Research of Applying Newton’s Laws of Motion to The Countermovement Vertical Jump

Introduction

The counter movement jump (CMJ) has become a commonly used indicator for assessment of an individual’s “physical fitness, specifically lower limb power and strength which has been utilised by both the general population and high performance sports”. The vertical jump height is measured as the variance between the position of the centre of mass of the individual in the starting position (a standing position) and its position at the maximum height.

There are numerous methods of collecting data from the CMJ, but a widely accepted and reliable way requires the usage of a force plate which uses ground reaction forces to calculate variables such as peak power, maximum rate of force development and jump height. “Force plates are highly sensitive to errors in force magnitude and centre of pressure location and are also used to assess foot placement and its variability during human walking, again with a high sensitivity to error”. This equipment also measures the force produced over time, how much force is happening and when it is happening, and “if the body of a mass is known, the kinetic data can be used to inform kinematics of the body’s centre of mass in terms of acceleration, velocity and displacement”. “On the other hand, it appeared that centre of gravity models can cause errors that disqualify their use as validation criteria for kinetic parameters”.

There have been several studies which have attempted to explain force-time graphs drawn from the CMJ, but with mixed results regarding sex differences. For example, Laffaye (2014) attributed sex differences in CMJ height to men’s ability to demonstrate larger relative (to body mass) peak concentric force, along with greater absolute and relative mean eccentric rate of force development (RFD). However, contrasting this, Ebben (2007) found no sex differences in CMJ RFD or movement time. Similarly, Rice (2017) reported no sex differences in peak force or RFD calculated from the CMJ.

In order to begin analytic research and coaching from the statistics and information provided, it is essential that Newton’s laws are understood and used to explain how individuals control their movements with force. Newton devised three laws which perfectly describe the relationship between force and movement. The purpose of the current study, therefore, is to distinguish the relationship between Newton’s three laws and the CMJ and use these laws to explain changes of force throughout the CMJ.

Methodology

Participants

Two participants (one male: age: 20 years, height: 185cm, body mass: 78.2kg; one female: age: 20 years, height: 162cm, body mass: 59.8kg) with no history of musculoskeletal impairments gave written consent to participate in this study. Ethical approval was sought and granted from the University Research Ethics Committee.

Procedures

Prior to data collection, participants performed a dynamic warm-up and were familiarised with all procedures. Participants were instructed to stand with the feet positioned shoulder width apart and to place the hands on the pelvis. Participants had to squat to a self-selected depth and to perform the CMJ as fast and as high as possible.

Data Collection

The CMJ’s were recorded using two force plates with a sampling frequency of 1000 Hz. Body weight was determined prior to the commencement of the CMJ. Raw vertical force-time data were exported and analysed using a Microsoft Excel spreadsheet.

Data Analysis

The data was analysed through excel spreadsheet (version 2016, Microsoft Corp., Redmond, WA, USA). Net force was calculated by subtracting the weight of the participant from the original force. Acceleration was then solved by dividing net force by body mass; velocity was figured out via the trapezoid rule (integration) using acceleration data in respect to time; displacement is then calculated by velocity in respect to time.

Results

The overall findings of this lab suggest that males can produce more force overall and more force per kg of their bodyweight. The male also achieved a greater acceleration and velocity but had a lower displacement to the female. Although the male’s displacement was lower, they still attained a higher jump than the female which suggests there is a relationship between normalised force and jump height.

Discussion

There are three stages to the CMJ; unweighting phase, braking phase and propulsive phase. Each one can be explained via Newton’s laws of motion. Newton’s 1st law of inertia explains the unweighting phase by stating that “Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it” (Newton, 1987). As seen from Figures 1 and 2, both individuals cause a negative external force, breaking their state of inertia at rest and resulting in a negative velocity. Peak downward velocity is achieved at the end of the unweighting phase, therefore, an upward force has to be applied to increase velocity back to zero which is seen from Figures 1 and 2 during the braking phase where a massive amount of force is applied. Additionally, throughout the entire movement, Newton’s 1st law is always in effect because there is a constant change in velocity which must mean there is a constant force over bodyweight applied.

Newton’s 2nd law states that “the acceleration of an object depends directly upon the net force acting upon an object, and inversely upon the mass of the object”. As seen from Figures 1 and 2, there is a proportional change of shape in acceleration as there is a change in force explaining that ‘F = M x A’. Furthermore, when either subject applies a downward force, a negative acceleration occurs and when a positive force is applied, a positive acceleration occurs. Newton’s 2nd law also says that “acceleration for any given force is inversely proportional to the mass”. The peak force produced by participant 2 is roughly 1400N which causes an acceleration of 15m/s². However, looking upon participant one’s results, whom has the larger mass, the acceleration that is produced at 1400N is below 10m/s² which supports Newton’s 2nd law further.

The braking phase consists of the subject continuing to travel down and does not end until the subject stops and has zero velocity, which is when the massive spike of force applied can be seen as this is the point where the subject applies a positive force to change their motion from downwards to upwards. Near the end of the braking phase when the subject stops and reaches zero velocity is the moment when peak force is at its highest. This surge of force can be explained by Newton’s 3rd law which states that “when two bodies interact to produce a force, the force on one body is equal in magnitude and opposite in direction to the force on the other body”. This is exemplified throughout the braking phase because the subjects slow down due to them pushing down on the ground meaning the ground pushes back up with an equal and opposite force.

During the propulsive phase, both the 2nd and 3rd law is displayed. As the participants are pushing down on the ground, an equal and opposite ground reaction force can be seen because the participant accelerates upwards and there is a positive change in their displacement. However, the 2nd law explains that only the participants body moves because they interacted with a more massive object being the earth.

However, when comparing results between individuals there are several variables which must be taken into consideration such as training and sporting background. For instance, certain participants may have experience in technique or training relating to the CMJ which would allow them the ability to produce more force and a higher jump. Some individuals may also have a greater stretch-shortening cycle (SSC) which refers to the countermovement action and allows the individual to produce more force and move quicker. “A non-fatiguing SSC exercise demonstrates considerable performance enhancement with increased force at a given shortening velocity”. This can explain why there is such significant differences in results between the CMJ and squat jump and why the SSC should be taken into consideration when comparing these sorts of results.

Some limitations exist in the current study. First, the current study has a low sample size to compare male and female individuals. However, 57 individuals had previously been a part of a study designed to examine the performance in vertical jump by imposing different stretch loads on leg extensor muscles. Komi (1998) found from this lab that the females differed substantially from the two male groups and their performances were from 54 to 67 percent below that of their male counterparts. Therefore, this lab supports the current study. Secondly, the current study’s reference to the different phases of the CMJ may differ to that of other study’s which could implicate discussions and comparisons. Nevertheless, it is important that researchers refer to normalised force and force per KG so that different projects are compatible, and data can be compared to either prove or disprove certain theories. Finally, the current study has the subjects perform just one CMJ whereas other researches prefer three or more. However, there is significant research which proves either way that males produce more force than females. McMahon (2017) conducted a study with the purpose to explore differences in CMJ phase characteristics between male and female athletes. Fourteen men and fourteen women performed three CMJs on a force platform from which a range of kinetic and kinematic variables were calculated. Relative force-time curves were similar between sexes, but relative power, velocity, and displacement-time curves were greater for men of normalized jump time. “The CMJ distinguished between sexes, with men demonstrating greater jump height through applying a larger concentric impulse and, thus, achieving greater velocity throughout most of the concentric phase, including take-off”.

Conclusion

From the discussion, it can be concluded that the experiment was successfully conducted with the purpose being able to apply Newton’s laws of motion to the CMJ. The results provided statistical support and the force patterns allowed Newton’s laws to explain what was happening and why. This was the purpose of the force plate data, but it also enabled dissection of the different phases and allowed comparisons to be made between male and female data.

The study has shown that Newton’s three laws are active throughout the CMJ and can be used to analyse jump performance. The study also shows that males produce a greater overall force, more force per kg of bodyweight and can achieve a higher jump height compared to females.

Research data is essential in sports, especially with high performing athletes as it provides feedback and ways of analysing data and improving performance. “Research plays in innovation and the development of effective evidence-based practices in high-performance sport, often leading to large rewards for success”. “The CMJ is also commonly used as part of athlete training programs to promote the development of lower body power to provide insight into neuromuscular function and fatigue” (McMahon, 2017). Therefore, the understanding of Newton’s laws and its application to the CMJ is paramount in performance analysis.