Value of g

1. V I C K Y L I U , K A T E Y E H , D E N N Y C H O I , A N G U S L I N
SA OPEN INQUIRY #1
September 13, 2013 PPT by Vicky Liu
Gravity

2. Gravity acts on each
and every food scrap
and leftover we throw
away. A report from the
United Nations Food
and Agriculture
Organization released
on Sept 11, 2013
claims that food waste
contributes to the third
highest source of
greenhouse gas
emissions.

4. Determine the value
of “g” (gravity) as
accurately as
possible.
Hypothesis: If air
resistance is
constant, then gravity
should be constant
regardless of mass.

6. Materials
O Experiment 1
O MASS: Cardboard “burger” (5 ingredients)
O MASS: Empty chip bag
O Meter stick
O iPad Stopwatch app (accurate to 2 decimal places)
O Scale
O Experiment 2
O MASS: “Denny’s” cup (Tim Hortons cup with crumpled papers inside; this will be
clipped and tied on to the string hanging off from the edge of the pole)
O Pole stand
O Scissors
O String
O Tape
O iPad Stopwatch app
O Scale

7. Dropping Method: Procedure & Process
1. Hold the item you wish to drop at the determined
height
2. Make sure your partner is ready to record with the
timer
3. Count to 3 with your partner and on the count of 3
4. Drop the item
5. Your partner will anticipate its land on the ground and
will press stop on the timer when it lands
Controlled Variables: Mass, height of drop

8. Dropping Method: Formula
𝒔 = 𝒅𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕 𝒐𝒇 𝒂𝒏 𝒐𝒃𝒋𝒆𝒄𝒕
𝒖 = 𝒊𝒏𝒊𝒕𝒊𝒂𝒍 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚
𝒕 = 𝒕𝒊𝒎𝒆 𝒕𝒂𝒌𝒆𝒏
𝒂 = 𝒂𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏
𝒗 = 𝒇𝒊𝒏𝒂𝒍 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚
Things we know =
𝑣 = 𝑢 + 𝑎𝑡
𝑎𝑡 = 𝑣 − 𝑢
a =
v − u
t
(Newton’s first equation of motion)
Things we know =
𝐴𝑣𝑔 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =
𝑠
𝑡
=
𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑡𝑖𝑚𝑒
𝐴𝑣𝑔. 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =
𝑢+𝑣
2
=
𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 + 𝑓𝑖𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
2

9. Put the two equations together, since they both = avg. velocities,
𝑢 + 𝑣
2
=
𝑠
𝑡
𝑠 =
𝑢 + 𝑣
2
𝑡
Isolating s (displacement)
Knowing 𝑣 = 𝑢 + 𝑎𝑡 from the first equation of motion, we have:
𝑠 =
𝑢 + 𝑢 + 𝑎𝑡
2
𝑡
𝑠 =
2𝑢 + 𝑎𝑡
2
𝑡
𝑠 = 𝑢 +
1
2
𝑎𝑡 𝑡
𝑠 = 𝑢𝑡 +
1
2
𝑎𝑡2

12. VICKY
Trial 1
[TIME (s)] Trial 2 Trial 3
Average
Descent Time (s) Mass (g)
Top bun 0.56 0.55 0.43 0.51 20.77
Lettuce 0.66 0.53 0.64 0.61 10.33
Tomato 0.38 0.59 0.51 0.49 9.570
Patty 0.43 0.31 0.28 0.34 25.41
Bottom
bun 0.33 0.60 0.46 0.46 10.57
Entire
burger (by
itself) 0.48 0.51 0.29 0.43 76.65
Bag 2.980
Stand 5.740

13. Mass (g)
4 sig figs
Acceleration
(m/s^2) 2 sig figs
Tomato
9.570 8.2
Lettuce
10.33 5.4
BB
10.57 9.3
TB
20.77 7.6
Patty
25.41 17
Entire
76.65 11
Average: before rounding 9.8
𝒔 = 𝒖𝒕 +
𝟏
𝟐
𝒂𝒕 𝟐
𝟏
𝟐
𝒂 =
𝒔
𝒕 𝟐
𝒂 =
𝟐𝒔
𝒕 𝟐
s = displacement of object
(1m)
u = initial velocity (0m/s)
t = time taken (s)
a = acceleration (m/s^2)
or gravity
Result: Mass is NOT
directly or inversely
proportional to
acceleration.

14. 0
2
4
6
8
10
12
14
16
18
20
9.57 10.33 10.57 20.77 25.41 76.65
ExperiemtalValuesforGravity(m/s^2)
Tomato/Lettuce/Bottom Bun/Top Bun/Patty/Entire Burger
MASS (g)
"Burger" Drop-Object Results - Vicky
Average Acceleration 9.8m/s^2
Acceleration (m/s^2)

15. KATE Trial 1
Time (s) Trial 2 Trial 3
Average
Descent
Time (s) Mass (g)
Top bun 0.43 0.49 0.41 0.44 20.77
Lettuce 0.44 1.2 0.61 0.74 10.33
Tomato 0.38 0.59 0.51 0.49 9.570
Patty 0.41 0.31 0.38 0.37 25.41
Bottom bun 0.43 0.53 0.41 0.46 10.57
Entire
burger (by
itself) 0.48 0.33 0.39 0.40 76.65
Bag 2.980
Stand 5.740

16. 𝒔 = 𝒖𝒕 +
𝟏
𝟐
𝒂𝒕 𝟐
𝟏
𝟐
𝒂 =
𝒔
𝒕 𝟐
𝒂 =
𝟐𝒔
𝒕 𝟐
s= displacement of object
(1m)
u = initial velocity (0m/s)
t = time taken (s)
a = acceleration (m/s^2) or
gravity
Result: Mass is NOT
directly or inversely
proportional to
acceleration.
Mass (g)
4 sig figs
Acceleration
(m/s^2)
2 sig figs
Tomato
9.570 10.2
Lettuce
10.33 3.7
BB
10.57 8.2
TB
20.77 15
Patty
25.41 9.6
Entire
76.65 12
Average:
Before rounding
9.84=> 9.8

17. 0
2
4
6
8
10
12
14
16
9.57 10.33 10.57 20.77 25.41 76.65
ExperiemtalValuesforGravity(m/s^2)
Tomato/Lettuce/Bottom Bun/Top Bun/Patty/Entire Burger
MASS (g)
"Burger" Drop-Object Results - Kate
Average Acceleration 9.84m/s^2
Acceleration (m/s^2)

18. Assumptions and Limitations
Assumptions:
 Assume that the force of friction due to air resistance is
constant
 Assume that objects are dropped straight down
(perpendicular to the ground)
Limitations:
 The accuracy of any measurement made using the meter
stick is only certain up to 1 millimetre
 The iPad stopwatch app used in the experiment can only
measure up to a hundredth of a second
 Human reaction time is approximately 0.15 – 0.30 seconds
 Vicky: 0.283 seconds SIG FIG  0.28s
 Kate: 0.314 seconds SIG FIG  0.31s

19. WAYS TO MINIMIZE ERROR
 Six trials for each object – average out the
result
 Alternate who is dropping the object and who
is operating the stopwatch
 Count “1,2,3” together for optimal
coordination

21. Pendulum Method - Procedure:
1. Prepare a thick, stable string and tightly tie at the tip of the pole
2. Using a paper clip tied to the end of the string, connect the string to the “
Denny’s cup”; put on extra tape to ensure that the cup is in a middle posi
tion and stable
3. Making sure the cup is not tilted, bring back the cup horizontally away fr
om the pole and let it go; at the same time, use a timer to obtain the amo
unt of time taken for each lap when the cup returns to its original positio
n (period of pendulum)
4. Run three trials of #3 and run 10 laps for each; record the data
5. Making the string shorter by taping a bit more portion onto the cup, agai
n run three trials with 10 laps for each; record the data
6. Measure the length of the pendulum by measuring from the bottom of th
e edge of the pole to the CENTRE of the mass (the gravitational force act
s upon the central part of the mass)
7. Using the formula, and converting it to isolate “g”, calculate the amount
of gravity, “g” for each trial for two different lengths of strings (the stand
ard gravity acted upon an object is always 9.8 m/s^2)

22. T= 2π x √L/g ; g = 4π^2L/T^2
T = period of pendulum, L = length of the string, g = g
ravitational acceleration
How formula was converted:
T = 2π x √L/g -> square both sides
T^2= 4π^2L/g -> isolate g through multiplying
each side by g and then dividing each side by T
^2
g = 4π^2L/T^2

24. DENNY & ANGUS L: 0.3160 m L: 0.4250 m
Period of Pendulum (T)
units: s
Trial 1
0.9, 1.1, 1.2, 1.2, 1.3, 1.1,
1.2, 1.2, 1.1, 1.2
1.3, 1.3, 1.3, 1.4, 1.2, 1.4,
1.3, 1.3, 1.3, 1.3
Trial 1 Average (AV1) 1.2 (1.15) 1.3 (1.30)
Trial 2
1.0, 1.2, 1.3, 1.3, 1.2, 1.3,
1.3, 1.3, 1.2, 1.2
1.1, 1.0, 1.3, 1.3, 1.3, 1.3,
1.3, 1.3, 1.3, 1.4
Trial 2 Average (AV2) 1.2 (1.23) 1.3 (1.26)
Trial 1 and Trial 2
gravitational force (m/s^2):
8.7 (9.43/8.25) 9.4 (9.43/7.86)
Trial 3
1.1, 1.1, 1.0, 1.2, 1.1, 1.2,
1.3, 1.0, 1.1, 1.3
1.1, 1.2, 1.2, 1.2, 1.4, 1.2,
1.3, 1.4, 1.2, 1.3
Trial 3 Average (AV3) 1.1 (1.14) 1.3 (1.25)
Trial 3 gravitational force: 10.3 (9.60) 9.4 (7.98)
** in bracket are the values with 3 sig figs

25. 0
2
4
6
8
10
12
1 2 3
GravitationalAcceleration(m/s^2)
Trial number
Deriving the gravitational force value from periods of
pendulum
L: 0.3160 m (sig figs)
L: 0.4250 m (sig figs)
L: 0.3160 m
L: 0.4250 m
Gravitational force

26. Observations/Analysis:
The pendulum swings grow smaller as time goes by, pro
ving that there is gravity force acting upon the mass. Th
e lengths of the strings, as mentioned in the formula, do
significantly influence the periods of pendulum since th
ere are longer distances for the mass to travel. Despite s
uch facts, the gravity force value calculated for each of t
he different string lengths were similar, only 0.7m/s^2
amount of fluctuation in the results. Important fact to n
ote is that the mass of the object used or the compositio
n of it (ex. “Denny cup”) do not influence the results as t
he gravitational force acts upon all objects with equal a
mount of acceleration.

27. We assumed that there was no air resistance during our experiment
although we were aware that air resistance was present and was directly
proportional to the surface area of the bob.
The length of the pendulum cannot be determined exactly as it is prone to
human error and it is only able to be calculated up to the 2nd decimal place.
The period of the pendulum cannot be determined accurately, as the stop
watch may not have been stopped at the highest points of each period.
Limiting Error
We took into account the reaction time of each person involved in the
experiment .
We determined the period of the pendulum to the 2nd decimal place.
We took 10 periods before averaging them out.
We tried different lengths, and determined that as length increases, the
period increases as well.
We deduced that mass and angle was not a significant factor in our
calculations.
Assumptions and Limitations

28.  
Thank you for listening and may gravity be on your side!