# Kinesthetic Activity Analysis

### By Jessi Winter

## Background Information

Early soccer balls began as animal bladders or stomachs that would easily fall apart if kicked too much. In 1838, Charles Goodyear and Domenico Nobili introduced the use of rubber and their theories of vulcanization, which dramatically improved to soccer ball. Vulcanization is the treatment of rubber to give it certain qualities such as strength, elasticity, and resistance to solvents. Vulcanization of rubber also helps the football resist moderate heat and cold. Charles Goodyear's innovation increased the bounce ability of the ball and made it easier to kick. During the 1900s, soccer balls were made out of rubber and leather, which was perfect for bouncing and kicking the ball. However, when heading the soccer ball (hitting it with the player's head), it was usually painful. This problem was most likely due to water absorption of the leather from rain, which caused a considerable increase in weight. Head and neck injuries became very common. Early soccer balls also deteriorated very quickly, as the leather used in manufacturing them varied in thickness and quality. Today, the ball's spherical shape, as well as its size, weight, and material composition, are specified by Law 2 of the Laws of the Game maintained by the International Football Association Board. Additional standards are specified by FIFA for the balls used in their competitions. Elements of the soccer ball today that are tested are the deformation of the ball when it is kicked or when the ball hits a surface.

The purpose of my study is to better understand the kinesthetic activity of a soccer ball. I am interested in finding the value of the force I apply on a soccer ball when I kick it, and when the ball hits the wall. I am also curious as to how Newton's Laws Of Motion apply to my study.

## Data Collection Methods

The soccer ball I used in my study was a Size 5 Mitra brand soccer ball. It weighs 14 ounces, or 0.4 kilograms. A video was taken of me kicking a soccer ball against a wall. The camera was held steady during the recording to make sure that my data points would not be off when I analyzed the video in Logger Pro. While I was analyzing the video, I used the length of the classroom doorway box to set my measurement scale. My data points during video analysis were consistently placed in the middle of the soccer ball. If the data points were not placed in the middle of the ball every time, my findings in Logger Pro would not be reliable.

## Newton's Laws of Motion

## Newton's First Law

Newton's first law of motion states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. In my study, the soccer ball begins at rest. It will continue to stay at rest, as long as the force of gravity and normal force are the only forces acting upon it. When at rest, the ball is at equilibrium because the opposing forces are balanced. Once another force acts upon the soccer ball, such as the applied force from me kicking it, the ball will no longer be at rest. It will begin to accelerate, move at a constant speed for a while, and then slowly come to a stop. In my study, the ball accelerates after I kick it, moves at a constant speed, and then hits a wall, which causes it to accelerate in the opposite direction. Because the ball is rolling along the floor, there is also a force of friction acting against the applied force. The unbalanced force is the applied force, because it is it is larger than its opposing force. To find the unbalanced force acting upon the soccer ball, I took the mass of the ball multiplied by the acceleration of the ball. This equation is Fu=ma. If there was no force of friction acting upon the soccer ball, it would keep rolling at a constant speed until another force acted upon it.

## Newton's Second Law

Newton's second law of motion states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. In simpler terms, this means that acceleration is produced when a force acts on a mass. When I apply a force to the soccer ball by kicking it, the ball moves and accelerates. When the ball hits the wall, the wall and ball produce a force against each other, which causes the ball to accelerate in the opposite direction.

## Newton's Third Law

Newton's third law of motion states that for every action, there is an equal and opposite reaction. The direction of force on the first object is opposite to the direction of force on the second object. In my study, the soccer ball is resting on the floor. The floor applies an upward force on the ball, and the ball applies a downward force on the floor. The downward force is the force of gravity, which can be calculated by multiplying the acceleration of gravity by the object's mass. -9.8 meters per second squared is the acceleration of gravity. The acceleration of gravity is negative because gravity pulls objects down towards the earth. When I kick the soccer ball, I apply a force on it. Because of this applied force, the ball moves. The force of my kick is the action force. As my foot hits the ball, it is pushing it to the left. The ball pushes back on my foot with the same amount of force, only the opposite way. The force that the ball exerts on my foot is called the reaction force. An action force and the reaction force that results are called a force pair. Newton's third law states that the forces in a force pair are equal in size, but opposite in direction. Because there is no opposite force acting against the applied force of my kick, the ball accelerates. The same applies for when the soccer ball hits the wall.

## Video Analysis of Kinesthetic Movement

**Analyzing The Motion Of The Ball In Logger Pro**

**Finding The Acceleration Of The Ball After I Kick It**

X Velocity (m/s) = -5.711 (m/s^2) * Time (s) + 6.911 (m/s)

I found the slope of this section of the graph to be -5.711 (m/s^2) * Time (s) + 6.911 (m/s). This means that the acceleration of the ball after I kick it is -5.711 meters per second per second. The acceleration is negative because it is moving to the left, in the negative direction according to a number line. So, the soccer ball moves at 5.711 (m/s) in the first second, but in the 2nd second, it is moving at 11.422 (m/s). After each second, the ball's acceleration increases by 5.711 meters per second.

The y-intercept of this section of the graph was 6.911 (m/s). The y-intercept is the starting velocity of the ball. The starting velocity of the ball was actually 0 (m/s), because the ball was initially at rest. I assume that I must not have placed a point on the ball before it began moving during video analysis.

**The Ball At Constant Velocity**

X Velocity (m/s) = 0.2310 (m/s^2) * Time (s) + -2.461 (m/s)

The slope of this graph is 0.2310 (m/s^2). This means that the acceleration of the ball increases by 0.23 (m/s) after every second the ball is moving.

The y-intercept of the graph is -2.461 (m/s). This means that the beginning velocity of the soccer ball was 2.461 (m/s)

**The Acceleration Of The Ball After It Hit The Wall**

X Velocity (m/s) = 5.398 (m/s^2) * Time (s) + -14.64 (m/s)

The slope of this graph was 5.398 (m/s^2). For every second the ball is rolling during this time, the ball's acceleration increases by 5.39 (m/s^2).

The y-intercept of this graph was -14.64 (m/s). This means that the starting velocity of the ball was -14.64 (m/s). The starting velocity of the ball is negative because it was moving in a negative direction before it hit the wall.

## Force Analysis of Kinesthetic Movement

**Force Diagram Of The Soccer Ball At Rest**

When the ball is at rest, only two forces are acting upon it: the force of gravity and normal force.

The force of gravity is always present. I calculated the force of gravity by multiplying the ball's mass (0.4 kg) by the acceleration of gravity (-9.8 m/s^2). This gave me a force of gravity of -3.92 newtons. The force of gravity is negative because gravity pulls objects down towards earth.

At rest, the ball is at equilibrium, meaning all of the opposite forces are equal. So, this means that the normal force must be equal to the force of gravity because they are acting opposite each other. The normal force of the soccer ball is 3.92 newtons. It is not negative because the normal force is opposite the force of gravity, so it must be positive.

**Force Diagram Of The Soccer Ball Being Kicked**

The force of gravity is always present. To find the force of gravity, I multiplied the acceleration of gravity (-9.8 m/s^2) by the soccer ball's mass (0.4 kg). This gave me a force of gravity of -3.92 newtons.

A normal force is present because the ball is resting on the floor as it is being kicked. The normal force is equal to the force of gravity, because the ball is exerting the same amount of force on the floor that the floor is exerting on the ball. The normal force is positive because it is the force that the floor is exerting on the ball. This force is exerted onto the floor from the ground, upwards. The normal force is also opposite the force of gravity. The force of gravity is negative, so the normal force must be positive.

When my foot hits the ball, it is applying a force to the ball. To calculate the force I applied on the soccer ball, I used the equation Fu=ma. Fu is the unbalanced force, m is the mass of the soccer ball, and a is the acceleration of the soccer ball. I found the acceleration of the ball in Logger Pro by highlighting the part of the graph that shows the ball accelerating after I kick it. I then added a line to this part of the graph, which gave me the line's slope. The slope of this line is equal to the ball's acceleration. Multiplying the ball's mass (0.4 kg) by the ball's acceleration (5.71 m/s^2) gave me an unbalanced force of 2.28 newtons. The unbalanced force is equal to the applied force because there is no opposite force acting against the applied force.

**Force Diagram Of The Soccer Ball Hitting The Wall**

As always, the force of gravity is always present. To calculate the force of gravity, I multiplied the acceleration of gravity (-9.8 m/s^2) by the mass of the soccer ball (0.4 kg). This gave me a force of gravity of -3.92 newtons. The force of gravity is negative, because it is pulling the ball down towards the ground.

A normal force is present because the ball is rolling along the floor. The normal force is equal to the force of gravity, because the ball is exerting the same amount of force against the floor that the floor is exerting on the ball. The normal force is positive because it is the force that the floor is exerting on the ball. This force is exerted onto the floor from the ground, upwards. The normal force is also opposite the force of gravity. The force of gravity is negative, so the normal force must be positive.

The applied force is the wall pushing back against the ball, causing the ball to move in the opposite direction. To find the applied force, I used the equation Fu=ma. **Fu** is the unbalanced force, **m** is the mass of the soccer ball, and **a** is the acceleration of the soccer ball. I found the acceleration of the ball in Logger Pro by highlighting the part of the graph that shows the ball accelerating after hitting the wall. I then added a line to this part of the graph, which gave me the line's slope. The slope of this line is equal to the ball's acceleration. Multiplying the ball's mass (0.4 kg) by the ball's acceleration (5.398 m/s^2) gave me an unbalanced force of 2.16 newtons. The unbalanced force is equal to the applied force because there is no opposite force acting against the applied force.

## Conclusion

## Summary of Forces

The first phase of motion is when the ball is at rest. The forces acting upon the ball while it is at rest are the force of gravity and normal force. I found the force of gravity to be 3.92 newtons by multiplying the mass of the soccer ball (0.4 kg) by the acceleration of gravity (9.8 N). Because the ball is at equilibrium while at rest, opposite forces are equal to each other. So, the value of normal force is the same as the value of the force of gravity.

The second phase of motion is when I kick the ball. The forces acting upon the ball during this phase are the force of gravity, applied force, force of friction, and normal force. The force of gravity and the normal force are the same during the second phase as they were in the first phase. First, I found the unbalanced force, which is 2.28 newtons. To find the unbalanced force, I multiplied the soccer ball's mass (0.4 kg) by the acceleration of the soccer ball (5.71 m/s^2). I then found the force of friction by adding the force of gravity (3.92 N) to the unbalanced force (2.28 N). I found the force of friction to be 6.2 newtons. To find the applied force, I added the unbalanced force (2.28 N) to the force of friction (6.2 N).

The third phase of motion is when the ball hits the wall. The force of gravity and the normal force are still the same during this phase. There was an applied force acting upon the ball as well: the wall pushing back against the ball. To find the applied force, I just used the equation Fu=ma because the applied force is the unbalanced force in this situation. So, I multiplied the soccer ball's mass (0.4 kg) by the acceleration of the ball (5.398 m/s^2) to find an applied force of 2.16 newtons.

## Restatement Of Newton's Three Laws

I used Newton's three laws to explain the motion of the soccer ball in depth. Using Newton's three laws of motion, I explained how each force directly affected the soccer ball's motion. Newton's first law states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. In my study, the soccer ball began at rest. If I did not kick the soccer ball, it would have stayed at rest until another force acted on it. Also, if I did kick the ball but there was no wall for the ball to hit and no force of friction acting against the ball, it would keep rolling at a constant velocity until another force acted on it. Because there was no opposite force acting against the applied force of my kick, I knew that the force applied by my foot was the unbalanced force. This also applies to when the ball hits the wall. There is no opposite force acting against the force applied by the wall, so it is unbalanced.

Newton's second law states that acceleration is produced when a force acts on a mass. When the force of my foot acted on the mass of the ball, it produced an acceleration. The ball was not at rest anymore, so the ball was not at equilibrium, and the forces did not balance. The unbalanced force was the force applied by my foot because there was not force acting against the force of my kick. According to Newton's second law, this means that the force of my kick caused the ball to accelerate. Examples of Newton's second law were found when the ball hit the wall as well. The ball hit the wall with a force, and the ball produced that same amount of force back onto the ball. The force of the wall acted on the mass of the ball, causing it to accelerate back the way it came from. When the ball is moving, it is not at equilibrium, so the forces do not balance. The unbalanced force was the force applied by the wall, which produced an acceleration of the ball, according to Newton's second law.

Newton's third law states that for every action, there is an equal and opposite reaction. When the soccer ball is resting on the floor, the floor applies an upward force on the ball, and the ball applies a downward force on the floor. When I kick the soccer ball, I apply a force on it. The ball pushes back on my foot with the same amount of force, only the opposite way. Newton's third law states that the forces in a force pair are equal in size, but opposite in direction. My foot is pushing the ball to the left, and the ball is pushing against the ball to the right. Because there is no opposite force acting against the applied force of my kick, the ball accelerates, according to Newton's second law. The same applies for when the soccer ball hits the wall, only the forces are opposite in direction.

## Real Life Application

My study could possibly be used by a soccer player to find out how much force they need to apply on a soccer ball to get it to move a certain distance. It could also be helpful for people who want to learn how Newton's laws affect the motion of an object.