The Concept of Free-fall

The concept of free-fallvides under pinning knowledge in order to understand air resistance and consequently how fast objects fall. Without proper knowledge of these concepts, it wouldn’t be possible for people to use parachutes or go skydiving, for instance. The objective of the experiment was to neglect the drag force caused by air resistance and try to calculate the acylation using suvat equations. Comparing the results with the actual acceleration then gives insight on how air resistance affects these bodies. Theory To understand the concept of free-fall, it is first necessary to refer to Newton’s Second Law of Motion, which states and is commonly known by the formula Where F is the force (N), m is the mass (kg) and a is acceleration (m/s²).

In the scenario of any given object falling freely within the Earth’s gravitational field, its acceleration will always be the one due to gravity, amounting to approximately 9.8 m/s². This acceleration is independent of the mass of the object since gravity will act equally on each object. If there weren’t any other forces acting on the objects, then every object in free fall under the same conditions would fall at the time. However, this doesn’t happen due to an opposing Force exerted by the air, known as drag. In anybody falling towards Earth, the acceleration will be directed downwards and the drag upwards. This drag force helps deaccelerate the body and is expressed by the formula Where p is the density of the air, A is the area of the object that is in contact with the air, Cd is the drag coefficient and v is the velocity. As the body starts to deaccelerate, it reaches one point where equation 1 will be equal to equation two and at that point, the velocity will be constant. This concept is crucial as it helps us predict how fast an object will fall and what to do to reduce its landing speed.

On the other hand, there are cases where the drag force is too small that it can be ignored and in these instances, we can use SUVAT equations to determine either the time, the acceleration of the distance of something in free-fall. Given the suvat equation, Wheres is the total distance, u0 is the initial velocity, t is the time a is acceleration. Using equation 5 you can find out the acceleration, but there’s also the possibility of plotting a graph of the time squared against the distance, which would mean that the slope of the graph would be half the amount of a, due to the fact that in the formula we’re using 2s. Experimental method In order to calculate the acceleration of the two balls, we used a set of devices that when connected between each other could precisely calculate the time between the ball dropped and it reached the floor. A magnet drop box was placed at the top in a way that when it was on, it would hold the balls (a small magnet was added to the plastic balls so it could be held suspense). Once the timer was activated, the drop box released the ball and when it reached the detector pad at the bottom, the smart timer would give the total amount of time taken. This can see in more detail on the pictures below: The drop box was also set up in a way where its height was adjustable, and it was possible to try the experiment with several different heights.

The total distance was calculated used a measuring tape. After collecting the time measurements for different distances for each ball, a plot of time squared against distance was done using equation … and the gradient of that times 2 would give us the acceleration. Alternatively, it was also possible to rearrange the formula in terms of a and get the acceleration from that. In this experiment, however, the first method was used for both balls. With that data, it was then possible to compare the results with the expected acceleration due to gravity.

Results Looking at the graph, it is noticeable that both lines are close to each other, but that their gradient, and consequently their acceleration, is different. The calculation of the gradient was done using equation … and then it was multiplied by 2. For the plastic ball the gradient was Mpb =9.12m/s2 and for the steel ball, it was MSB = 9.67 m/s2.