 s0.80 s
Height (m)Height (m) 84.84.
55
83.783.7 83.83.
55
84.84.
22
85.285.2 84.2 cm84.2 cmThe time showing on the timer is twice the time for the ball to fall. DivideThe time showing on the timer is twice the time for the ball to fall. Divide
the time on the timer by 2 to get "t". "d" is the height the ball bounces to.the time on the timer by 2 to get "t". "d" is the height the ball bounces to.
"g" is the "g" in d = 1/2 g. Therefore g = 2d / t2"g" is the "g" in d = 1/2 g. Therefore g = 2d / t2
g = 2d / tg = 2d / t^^22
t = 0.80/2 = 0.40 st = 0.80/2 = 0.40 s
d = 84.2 cmd = 84.2 cm
g = 2(84.2)/(0.40)^2g = 2(84.2)/(0.40)^2
g = 1052.5 cm/s = 10.525 m/s^2g = 1052.5 cm/s = 10.525 m/s^2

6. Experiment 1-2Experiment 1-2

7. Experiment 1-2Experiment 1-2
Trials #Trials # 11 22 33 44 55 66 77 88 99 1010 AverageAverage
Time (s)Time (s) 0.820.82 0.840.84 0.980.98 0.880.88 0.740.74 0.750.75 0.790.79 0.740.74 0.810.81 0.890.89 0.824 s0.824 s
Height (cm)Height (cm) 81.581.5 81.581.5 82.582.5 81.581.5 81.381.3 78.478.4 82.582.5 81.081.0 79.379.3 80.580.5 81.0 cm81.0 cm
The calculation is same as Experiment 1-1The calculation is same as Experiment 1-1
g = 2d / tg = 2d / t^^22
t = 0.824/2 = 0.412t = 0.824/2 = 0.412
d = 81.0 cmd = 81.0 cm
g = 2(81)/(0.412)^2g = 2(81)/(0.412)^2
g = 954.378 cm/s = 9.54 m/s^2g = 954.378 cm/s = 9.54 m/s^2

8. Experiment 2
MMeasure the value of "g" by dropping an objecteasure the value of "g" by dropping an object fromfrom
a high distance to the ground.a high distance to the ground.
Material:
 Object - ball
 digital timer
 String
 meter stick
 Scissors
Procedure:Procedure:
 Measure the distance to the ground byMeasure the distance to the ground by
using the string and meter sticks.using the string and meter sticks.
 Drop the object several times. In eachDrop the object several times. In each
case, start the timer when the object iscase, start the timer when the object is
released and stop the timer when thereleased and stop the timer when the
object hits ground.object hits ground.
 Keep track of the time in a tableKeep track of the time in a table..

9. Experiment 2

10. Experiment 2
Trials #Trials # 11 22 33 44 55 66 77 88 99 1010 AveragAverag
ee
Time (s)Time (s) 1.051.05 1.041.04 1.061.06 1.041.04 1.071.07 1.051.05 1.031.03 1.081.08 1.011.01 1.091.09 1.052 s1.052 s
The height is 5.63 m.The height is 5.63 m.
g = 2d / tg = 2d / t^^22
t = 1.052 st = 1.052 s
d = 5.63 md = 5.63 m
g = 2(5.63)/(1.052)^2g = 2(5.63)/(1.052)^2
g = 10.17 m/s^2g = 10.17 m/s^2

11. Sources of Error – ExperimentSources of Error – Experiment
OneOne
• Floor may not be flat
• Meter ruler is not perfectly right angled to the floor
• Blackboard eraser is not perfectly right angled to the meter
ruler
• Bouncy ball does not bounce in an exact straight line
• Timing reaction is not perfectly exact due to human reaction
time to when the ball is released and when it hits the ground
• Hard to read exact measurements of the bouncing ball (even
when using slow motion video playback)

12. Sources of Error Experiment 2Sources of Error Experiment 2
• Floor may not be flat
• The height of the second flood (distance) is hard to
make exact
• Timing is based on human reaction time, which is not
100% accurate
• Ball may not drop straight down

13. Results
Experiment 1-1: g = 10.525 m/s^210.525 m/s^2
Experiment 1-2: g = 9.54 m/s^29.54 m/s^2
Experiment 2: g = 10.17 m/s^210.17 m/s^2