Lab: Acceleration of free fall
Purpose:
To determine the acceleration due to gravity of an object in free-fall near sea level and compare the
experimental value to accepted values.
To use and assess a variety of technologies and methods for measuring the variables that can be
used to determine the acceleration due to gravity.
Theory:
Over twenty-two centuries ago, a Greek philosopher and scientist named Aristotle proposed that
there is a natural force that causes heavy objects to fall toward the center of Earth. He called this
force “gravity”. In the seventeenth century, the English scientist Isaac Newton was able to show
that gravity is a universal force that extends beyond Earth. It is the force that causes the moon to
orbit the Earth and the Earth to orbit the Sun.
When an object is in “free fall”, the only force acting on it is the force of gravity. As an object falls
freely, it accelerates. For a falling object near the surface of Earth, the rate of change of velocity is a
constant value. This value is the acceleration due to gravity, g. If you ignore air resistance, a falling
ball accelerates as if it is in free fall. You can measure the motion of the falling ball to find the value
of the acceleration due to gravity.
An object that has been launched in any direction is in a state of free fall when friction is absent and
no other forces are acting. Even an object moving upward slows down and has a negative
acceleration.
Materials:
Xplorer GLX/ SPARK
projectile launcher with ball
collision in 2-D apparatus
motion sensor (100 Hz sample rate) stopwatch
photogate (digital adapter)
time-of-flight pad
video recording device (optional)
metre stick
Procedure:
Station A:
Drop with Motion Sensor
 A motion sensor attached to a horizontal rod was directed vertically downward.
 The object was held directly below the sensor and the datalogger was started.
 The object was dropped and the motion was measured until after the object hit the floor.
 This was repeated until three similar sets of data were collected.
 For each free fall event, initial and final velocities with corresponding times were recorded in Table 1.
 A sketch the postion-time graph of the motion for the first good run was drawn and the important positions
and corresponding times were labelled (Figure 1a).
 A sketch of the velocity-time graph of the motion for the same first good run was drawn and the important
velocities and corresponding times were labelled (Figure 1b).
Table 1.
Run #
Velocities and times for free fall of a dropped ball using a motion sensor.
Initial velocity,
u / m s-1
Time for u,
ti / s
Final velocity,
v / m s-1
Time for v,
tf / s
Velocity change,
Δv / m s-1
Time interval,
Δt / s
Average acceleration, ao =
Uncertainty of acceleration, Δa =
Acceleration,
a / m s-2
Station B:
Drop with Stopwatch
 A long vertical distance was selected (stairwell) and measured and secured for safety.
 The object was dropped or launched horizontally from a specific point and the time interval to fall to the
bottom was measured.
 The time interval was measured until at least three consistent values were found.
 For each free fall event, the time interval was recorded in Table 2.
Table 2.
Time intervals for a ball falling a distance of ______________ m.
Measured time intervals, t / s
Average time,
to / s
Uncertainty,
Δt / s
Station C:
Vertical launch using Initial Velocity and Maximum Height
 The projectile launcher was placed on a horizontal surface and directed vertically upward.
 The photogate was attached to the launcher and to the digital adapter.
 “Photogate timing” was the sensor selected and “Velocity in gate” was the measurement.
o The ball was 0.025 m in diameter and the “Digits” was used to display the data
 The ball was placed in the launcher and pushed down to the lowest point using the plunger.
 Recording was started and the ball was launched upward.
 The ball was launched repeatedly until at least three consistent launch velocities were found.
 For each launch, the initial velocity was recorded in Table 3.
 The launch height was adjusted until the ball barely reached the ceiling.
 The height from the photogate to the ceiling was measured.
Table 3.
Initial velocities for a ball launched to a maximum height of ______________ m.
Measured initial velocity, u / m s-1
Average initial
velocity, uo / m s-1
Uncertainty,
Δu / m s-1
Station D
Horizontal launch using Time-of-Flight Accessory
 The projectile launcher was set to fire the ball horizontally from a measured height.
o The height is the vertical distance from bottom of launcher barrel to top of Time-of-Flight pad
 One photogate was attached to the launcher and to the digital adapter.
 The Time-of-Flight accessory (pad) was connected to a second digital adapter.
 “Time of Flight” was selected from the sensor options and Digits were the Display mode.




The ball was placed in the launcher to the first or second position and fired.
The Time-of-Flight Accessory pad was moved to be struck by the ball.
With the datalogger recording, the time of flight was recorded until at least three consistent times were
recorded.
For each free fall event, the time of flight (time interval) was recorded in Table 4.
Table 4.
Time of flight for a ball falling a distance of ______________ m.
Measured time of flight, t / s
Average time,
to / s
Uncertainty,
Δt / s
Processed Data
Table 5.
Calculated acceleration values from each of the stations.
Mean Value of
Acceleration, ao / m s-2
Station
Uncertainty of
acceleration, Δa / m s-2
Absolute error in
acceleration / m s-2
A: Drop using motion sensor
B: Drop using stopwatch
C: Vertical launch using initial velocity
and maximum height
D: Horizontal launch using time-of-flight
Calculations
Show how the acceleration was calculated for each station.
Standard calculations such as simple differences, means, and standard deviation calculations
do not need to be shown
Conclusion and evaluation
State your concluded value and uncertainty of the acceleration of free fall.
Compare your value with a cited value for the acceleration due to gravity.
Analyse the evidence of random and systematic errors in the overall investigation.
Compare the effectiveness of each method for determining the value of the acceleration due to
gravity. Identify strengths and weaknesses of the methods as well as specific sources of error
or limitations.
Identify at least three specific changes that would improve specific aspects of this
investigation. Explain the effect of each change.