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Physics HL Grade 11 Physics Free Fall IA Word Count: 2475 Research Question: How does the drop height affect the time taken for an object to hit the ground?
Introduction: The law of falling objects is among the most basic elements of physics in particular when carrying out experiments related to gravity, time, distance and speed and is also extensively applied in our day to day lives as we constantly observe the phenomenon of gravity. It is also possible to determine how the relationship between a drop height of an object and the time required to impact an object on the ground using this information, which makes it possible to discuss some aspects of both kinematics and energy and answers the purpose of this investigation since this experiment continues to examine how the drop height of a ball influences the time of impact of the object on the ground. The experiment research question is: What is the relationship between drop height and the time required to hit the ground? which was investigated and implemented with the free fall apparatus. It was through the investigation that we were able to see a pattern between the drop height of a steel ball and the time that it took to hit the ground since a graph was drawn to include a linear positive relationship between the two variables that showed that the longer the drop height of the ball was, the longer the time the ball took to hit the ground.
Background Research:
● Drop height: A drop height of a certain object is the maximum vertical height at which a certain object is dropped from, showcasing the distance it travelled given the impact of gravity. The drop height is measured assuming that the object that is being dropped has been released from rest.
● Free fall: Free fall is the motion of an object where the only force acting upon the object is gravity which results in a constant downward acceleration as gravity is a direct downward force without the influence of any other direction.
● Acceleration due to gravity: Acceleration due to gravity is the rate at which the velocity of an object increases given the force of gravity which is around 9.81 ms^-2 on earth which indicates that a falling object’s speed is altered based on its acceleration due to gravity.
● How does drop height affect potential and kinetic energy?
- The drop height of an object affects the initial gravitational potential height of the same object as both potential energy is proportional to height which can be proven by the formula PE = mgh. This hence indicates that the higher the drop height refers to a higher initial potential energy which can then be converted to a high amount kinetic energy as the object falls as the law of energy states that energy cannot be gained nor lost but can be transferred.
● Air resistance: Air resistance is a force that opposes and acts against the motion of an object as it falls and travels through air. Air resistance in experiments such as the free fall experiment causes the fall of objects to slow down to an extent as the object has to push through an opposing force.
● Derivation of relevant equations from SUVAT: Relevant equations linking to this particular investigation includes the SUVAT equation s=ut+½ at^2 where displacement is represented by the variable s , initial velocity as the variable u , time presented by t and acceleration represented by a. Since this experiment is a free fall experiment, initial velocity of the experiment is 0, the displacement can also be considered as height and lastly acceleration occurs due to gravity as the object to falling downwards. This allows us to derive the equation, s=ut+½ at^2 to h=½ gt^2, where g is 9.81 (the constant for gravity).
● Theoretical prediction: Supported by the SUVAT equation, we can theoretically predict that height is directly proportional to the square of time taken for the fall meaning that if you plot h (x-axis) against t^2 (y-axis) on a graph, a straight line should be produced.
Hypothesis: I predict that if the drop height of the ball is increased, the time taken for the same ball to hit the ground will also increase.
Scientific Reasoning: My hypothesis of the height of the drop increasing to cause an increase in the time taken to strike the ground on the ball can be supported by the scientific formula and law that apply in the field of physics, s=ut+½ at^2. It can be worked out to h=½ gt^2 because it is a free fall experiment and the beginning velocity of the experiment is 0 and the distance can be defined as the height. Finally, acceleration is also calculable since the object is falling in a straight downward direction and the object is being acted upon by gravity and therefore, we can state that acceleration is the gravity (g is 9.81). The derived equation of this experiment can be used to observe how height which has been derived out of the displacement will also be proportional to time which means
Setup:
Figure 2: Picture of Setup
Methodology:
- Turn the power supply on to enable the free fall apparatus.
- Set the height of the apparatus to 27 centi-metres by measuring it using the meter stick.
- Attach the steel ball to the top component on the apparatus. The ball is meant to be attracted to the upper part of the apparatus due to magnetic attraction between the two components.
- Wait for the steel ball to drop into the trap plate.
- Record the time.
- Repeat steps 3-5 multiple times (preferably 3-5 times) to get multiple trials in order to limit inaccuracy and to avoid random or systematic errors.
- Once 3-5 trials have been gained for each height, adjust the metre stick to multiple heights (preferably 5-8 different heights) and receive multiple trials for each height by following steps 3-5 to produce a relationship between the two variables and record the time for each trial for each height.
Raw Data Table:
Height Trial 1 Trial 2 Trial 3 Trial 4 average
27cm 0.244 0.242 0.243 0.243 0.
34cm 0.270 0.270 0.269 0.269 0.
41cm 0.295 0.294 0.294 0.295 0.
48cm 0.316 0.318 0.317 0.316 ≈0.
55cm 0.341 0.339 0.339 0.337 0.
62cm 0.359 0.359 0.360 0.359 ≈0.
69cm 0.379 0.378 0.379 0.378 0.
76cm 0.397 0.397 0.397 0.398 ≈0.
Sample calculations for finding average time for a drop height:
Example 1: Change
Height: 27 cm Trials: 0.244, 0.242, 0.243, 0.
Calculation: (0.244 + 0.242 + 0.243 + 0.243)/4 = 0.243 seconds (Adding all the trials together and dividing it by the number of trials taken).
Graphs:
Analysis:
The graph indicates an evident upward trend: the higher a height is, the higher an average time is. This is reasonable since the more distant an object is, the more time it takes to get to the ground. On the surface of it, a time-height curve would appear almost linear, when we know that the second-degree t^2 vs. h is a more valid relationship than that.
According to the kinematic formula s=ut+½at^2 , when an object is falling (u = 0 , a = g) the equation changes to h=½gt^2. This is an indication that the square of time is proportional to height. Plotting t^2 vs. h , the points will be aligned in a linear line, which demonstrates the formula to be correct. The angle of this line yields the value of g which is quite close to the known value of gravity, 9.8 ms-2. This proves that the multiple equations of motion are in agreement with free fall, hence simultaneously proving my hypothesis, “I predict that if the drop height of the ball is increased, the time taken for the same ball to hit the ground will also increase.” is correct.
At maximum error the time recorded was all over shot by the time error of ±0.001 s. This brought the best-fit line slightly above the original which resulted in a steeper slope in t^2 vs. h graph. The slope of this line is 2/g, as given in the SUVAT equation h=½gt^2. Increasing the slope causes the value of ‘g’ to be less calculated. Based on the max-error line, the gravitational
Strengths, Limitations and Improvements :
A strength of this experiment is that a series of experiments were conducted on each of the drop heights and averages were established, thus minimizing the impact of random errors and providing more credible results. A variety of drop heights were used in the experiment as well, enabling the more distinct relationship between height and time to be seen. The error in human reaction time was less with the free-fall apparatus than with manual stopwatch timing and the addition of uncertainties to both height and time made the results more believable. All in all, the data generated a good linear relationship on the t^2 vs. h graph which proves the predictions in theory and indicates high accuracy.
The significant limitation of the experiment was potential systematic errors of the apparatus. There can be a slight delay between the release mechanism of the free-fall release and the initiation of the timer (giving a consistent positive difference in the times), this is due to the free-fall release. Likewise, the trap plate or timer may fail to record the hit immediately which is one more delay. Such systematic errors would be used in explaining the small positive intercept of the graphs, since all times are not only shifted higher. Another limitation is air resistance in the room which may slightly slow down the ball resulting in measured times longer than the predictive times. Such causes do not allow the experiment to be fully accurate, although the findings are close to the theoretical beliefs.
Though the device minimizes mistakes of reaction time, there are still possibilities of human errors in reading measurements like setting the drop heights or recording them incorrectly. The other potential error is parallax on positioning the meter stick which might result in a few inaccuracies in height measurements. There can also be random errors that are caused by minor changes in the way the ball is released by the magnet. To enhance the experiment, the air resistance could be removed by a vacuum chamber and electronic timing and light gates instead of the trap plate could remove the release and detection delays. The results would also be more robust by having more trials and testing more heights. In solving these problems, the experiment would give an even closer estimate of the value of gravitational acceleration and further support the equations of SUVAT.
