Worksheet4: Free Fall
Galileo, with his numerous experiments was able to find out 2 very important
things:
1) All objects, independent of their size, shape or mass fall towards the earth in
the same way. This means that a feather and an elephant will take the same
time to fall from the same cliff.
2) The so-called “free fall movement" is an accelerated movement, with constant
acceleration. It is similar to the movement of a car accelerating on a freeway,
with the difference that it is an up-down acceleration.
Let's explore a bit what all this means:
A) Go to the web site: http://www.explorescience.com/freefall.htm
Here we can experiment with different sizes and masses of a ball in different
types of atmosphere. This is all done by “computer simulation”. Simulations are
just like games, where the laws of physics tell us what is going on.
In this page:
 Mass (kg): Mass of the ball being released by the hand above. We can adjust
the mass of the ball between 0.01kg (10 grams) and 0.5kg (500 grams)
 Radius (m): radius (size of the ball). One diameter is 2 times the radius of a
ball. We can have a ball as small as 0.01m radius (10 cm radius = 20 cm
diameter) and a ball as large as 1m radius (2 m diameter. This is a VERY BIG
ball). Unfortunately the simulation does not change the sizes in the drawing,
but we can use our imagination to check it out.
 Height (m): Height from which we drop the ball. It goes from 1m to 100m.
 Wind speed (m/s): This is a tricky one. We can make downward-going wind
and upward-going wind in this game… The upward-going strongest wind is –
1m/s and the downward-going strongest wind is +1m/s.
 Air density (kg/m3): How “heavy” is the air or atmosphere we are playing with
here? 1kg/m3 air density means that 1 cubic meter of air weighs 1 kg. 1kg/m3
is the same as 0.001g/cm3. To give you the idea, water’s density is 1g/cm3
but we will not be using this button….
 Delta t in seconds: is the size of the time intervals we look at our falling ball.
We will not be dealing with it either….
Other controls are bouncing, and how to plot the graph.
QUESTION 1: The table below describes the settings for this question.
Setting
Mass(kg)
Radius(m) Height(m)
Wind(m/s)
1
2
3
4
0.01
0.5
0.01
0.5
0.01
0.01
1
1
0
0
0
0
10
10
10
10
Air Dens.
(kg/m3):
0
0
0
0
Delta
T(s)
0.03
0.03
0.03
0.03
What is the time it takes for the ball to fall for each one of the settings above?
Record your answer below. (The time is shown next to the graph on the left.)
Setting
1
2
3
4
Time it takes (s)
What is your conclusion?
QUESTION 2: The table below describes the settings for this question.
Setting
Mass(kg)
Radius(m) Height(m)
Wind(m/s)
1
2
3
4
5
5
5
5
0.01
0.01
0.01
0.01
0
0
0
0
10
10
10
10
Air Dens.
(kg/m3):
0
1.5
3.5
5
Delta
T(s)
0.03
0.03
0.03
0.03
What is the time it takes for the ball to fall for each one of the settings above?
Record your answer below. (The time is shown next to the graph on the left.)
Setting
1
2
3
4
What is your conclusion?
Time it takes (s)
QUESTION 3: The table below describes the settings for this question.
Setting
Mass(kg)
Radius(m) Height(m)
Wind(m/s)
1
2
3
4
5
5
5
5
0.30
0.30
0.30
0.30
0
0
0
0
10
10
10
10
Air Dens.
(kg/m3):
0
1.5
3.5
5
Delta
T(s)
0.03
0.03
0.03
0.03
What is the time it takes for the ball to fall for each one of the settings above?
Record your answer below. (The time is shown next to the graph on the left.)
Setting
1
2
3
4
Time it takes (s)
What is your conclusion?
QUESTION 4: The table below describes the settings for this question.
Setting
Mass(kg)
Radius(m) Height(m)
Wind(m/s)
1
2
3
4
5
5
5
5
0.01
0.4
0.7
1.
0
0
0
0
10
10
10
10
Air Dens.
(kg/m3):
0.3
0.3
0.3
0.3
Delta
T(s)
0.03
0.03
0.03
0.03
What is the time it takes for the ball to fall for each one of the settings above?
Record your answer below. (The time is shown next to the graph on the left.)
Setting
1
2
3
4
What is your conclusion?
Time it takes (s)
ANSWERS
QUESTION1: The table below describes the settings for this question.
Setting
Mass(kg)
Radius(m) Height(m)
Wind(m/s)
1
2
3
4
0.01
0.50
0.01
0.50
0.01
0.01
1
1
0
0
0
0
10
10
10
10
Air Dens.
(kg/m3):
0
0
0
0
Delta
T(s)
0.03
0.03
0.03
0.03
What is the time it takes for the ball to fall for each one of the settings above?
Record your answer below. (The time is shown next to the graph on the left.)
Setting
1
2
3
4
Time it takes (s)
1.4
1.4
1.4
1.4
What is your conclusion? A: In the absence of air, all objects, independent of
their shape and mass will fall towards the earth the same way. This is because
the only acceleration acting upon them is gravity.
QUESTION2: The table below describes the settings for this question.
Setting
Mass(kg)
Radius(m) Height(m)
Wind(m/s)
1
2
3
4
0.50
0.50
0.50
0.50
0.01
0.01
0.01
0.01
0
0
0
0
10
10
10
10
Air Dens.
(kg/m3):
0
1.5
3.5
5
Delta
T(s)
0.03
0.03
0.03
0.03
What is the time it takes for the ball to fall for each one of the settings above?
Record your answer below.
Setting
1
2
3
4
Time it takes (s)
1.4
1.4
1.4
1.4
What is your conclusion? A: Oh! The same result, even for varying air density.
Why? We will see in the next question, when we vary the size of the object that
the air matters. This is because of friction of the air and the surface of the ball.
The larger the surface of the ball, i.e., the larger the contact between the surface
of the ball and particles of air, the larger the force “holding the ball up”: friction!
QUESTION3: The table below describes the settings for this question.
Setting
Mass(kg)
Radius(m) Height(m)
Wind(m/s)
1
2
3
4
0.50
0.50
0.50
0.50
0.30
0.30
0.30
0.30
0
0
0
0
10
10
10
10
Air Dens.
(kg/m3):
0
1.5
3.5
5
Delta
T(s)
0.03
0.03
0.03
0.03
What is the time it takes for the ball to fall for each one of the settings above?
Record your answer below.
Setting
1
2
3
4
Time it takes (s)
1.4
2.4
3.4
4.0
What is your conclusion? A: We did the same experiment as in question2, but
this time the ball was larger. The contact of the surface and the air was much
larger, so that friction started to matter, and the heavier, denser the air, the
slower the ball falls. The heavier the air, the larger the number of air molecules or
atoms that will be in contact with the surface of the ball.
QUESTION4: The table below describes the settings for this question.
Setting
Mass(kg)
Radius(m) Height(m)
Wind(m/s)
1
2
3
4
0.50
0.50
0.50
0.50
0.01
0.40
0.70
1.0
0
0
0
0
10
10
10
10
Air Dens.
(kg/m3):
0.3
0.3
0.3
0.3
Delta
T(s)
0.03
0.03
0.03
0.03
What is the time it takes for the ball to fall for each one of the settings above?
Record your answer below.
Setting
1
2
3
4
Time it takes (s)
1.4
1.8
2.5
3.3
What is your conclusion? A: Again the same thing, but this time instead of
varying the density of air, we varied the size of the ball… the important thing to
remember here is that friction depends on the area of contact. This might be a
little hard to see with the simulation, especially since the ball in the picture does
not change sizes.