Free Fall Experiment

Amparo Canto Rodríguez, María Castro Belluzzo and Rosalía Otero Naranjo 10B

Free Fall

How does the height from which the marble is dropped affect the penetration of the depth of the marble into the jelly solution?

Background Information:

A free-falling object is an object that falls because of the gravity force, so it is
in a state of free fall movement. The object has an acceleration of 9.8 m/s. Here there are the free fall/kinematic equations (Physicsclassroom.com, 2014):

In these formulas “d” represents distance, “v_i”   initial velocity and “v_f” final velocity, “t” is time and “a” is acceleration, which as I said before, it is 9.8 m/s².

There are some basic skills that we need to know: When the acceleration goes down, the number is negative (-9.8 m/s²) so a free fall object always has a negative acceleration. Acceleration and velocity are a vector, which is defined as the rate that its velocity changes. A vector is a quantity that describes the motion of objects; it marks the direction of which an object is moved or it can also be a magnitude. If the acceleration goes down, the vector goes down. If an object has been dropped from a certain height, the initial velocity (v_i) is 0 m/s. If we throw an object up straight vertical and then it returns down, the initial and final velocities are 0 m/s and when it goes up, the velocity is positive (for example 20m/s) and when it goes down the velocity is negative (for example -20m/s).

With these basic skills we can solve free fall problems using the equations in the diagram above.

In a free fall, we have the uniformly accelerated rectilinear movement (UARM) which is that in a rectilinear movement, like in free fall, the acceleration is constant. The velocity increases, but the acceleration in this case is gravity, so it doesn’t change.

Hypothesis:

If a ball is dropped from different heights, the other factors also change. Some of them stay the same, like gravity/acceleration which is always -9.8 m/s² in a free fall motion. In my experiment, the initial velocity (v_i) will also stay the same because the ball will be dropped from a specific height, so the initial velocity will always be 0 m/s. However, most of the factors do change. The final velocity (v_f) will be the one that will change the most because depending in the distance, the velocity increases or decreases. If there is more distance between the ball and the floor, the velocity will have more time to change and the gravity would give more pressure to the ball. If there is less distance, the final velocity will be less because there was less time for the ball to fall, and the gravity gave less pressure to it. Besides, time also changes a lot. If there is less distance, the ball has less time to reach the floor, and on the other hand, if there is more distance, the ball lasts more time to touch the floor. All of these hypotheses can be proved with this equation:

  

In our experiment (free fall) the acceleration stays the same in a rectilinear movement (UARM). The velocity and time change but the acceleration in this case is the same as gravity so it doesn’t hange.

If the ball has more distance, it will make a bigger hole in the plasticine surface. On the other hand, if the ball has less distance it will make a smaller hole in the plasticine surface. Depending on what material the surface is made, the hole can be deeper or not. For example, flour has smaller grains than sand or soil, so the holes would be deeper than the on the other surfaces. A plasticine surface is much harder and dense than flour, so the hole will be smaller. In my experiment I’m going to use plasticine. So if the ball is dropped from a higher space, the hole made in the plasticine would be deeper and bigger. On the other side, if the ball is dropped from a less height, the hole in the plasticine could be smaller; or maybe if the ball is dropped from a miserable distance, it wouldn’t make a very visible hole in the plasticine, or even not do it.

Variables:

-          Independent variable: The independent variable is the distance which is dropped the ball.

-          Dependent variable: The dependent variable will be how deep the hole in the plasticine surface is.

-          Controlled variable: The controlled variables which are the ones that will not change are the acceleration (-9.8 m/s^2)the initial velocity (0 m/s) , the ball (same mass, shape…) and the materials used in the experiment.

Materials:

•       Marble
•        jelly solution (250 mL H20+ 3,5g powder) 
• beaker
• scale
•  Ruler/meter
• Video camera
•   Logger Pro

Data:

3,50 grams of pouder and 250 ml of water

Height (cm)	Depth of the plasticine (cm)
10	1
20	1,9
30	2,5
40	2,9
50	3,2
60	3,5
70	5,1

Method:

1. First, we write down in the notebook the vi and the acceleration, which are always the same.
2. After that, we prepare the jelly solution, adding 250 mL of water to 3,5 grams of powder.

 

1. 3.     After that, we measure the distance from the jelly solution surface and the ball, so the height must be the exact one that I have chosen. The measures between the jelly solution and the ball have to be written on the table of the data (so its what we did). The measures have a difference of 10 cm between each other.

1. 4.      Continually, we drop the marble and when it touches the surface of the jelly solution, we have to measure the depth of the hole made in this solution, with the ruler.
   5.      At the same time, take pictures of it with the video camera.
   6.      Then we write it down in the table. 
   7.      Finally, we do the same with the other measures and we compare the hypothesis with the results.