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

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.

Determine the value of “g” (gravity) as accurately as possible.

Hypothesis: If air resistance is constant, then gravity should be constant regardless of mass.

MaterialsO 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

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

Dropping Method: Formula

𝒔 = 𝒅𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕 𝒐𝒇 𝒂𝒏 𝒐𝒃𝒋𝒆𝒄𝒕𝒖 = 𝒊𝒏𝒊𝒕𝒊𝒂𝒍 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚

𝒕 = 𝒕𝒊𝒎𝒆 𝒕𝒂𝒌𝒆𝒏𝒂 = 𝒂𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏𝒗 = 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

Put the two equations together, since they both = avg. velocities, 𝑢 + 𝑣

2=𝑠

𝑡

𝑠 =𝑢 + 𝑣

2𝑡

Isolating s (displacement)Knowing 𝑣 = 𝑢 + 𝑎𝑡 from the first equation of motion, we have:

𝑠 =𝑢 + 𝑢 + 𝑎𝑡

2𝑡

𝑠 =2𝑢 + 𝑎𝑡

2𝑡

𝑠 = 𝑢 +1

2𝑎𝑡 𝑡

𝑠 = 𝑢𝑡 +1

2𝑎𝑡2

VICKYTrial 1

[TIME (s)] Trial 2 Trial 3Average

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

Mass (g) 4 sig figs

Acceleration

(m/s^2) 2 sig figs

Tomato9.570 8.2

Lettuce10.33 5.4

BB10.57 9.3

TB20.77 7.6

Patty25.41 17

Entire76.65 11

Average: before rounding 9.8

𝒔 = 𝒖𝒕 +𝟏

𝟐𝒂𝒕𝟐

𝟏

𝟐𝒂 =

𝒔

𝒕𝟐

𝒂 =𝟐𝒔

𝒕𝟐

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.

0

2

4

6

8

10

12

14

16

18

20

9.57 10.33 10.57 20.77 25.41 76.65

Ex

pe

rie

mta

l V

alu

es

for

Gra

vit

y (

m/s

^2

)

Tomato/Lettuce/Bottom Bun/Top Bun/Patty/Entire BurgerMASS (g)

"Burger" Drop-Object Results - Vicky

Average Acceleration 9.8m/s^2

Acceleration (m/s^2)

KATE Trial 1Time (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

𝒔 = 𝒖𝒕 +𝟏

𝟐𝒂𝒕𝟐

𝟏

𝟐𝒂 =

𝒔

𝒕𝟐

𝒂 =𝟐𝒔

𝒕𝟐

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

Tomato9.570 10.2

Lettuce10.33 3.7

BB10.57 8.2

TB20.77 15

Patty25.41 9.6

Entire76.65 12

Average:Before rounding

9.84=> 9.8

0

2

4

6

8

10

12

14

16

9.57 10.33 10.57 20.77 25.41 76.65

Exp

eri

em

tal V

alu

es

for

Gra

vity

(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)

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

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

Pendulum Method - Procedure:

1. Prepare a thick, stable string and tightly tie at the tip of the pole2. 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 position and stable

3. Making sure the cup is not tilted, bring back the cup horizontally away from the pole and let it go; at the same time, use a timer to obtain the amount of time taken for each lap when the cup returns to its original position (period of pendulum)

4. Run three trials of #3 and run 10 laps for each; record the data5. 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 data6. 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 acts 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 standard gravity acted upon an object is always 9.8 m/s^2)

T= 2π x √L/g ; g = 4π^2L/T^2

T = period of pendulum, L = length of the string, g = gravitational acceleration

How formula was converted:

T = 2π x √L/g -> square both sidesT^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

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 21.0, 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 31.1, 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

0

2

4

6

8

10

12

1 2 3

Gra

vit

ati

on

al

Acc

ele

rati

on

(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

Observations/Analysis:

The pendulum swings grow smaller as time goes by, proving that there is gravity force acting upon the mass. The lengths of the strings, as mentioned in the formula, do significantly influence the periods of pendulum since there are longer distances for the mass to travel. Despite such facts, the gravity force value calculated for each of the different string lengths were similar, only 0.7m/s^2 amount of fluctuation in the results. Important fact to note is that the mass of the object used or the composition of it (ex. “Denny cup”) do not influence the results as the gravitational force acts upon all objects with equal amount of acceleration.

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 ErrorWe 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

Thank you for listening and may gravity be on your side!