IB Physics Required Practical
Determining Acceleration due to Gravity by Method of Free
Fall
Form V IB HL
By: Kirsten Werner
Title: Determining the Acceleration due to Gravity by Method of Free Fall
Introduction and Background Information
Gravity is defined as a force by which a planet or other body draws objects toward its center1.
Essentially, gravity is what prevents us from spiraling into outer space by attaching our feet to
the surface and keeping us grounded to earth. Additionally, it is the causative of freely falling
objects gaining acceleration. This acceleration is known as ‘acceleration due to gravity’ and is
commonly represented by a lowercase ‘g’.
Firstly, it is important that the term ‘free fall’ is clearly understood before advancing. Free fall
refers to when gravity is the only force acting on object. Regardless of the direction of the
object’s movement, if gravity is the only force acting upon said object, then the object is said to
be in a state of free fall. Any object in such state experiences acceleration due to gravity.
As the name suggests, ‘acceleration due to gravity’ is the acceleration gained by an object due to
gravitational force2. We understand weight to be the measure of the force of gravity acting on a
body3. From this we can conclude that weight measures the force upon a freely falling object
since the only force acting on an object in such state is gravity. Therefore, when weight is the
only force acting upon an object:
 𝐹 = 𝑊 = 𝑚 × 𝑔 (Force acting on a freely falling object = Weight of the freely falling
object = mass of the object × object’s acceleration due to gravity)
Newton’s Second Law of Motion states that the acceleration of an object is dependent upon two
variables – the net force acting upon the object and the object’s mass4, giving us the equation
𝐹 = 𝑚 × 𝑎 (where F=Force acting upon a body, m=mass of the body, and a=acceleration of the
body). According to the equations above we can assume that:
𝐹
𝑊
𝑚×𝑔
 𝑎=𝑚=𝑚 = 𝑚
where:
𝑚×𝑔
𝑎 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛
 𝑎 = 𝑚 ;𝑚 ≠ 0
𝐹 = 𝑛𝑒𝑡 𝑓𝑜𝑟𝑐𝑒
𝑊 = 𝑤𝑒𝑖𝑔ℎ𝑡
 𝑎𝑚 = 𝑔𝑚; 𝑚 ≠ 0
𝑚 = 𝑚𝑎𝑠𝑠
𝑔 = 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑢𝑒 𝑡𝑜 𝑔𝑟𝑎𝑣𝑖𝑡𝑦
 𝑎 = 𝑔; 𝑚 ≠ 0
Proving, that for this investigation the acceleration of the freely falling object will be equal to the
acceleration due to gravity on the surface on which the experiment is carried out on. For this
report the experiment was conducted in Miraflores, Lima, Peru.
There are four factors which can affect the value of ‘g: altitude above the planetary body’s
surface, the shape of the planetary body, depth below the planetary body’s surface and rotational
motion of the planetary body5. The acceleration due to gravity on the surface of the Earth is
NASA Space Place – NASA Science for Kids. “What Is Gravity?” Accessed March 29, 2023.
https://spaceplace.nasa.gov/what-is-gravity/en/.
2
“Acceleration Due to Gravity - Formula, Values of g and Variations.” BYJU’S, May 13, 2019.
https://byjus.com/jee/acceleration-due-to-gravity/.
3
“What Is Mass & Weight? - Definition, Difference, Relation.” BYJU’S, December 11, 2017.
https://byjus.com/physics/mass-and-weight/.
4
“Newton’s Second Law of Motion.” Accessed March 29, 2023.
https://www.physicsclassroom.com/class/newtlaws/Lesson-3/Newton-s-Second-Law.
5
UN academy. “Acceleration Due To Gravity On The Surface of Earth,” April 26, 2022.
https://unacademy.com/content/neet-ug/study-material/physics/acceleration-due-to-gravity-on-the-surfaceof-earth/.
1
9.81 ms-2. However, certain places have been proven to have a different value of ‘g’ precisely
because of variations in altitude above the Earth’s surface. Mount Nevado Huascaran in the
mountains of Peru is an example of this; its gravitational acceleration of 9.7639ms-2 is the lowest
on earth. This evidences how the four previously mentioned factors can alter the value of ‘g’ in
different places.
In this experiment I aim to determine the value of the acceleration due to gravity in Lima via a
free-falling object. I will measure the object’s displacement and the time it takes for it to fall to
calculate the final velocity and find acceleration. The initial velocity ‘u’ for this experiment will
be 0 as the object will be stationary before it is dropped. To calculate the acceleration due to
gravity I will use the third equation of motion 𝑣 2 = 𝑢2 + 2𝑎𝑠 (where v=final velocity, u=initial
𝑣2
velocity, a=acceleration and s=displacement), rearranged as 𝑎 = 2𝑠 to give the value of ‘a’ which
as stated before is equal to ‘g’ giving us the acceleration due to gravity in Lima.
Research Question: What is the acceleration due to gravity in Lima?
This investigation aims to answer the question “What is the acceleration due to gravity in
Lima?”. To do this I will measure the object’s displacement and the time it takes to fall, which
will allow me to calculate the body’s acceleration as I mentioned above, and from this I can find
the acceleration due to gravity on the surface where the experiment is conducted, which is Lima.
Variables:
Independent Variable: Distance from the point from which the tube will be dropped to the light
gate’s laser. In this experiment these distances vary from 0.10m to 1.00m, in intervals of 0.10m.
Dependent Variable: Time taken for the tube to pass through the light gate. This variable will be
measured in seconds by the LoggerPro, by measuring at which times the tube entered and exited
the light gate. Because of the configuration of the LoggerPro used in this experiment, the Time in
is always 0 s as the device starts timing when the tube enters the light gate. Due to this the Time
out is equal to the Time in gate.
Controlled Variables:
Controlled Variable
Length of the tube
0.056m
Timing Device
Logger pro
Measure taken to control variable
Use the same tube throughout all trials in the
experiment. If the length of the tube
fluctuates, different sizes will take different
amounts of time to entirely go through the
light gate making the results inaccurate.
Us the same timing device throughout the
experiment. I chose to use a LoggerPro for
this experiment as it is more accurate in
comparison to a manually held stopwatch
since factors such as human reaction time
won’t interfere with the results. The same
String material
Diameter of the tube
measuring instrument must be used for taking
all the measurements since different devices
have different uncertainties and errors.
The same piece of string is used throughout
the experiment as different string materials
provide different friction or elasticity,
contributing to systematic errors and
interfering with the results.
The same tube will be used for all the
experiment as variations in the diameter
prevent air resistance from remaining constant
for all trials.
Materials
 Plastic tube
 4 clamp stands
 Hook weight
 Meter ruler
 20cm ruler
 String, longer than a meter
 LoggerPro
 Light gate
Methodology
Before assembling check that no wind will contact the apparatus as it could cause external
factors to interfere with the experiment. This can be prevented by setting up the equipment
indoors.
Using a 20cm ruler measure the length of your plastic tube; record this measurement as it will be
used later for calculations. Insert the piece of string through the plastic tube and making sure it
doesn’t fall out, tie one end of the string to a clamp stand and the other end to a hook weight.
Place the clamp stand attached to the string on a surface that is elevated at least one meter above
the floor. Position the hook weight under the clamp stand trying to maintain the string as straight
as you can. Adjust the clamp stand as needed to make the string as tense as possible. Attach the
light gate to a clamp stand and position it around the string verifying that it does not block the
light gate’s laser (Fig 1.1). If required, use an additional clamp stand to hold the light gate in
place and prevent it from rotating. Connect the light gate to the LoggerPro. Use a clamp stand to
hold a ruler in place next to the light gate as shown in Fig 1.2; the ruler should start measuring
approximately from the light gate’s laser hole. Again, check that no object is obstructing the
object’s path or blocking the laser. Hold the top of the tube to the 1.00m mark on the ruler. Drop
the tube while recording the time taken for it to enter and exit the light gate using the LoggerPro.
Carry out 3 successful trials for each distance. Upon completion repeat this but decrease the
distance between the point from which the tube is being dropped and the light gate by 0.10m.
Repeat this until you have completed three trials with the distance from which the tube is being
dropped is 0.10m.
Ruler
Clamp stand
Ruler
Clamp stand
Ruler
Light gate
Ruler
String
Ruler
Tube
Ruler
Hook weight
Ruler
LoggerPro
Ruler
Fig 1.1
String
Ruler
Clamp stand
Ruler
Ruler
Clamp stand
Ruler
Clamp stand
Ruler
Light gate
Ruler
Fig 1.2
Tube
Ruler
Raw Data Table 1
Justification for the Range:
Since the biggest ruler available was a meter ruler, the largest distance I could measure with the
smallest uncertainty was one 1.00m. To investigate a bigger distance, I would have had to use
two rulers placed one next to each other, which would have affected the accuracy of the
measured distance between the tube and the light gate by increasing random (human) error and
the uncertainty of this distance. To get a vast pool of data I chose to measure distances between
1.00m and 0.10m, with intervals of 0.10m.
Justification for Uncertainties:
The distance between the point from which the tube is being dropped and the light gate has an
uncertainty of ±0.003m because neither the ruler nor the string was perfectly straight, therefore, I
was measuring a hypotenuse rather than a straight line. Also, because of human error such as
involuntary, random hand movements the actual distance from which the tube was dropped
varied by some millimeters from the distance recorded on the tables of results. The uncertainties
of the Time in, Time out and Time in gate are of ±0.00001s as the logger pro is precise to
0.00001s.
Sample Calculations:
On the processed data table, all results were rounded to their corresponding number of
significant figures.
Sample calculation for the time in gate:
 𝑇𝑖𝑚𝑒 𝑖𝑛 𝑔𝑎𝑡𝑒 (𝑠) = (𝑇𝑖𝑚𝑒 𝑜𝑢𝑡) − (𝑇𝑖𝑚𝑒 𝑖𝑛)
 0.01563 𝑠 = 0.01563 − 0.00000
Sample calculation for the average time in gate:

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑡𝑖𝑚𝑒 𝑖𝑛 𝑔𝑎𝑡𝑒 (𝑠) =
(𝑇𝑟𝑖𝑎𝑙 1 𝑡𝑖𝑚𝑒 𝑖𝑛 𝑔𝑎𝑡𝑒 )+(𝑇𝑟𝑖𝑎𝑙 2 𝑡𝑖𝑚𝑒 𝑖𝑛 𝑔𝑎𝑡𝑒)+(𝑇𝑟𝑖𝑎𝑙 3 𝑡𝑖𝑚𝑒 𝑖𝑛 𝑔𝑎𝑡𝑒)
0.1563+0.1564+0.1567
 0.01565 𝑠 =
3
Sample calculation for 2s:
 2𝑠 (𝑚) = 2 × 𝑠
 2.0 𝑚 = 2.0 × 1.0
Sample calculation for the uncertainty in 2s:
 2𝑠 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 (𝑠) = 𝑠 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 × 2
 0.006 𝑠 = 0.003 × 2.000
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠
Sample calculation for the percentage uncertainty in time:
𝑡𝑖𝑚𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦
 %𝛥 𝑇𝑖𝑚𝑒 = (𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑡𝑖𝑚𝑒 𝑖𝑛 𝑔𝑎𝑡𝑒) × 100%
0.00001
 0.064% = (0.01565) × 100%
Sample calculation for the velocity:
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑢𝑏𝑒
 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (𝑚𝑠 −2 ) = 𝑡𝑖𝑚𝑒 𝑖𝑛 𝑙𝑖𝑔ℎ𝑡 𝑔𝑎𝑡𝑒
0.068
 4.344 𝑚𝑠 −2 = 0.01565
Sample calculation for the percentage uncertainty in the length of the tube:
𝑟𝑢𝑙𝑒𝑟 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦
 %𝛥 𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑢𝑏𝑒 = (𝑙𝑒𝑛𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑢𝑏𝑒 ) × 100%
0.001
 1.471% = (0.068) × 100%
Sample calculation for the percentage uncertainty in velocity:
 %𝛥 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = %𝛥 𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑢𝑏𝑒 + %𝛥 𝑇𝑖𝑚𝑒
 1.534 % = 1.471 + 0.064
Sample calculation for velocity uncertainty:
 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 (𝑚𝑠 −2 ) = 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 × %𝛥 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦
 0.067 𝑚𝑠 −2 = 4.346 × 0.01534
Sample calculation for velocity squared:
 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2 (𝑚𝑠 −2 ) = 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 × 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦
 18.888 𝑚𝑠 −2 = 4.346 × 4.346
Sample calculation for the percentage uncertainty in velocity squared:
 %𝛥 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2 (𝑚𝑠 −2 ) = 2 × %𝛥 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦
 3.069 % = 2 × 1.534 %
Sample calculation for velocity squared uncertainty:
 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 = 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2 × %𝛥 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2
 0.6 = 18.9 × 3.069
Processed Data Table 1
Graph 1 Showing V^2 Against 2s:
Graph 1 made using Excel Office
Graph shows a positive linear correlation between V2 and 2s. This is because both variables are
directly proportional, meaning that if one increases so will the other. Additionally, it means that
our gradient will be positive, and as the gradient is equal to acceleration then the value we obtain
for ‘g’ will also be positive. We can observe how all points pass through the lines of best fit;
therefore, there are no anomalous points.
Calculating the acceleration due to gravity:
To calculate the acceleration due to gravity I will use the equation 𝑣 2 = 𝑢2 + 2𝑎𝑠 (where
𝑣2
v=final velocity, u=initial velocity, a=acceleration and s=displacement), rearranged as 𝑎 = 2𝑠 , as
previously mentioned. The result of this equation will give us ‘g’ as I demonstrated before that
Δ𝑦
a=g. The equation of the trend line’s gradient is 𝑚 = Δ𝑥 . As for this graph Δ𝑥 = 2𝑠 and Δ𝑦 = 𝑣 2
(as each variable is plotted on the xy-axis respectively) so the equation of the gradient can also
be written as 𝑚 =
𝑣2
, and therefore, 𝑚 =
2𝑠
𝑣2
2𝑠
= 𝑎 = 𝑔.
Δ𝑦
First, I calculated the minimum and maximum gradients using the equation 𝑚 = Δ𝑥 :
(16.8−9.2)

𝑚min=

𝑚max=
= 9.5
(1.8−1)
(15.2−11.2)
(1.6−1.4)
= 10
I averaged these values to calculate a ‘best gradient’:
(10+9.5)
 𝑚best= 2
= 9.75
Then I calculated the absolute uncertainty in the gradient by using the equation Δ𝑚best= 𝑚maxmmin:
 Δ𝑚best= 10 − 9.5 = 0.5
Meaning that the value of the acceleration due to gravity in Lima is 9.750.5 ms-2.
Conclusion
From this experiment we can conclude that the value of the acceleration due to gravity in Lima is
9.750.5ms-2. Even though this value isn’t precisely accurate, and although it didn’t allow me to
answer my research question completely, I can conclude that the experiment was successful and
accurate since the theoretical value of ‘g’ (9.81ms-2) fits into the range of possible values
(9.75+0.5=9.8). Since the value I obtained is valid, the result of determining acceleration due to
gravity via method of free fall will be accurate. Measuring a freely falling body to collect data
will provide correct results.
Evaluation
Although the result was accurate, some factors inevitably affected the experiment. Despite it
remaining constant throughout all trials, air resistance still affected the time taken for the tube to
pass through the light gate. Additionally, friction between the string and the tube may have
caused it to slow down by some milliseconds. Also, neither the string nor the ruler was perfectly
straight. Even though the string was as tense as possible, if too much force was applied it became
a curve instead of a straight line as it would bend to one side by some millimeters. This increased
the uncertainty for distance which could’ve affected the results. A firmer object, such as a rod,
attached to the floor and a clamp stand (in the same way as the string in this experiment was)
could have been used in place of a string to prevent this. Random errors in the distance could be
reduced by using a ruler larger than one meter, which would allow the range in the distance to be
extended to 2.00m (for example) and take more measurements, expanding the pool of data.
On the other hand, this experiment shows that measuring time electronically with a LoggerPro is
the best way to record time as it prevents random human error from affecting the measurements’
precision and contributes to making the final calculations as accurate as possible. Overall, the
results of the experiment were correct, meaning that this method for measuring acceleration due
to gravity is valid.
Bibliography:
“Acceleration Due to Gravity - Formula, Values of g and Variations.” BYJU’S, May 13, 2019.
https://byjus.com/jee/acceleration-due-to-gravity/.
“Free Falling Object.” Accessed March 29, 2023. https://www.grc.nasa.gov/www/k12/VirtualAero/BottleRocket/airplane/ffall.html.
Aron, Jacob. “Gravity Map Reveals Earth’s Extremes.” New Scientist, August 19, 2013.
https://www.newscientist.com/article/dn24068-gravity-map-reveals-earthsextremes/#:~:text=Mount%20Nevado%20Huascar%C3%A1n%20in%20Peru,at%209.83
37%20m%2Fs2.
NUSTEM. “Measuring g via Free Fall,” June 2, 2017. https://nustem.uk/activity/measuring-g/.