Newtons Laws In Human Motion Philosophy Essay

At this stage we are ready to move on to the second part of our studies. So far in part one of the text, we have covered the relevant anatomy and physiology to give us the fundamentals to understand to understand kinesiology and basic biomechanics. In part two of the text we will focus more on the mechanics of movement and look at numerous factors ranging from gravity, to force, to buoyancy, to acceleration, etc. and evaluate how they are affect various sports performance or even simple exercise movements. Part two of the text will also allow us to see more clearly how these kinesiological and mechanical factors affect our everyday routines by considering how simple household tools, like can openers, or shovels, allow us to use mechanical concepts to perform work more easily.

In order to do this it is best to we start with a review of Newton’s laws of motion. You will recall from the earlier, chapter 2, that Sir Isaac Newton lived from 1642 to 1727 AD. Sir Isaac Newton was an English physicist, mathematician, astronomer, and theologist to name but a few and he is arguably one of the foremost intellects of all times. His original findings form the basis for the studies of many modern-day sciences and his findings remain unchanged to this day. Newton’s book (Philosophaie Naturalis Principia Mathematica) was published in 1967 and is generally considered amongst the most influential books in science. It is often referred to as the ‘Principia’ and it was here that Newton described his three laws of motion and his concept of universal gravitation. He identifies length, time, and mass, as the fundamental components of mechanics and these factors either separately or in combination determine the outcome of Newton’s laws. These laws are integral to our understanding of sports kinesiology and they are universal in their effect. Their influence is profound in sports affecting motion of projectiles, speed of movement, resistance and much more. For these reasons we will also look at elements of movement and motion to get a better understanding of how these Newtonian Laws actually apply. So let us now take a more detailed look at Newton’s Laws.

Newton’s first law: the law of inertia

Newton’s first law, the law of inertia, is often formally stated as “an object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and in the same direction, unless acted upon by an unbalanced force”.

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You will note this description has two parts: one referring to objects at rest, the other referring to objects in motion. In other words, objects will keep doing what they are doing unless some other force is applied. Examples of this law abound around us. For example, your television set continues to sit in the corner of the room until you apply a force to move it, it just doesn’t move by itself. It is easier for us to understand this law since it applies to stationary objects versus objects in motion. Sometimes the analogy of carrying a tray of water is used to illustrate both the stationary and motion components of the law on inertia. Imagine you picked up a tray of water and began to walk with it. You would notice that more water spills when you start and when you stop versus when you are walking. This spillage at the start was basically because the water wanted to stay where it was in its stationary state so when you move he water flows backwards towards you. This spillage that occurred when you stopped moving was basically because the water wanted to keep moving and in this case spills away from you. In both cases the water wanted to keep doing what it was doing and its movement was towards its current state (of motion). In sports and activities we often see this type of motion at work. Think about riding your bike and flying over the handlebars when you hit a stump or a car. Think about when you trip on something, your momentum makes you fall forward. In these examples your motion continues in a forward direction and never in a backward direction (unless you’re moving backward). An entertaining example occurred when I was a boy. A friend and I had been a kayaking for the day and when we finished we put the kayaks on the roof of our car. As we began driving the straps holding down the kayak became loose. After a few miles we drove around a corner and a pig ran onto the road. I slammed on the brakes only to witness the kayaks fly the roof and skid down the road for 15-20 meters. Fortunately the kayaks missed the pig, but we got a nice illustration of objects in motion staying in motion. Now, had we not tied to kayaks on in the first place, they would have slid off the road as soon as we accelerated to leave the lake. This would have given us our stationary inertia example but the straps interfered with the natural tendency. Sometimes we interfere with these natural tendencies in order to protect ourselves. Safety belts in cars are one such example. If you crash (or quickly apply the brakes), the natural tendency is for you to be thrown forward. Seatbelts prevent this inertial reaction with the assumption that you will suffer less injury if you are not thrown forward since you might hit something else but instead remain attached the larger object, the car.

Simply put, the term inertia relates to the resistance an object has to its state of motion. Now, the more difficult aspect to understanding the law of inertia is how and when it applies to moving objects. We all know that moving objects eventually stop and the reason for this is that another force begins to act on the object. That force is friction (we will talk more about this later).

So what other factors affect inertia? Well, the main factor that affects inertia is the object’s mass. Heavier objects are more difficult to start moving and stop moving. Think about how hard it is to push a car versus a bicycle. Then think about how hard it is to stop either! The car would be harder in both cases. In other words inertia is a quantity that is solely dependent on mass. Big objects are harder to move and harder to stop. Take a look at the following simple questions to test your understanding of these concepts so far!

Practice questions

Consider that there is significantly less gravity on the moon. Let’s assume for a moment that there was no gravity or frictions. What would happen in the following situations?

Throwing a stone.

Hitting a golf ball.

Answer:

a). it will eventually stop.

b). it will continue in the same direction at the same speed.

The answer is ‘b’.

A 5 kg object is moving horizontally at 5 m/s. How force is needed to keep it moving in the same direction?

Zero.

5N

Less force than it took to start.

The answer is ‘a’.

In both of these problems the answer lies in the fact that the objects simply will keep doing what they were doing especially since there is no gravity or friction to affect their action.

Hopefully these simple practice questions will allow you to better understand this first law, especially as it applies to objects in motion. I always have a harder time understanding the motion piece versus the stationary piece. This discussion of mass and inertia is an appropriate lead in to our second Newton’s law which is the law of acceleration. Since objects with a larger mass of greater inertia they are also more difficult to accelerate and according to Newton an object will only accelerate if there is a net or unbalanced force acting upon it! Let us take a closer look at Newton’s second law.

Testing your understanding: Other Everyday Examples!

If you think for a moment you will find that you actually experience examples of Newton’s 1st Law many times every day. Have you ever been in an elevator and gotten a little motion sickness from the sudden acceleration or deceleration? If so, this is because of the movement of blood, or lack of movement of blood depending upon whether you are starting or stopping. Perhaps you were washing your hair and the shampoo bottle is nearly empty. In this case you turn it upside down and rapidly accelerate it and then stop it suddenly to let the remaining shampoo come to the top. Here, the shampoo wanted to keep moving and did so until it hit the cap of the bottle. Earlier on we used the example of seat belts in cars to stop you from flying forward during an accident when the car hits something in front of you, well, when you get hit from behind, the headrests are designed to prevent your head from flying backwards and causing whip-lash. So all around exist tools etc. that are designed to take advantage of or minimize the effects of Newtons 1st Law.

Newton’s second law: the law of acceleration

One could argue that of all the mechanical and kinesiological aspects in support, none is more important than acceleration. Acceleration (and speed) is key in virtually all sports and the ability to accelerate is an important component in the performance and training regime of many athletes. I have always believed that ‘speed kills’, whether you are playing sports or driving your car and this analogy allows us to see opposing outcomes of speed. The shorter the distance an object has to move, the more important the acceleration becomes. This is especially true if space is confined, such as on a basketball court, football field, or rugby field etc. The ability of an object to accelerate is dependent on two main factors, its mass and force applied to that mass. A variation in either of these two variables will therefore affect acceleration. For example, if the mass of an athlete stays constant then the athlete must be capable of producing greater force if they want to accelerate more quickly. As aforementioned, Newton’s law of acceleration states that the acceleration of an object is dependent on two factors: the net force acting upon the object, and the mass of the object! Therefore, the acceleration depends directly upon the force applied and is inversely proportional to the mass of the object (athlete). In lay terms this means a heavier object requires more force to accelerate (or heavier athletes require more strength and power to accelerate). As the mass of an object increases, the acceleration will decrease in response to a constant force. This relationship is often presented as acceleration (A) is equal to force (F) divided by mass (M).

A = F/M

A more common and formal presentation of this formula is F=MA .

Using simple mathematics we can rearrange this equation to give us another different variable and that is mass, M =A/F. Test your understanding of these concepts by filling in values for the letters on the table below. Remember to think about your units. The answers are presented below.

Net Force (N)

Mass (kg)

Acceleration (m/s/s)

5

a

2.50

b

2

5.00

5

4

c

d

4

2.50

5

e

1.00

10

6

f

a = 2kg, b = 10N, c = 1.25m/s/s, d = 10N, e = 5kg, f = 1.66m/s/s.

If you got those all right you’re in good shape. Thus, we can see that the acceleration of an object is clearly related to its mass and how much force is applied to it (and as you’ll see in a minute in what direction that force is applied). For acceleration to be maximal (or optimal) the force also needs to be applied in the direction in which the object wants to move. Thus, we can now add ‘direction of force application’ to our list of factors affecting acceleration.

In terms of sports this means that we have several different options by which we can change and improve our acceleration. Look at the following examples of our options:

1).The athlete can increase their strength and power (with no change in mass) thereby allowing greater force application leading to greater acceleration.

2).The athlete can improve their mechanics to ensure optimal application of directional force.

3).The athlete can decrease their mass without changing strength or power thereby increasing acceleration.

4).The athlete can decrease their mass and increase their strength and power leading to increased acceleration.

Naturally the question of interest is: which of the above scenarios would most likely result in the most improvement in our acceleration? We think probably the 4th option!

.

A nice practical application of this law of acceleration is often seen in 100m sprint races, where a shorter, lighter sprinter accelerates quickly and opens up an early lead only to be caught in the latter stages of the race by the taller, heavier sprinters. In other sports examples we often see very fast, agile athletes as being the shorter ones. At this stage having now looked at Newton’s first and second laws we can now start to piece together the integrative relationship in sports, i.e. a relationship between mass, speed and power. Shorter, lighter athletes can often accelerate faster, and this is explained by Newton’s 2nd Law of Acceleration. They can also change direction, and stop, and start work quickly, and this is explained by Newton’s 1st law. That is why it is often harder for a heavier athlete to catch or tackle a lighter athlete since the lighter athlete can easily change direction making it more difficult for the larger to catch them. In terms of conditioning practices it is the goal of most team sports athletes, speed athletes etc. to become stronger and faster without necessarily becoming heavier.

Additional Practice Questions

What is the acceleration of a 3kg medicine ball when a force of 12N is applied? (4m/s/s).

A sled is accelerating at a speed of 2m/s/s! What will be the acceleration be if the net force is tripled and the mass is halved? (12m/s/s). Explanation: the original value is tripled since acceleration and force are proportional and then mass cut in half since acceleration and mass are inversely proportional.

Newton’s Third Law: Law of Reaction

Newton’s 3rd law formally states that “for every action there is an equal and opposite reaction”! In more simple terms it means that for every action, or interaction, there are two forces (a pair of forces) acting on each interacting object. There are three simple clarifications to remember that help with the understanding of Newton’s 3rd law.

1).The magnitude of the force on the first object is equal in size to the force on the second object Ieach object in question is applying an equal force on the other).

2).The direction of the applied force on the first object is opposite to the direction of the force on the second object.

3). Forces are always exist in pairs, which are equal in magnitude and opposite in direction.

Thus, the greater the force that greater the reaction. At this stage you will see that we have been using the term force a lot. Let us take a few moments to deviate a little and discuss some definitions associated with ‘forces’. A force is basically a pushing or pulling on an object. Forces result from interactions with other objects. There are various forms of interaction or forces, and two broad terms commonly used are contact interactions and noncontact interactions. Contact interactions require contact between two surfaces and examples are pushing and pulling (tension) and friction. Noncontact interactions do not require direct contact for the forces to be created. Gravity is a nice example of a noncontact interaction force, as are magnetic forces, or wind etc. Forces are measured using the metric unit, the Newton (N), after Sir Isaac Newton. Forces are also what are termed vector quantities, which means they possess both magnitude and direction. One Newton is the amount of force required to accelerate a 1 kilogram (kg) mass to the speed of 1 m/s per second. Most people refer to 1kg as being equal to 10 N, in reality 1kg is actually 9.81N, which corresponds to the force of gravity of 9.81 m/s squared. Thus a 20 kg dumbbell sitting on the floor can be said to be applying a force downward of 200N (or in more accurate terms, 196.2N), while at the same time the ground is applying in upward force of 200N. We will discuss forces more later on but for now this will help in our understanding of Newton’s laws.

Newton’s 3rd law can often be difficult to follow due to the behavior of the two objects in question. For example, a hockey player (A) collides with another hockey player (B) and knocks them to the ground. If hockey player a exerted a force on hockey player B of 500 N, how much force did be exerted on A? Well, the answer is the same 500 N even though B ended up on the ground. The explanation for the outcome lies in several factors such as differences in mass or differences in speed or differences in acceleration. Regardless, the forces applied on each object are still equal and opposite. Another example is simple walking around. As we push our feet down, the road surface pushes back up (and forward). This allows us to move forward. This particular type of force is called a ‘ground reaction force’. This also helps explain why we can run faster on hard surfaces versus a soft surface, like a sandy beach, because more of the force is returned directly back upwards as opposed to being dispersed.

Newton’s Universal Law of Gravitation

Arguably Sir Isaac Newton’s greatest contribution to science is his universal law of gravitation (which we can now see is tightly linked with his 2nd law of acceleration). Gravity is the natural phenomenon that causes objects to fall to the ground. Gravity is a force through which objects with mass are attracted to each other. So even when an object falls to the ground that object and the earth are actually moving towards each other. Gravitation is what causes objects with mass to have weight. We are all familiar with the story of Newton’s observation of the falling apple and although this may not exactly be the true story, the general observation of the apple falling to the ground led to his greater understanding that objects with mass are attracted to each other. The word gravity comes from the Latin ‘gravitas’ which means heaviness. Newton’s book, the ‘Principia’, explains gravity as the following:

“Every particle of matter in the universe attracts every other particle with a force directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them”. In layman’s terms you could say that the the biggest thing around us is earth and therefore it possesses the greatest gravitational pull and that’s why everything falls towards earth. Through a series of experiments, Newton calculated that the force of the Earth’s gravity caused objects to fall towards earth, or really accelerate towards earth, at the speed of 9.81 m/s squared (for each second it falls). The square component describes an increase in velocity of 9.81 m/s for each second of travel. Therefore if an apple falls from a tree and takes 3 seconds to reach the ground it will be traveling at 29.43 m/s when it strikes the ground (3×9.81 m/s). If it were only traveling for 2 seconds it would be 2 x 9.81 m/s which would equal 19.62 m/s when it strikes the ground. Using these principles we can now calculate the speed of any free-falling object if we know how long it has been falling (and there are no other influencing factors, such as air trapped below the object). Students will often talk about the concept of terminal velocity related to a falling object. Terminal velocity is the term used to describe the velocity of an object when its speed becomes constant due to the restraining forces of air, water, etc. in more scientific terms a freefalling object achieves terminal velocity when the downward force of gravity equals the upward force of drag. This causes both forces to cancel each other out resulting in zero acceleration i.e. terminal velocity since the object is no longer accelerating but instead moving at a constant speed. The shape and mass of an object will pretty much determine its terminal velocity. This is why in some sports, for example, skydiving, athletes change their shape to increase acceleration. Another example is ski jumping were skiers actually seek to increase upward drag and therefore stay elevated for longer periods. Consider this: the terminal velocity of a sky diver in freefall position with parachute semi-closed is approximately 55 m/s (120 mph). However, if the same sky diver assumes a position with arms and legs by their side, the speed increases to about 90 m/s (200 mph). If the diver assumes a head down head first position, the speeds can reach 614 mph. This actually is the current world record for free-fall speed and is held by US Air Force Colonel Joseph Kittinger.

Negative Acceleration

Now, so far we have only talked about the force of gravity as an accelerating component. However, gravity can also cause deceleration, or negative acceleration, such as what happens when we throw a ball up in the air. Have you ever heard, “what goes up must come down”? Since the force of gravity is a constant, objects traveling upwards will naturally decelerate at -9.81 m/s squared (yes, they are being pulled back to the ground). Therefore, using some reverse logic if we throw a ball into the air and it travels upwards for 3 seconds we would have released it at a velocity of 29.43 m/s (remember our earlier calculation of 3 x 9.81m/s?). Which incidentally is the same speed at which we will catch it again if we catch it at the same height as it was released. In other words, a projectile released and caught again at the same height will have been released and then caught again at the same speed. Another interesting point is that the flight path will also be symmetrical in terms of the upward and downward flight path. This issue of negative acceleration is an important factor in many areas of sport as we often accelerate an object as much as we can in either a horizontal, upward (and in rare cases downward) direction only to have to counteract the fight against gravity. Riding a bike uphill is a good example. Think about coming down the hill where you gather up speed and momentum to try and get as far up the hill on the other side? The faster the speed you have as you start to climb the higher you get with less effort. Now, if the hill is long enough gravity will eventually cause you to stop. Consequently, you must expend energy to overcome the decelerating component of gravity to keep climbing. This requires more effort. Gravity, along with Newton’s other laws, clearly affect the flight path or motion of an object and indirectly can determine the type of motion an object displays. We generally identify 2 main types of motion, namely angular and linear motion. Both cause different outcomes so let us take a close look at these types of motion.

Types of Motion

We basically recognize 2 types of motion:

Linear motion (or translatory motion)

Angular motion (or rotary motion).

Linear motion is motion that occurs in a straight line where the motion is measured in one dimension (usually the direction the object is moving). Linear motion is the most basic form of motion and is also described as motion where “all body parts are moving in the same direction at the same speed.” Because linear motion is motion in a straight line it can be mathematically described using only one spatial dimension (e.g. direction). Linear motion can be uniform (or static) or non-uniform (dynamic) meaning that velocity can be constant (zero acceleration) or changing. While the concept of linear motion is fairly basic we can extend our understanding of it into slightly more complex applications. For example: Newton’s first law of motion is the law of inertia. We can also define this law as “unless acted upon by a net external force, a body, at rest will remain at rest and a body in motion will remain in motion.” The motion of an object is defined by its velocity and a body that is stationary is said to have zero velocity. Now, this also implies that if the net external force on a body is zero then the velocity is constant. To take this a few steps further look at this logic:

An object with constant velocity may be at rest or moving.

The object is not accelerating or decelerating.

If the object is moving, it will move in a straight line (linear motion) with a constant speed and no change of direction.

If the object is moving then it does so in a state of uniform linear motion.

If the object moves with uniform linear motion then the net force acting on the object is zero.

As an example: let’s imagine you had 5 miles of straightaway on the highway. If you applied your cruise control at 55 mph and then just sat there you would have a nice example of linear motion. A downhill ski racer in the tuck position is also an example.

Okay, now that we have given you a detailed background on simple linear motion we want to add a few definitions to our glossary. The examples we provided in this previous section are actually more accurate examples of rectilinear movement, which includes as part of its definition “every particle of the body follows a straight line path.” This form of motion is very ideal and rarely happens. In fact most object motion have some change of direction and so are either curvilinear or angular forms of motion.

Curvilinear Motion

By definition, curvilinear motion is motion where there is a change in direction. Singular motion also includes a change of direction and we will look at angular motion in the next section. Curvilinear motion is really an expanded form of linear motion that allows for change of direction along a curved line or path. A roller coaster ride would be a simple example of curvilinear motion. The flight path of a javelin throw would also be an example of curvilinear motion. Interestingly, the example of the javelin throw is often confused by many people as an example of angular motion (or rotary motion). Let’s take a closer look at angular motion.

Angular Motion

As aforementioned, angular motion is also referred to as rotary motion, singular motion is arguably the most common form of motion in humans as virtually all our movements involves rotation around a fixed point. All of our limbs rotate around a joint and the bone attached to a joint is a nice example of angular motion. Singular motion is basically defined as motion that occurs around a fixed point. I also like to add: where a body part etc. is maintained at a set and fixed distance from the axis of rotation. If you understand this then you can see that human movement e.g. walking is the outcome of a series of angular movements. The tibia rotates at the knee, the femur rotates at the hip, the humerus rotates at the shoulder, etc. A nice illustration is to think about is your elbow. No matter where you move your arm the distance from your elbow to your shoulder is always the same. You can’t get your elbow any closer to your shoulder. Wheels on a car, bike etc. are another simple illustration of angular motion. To determine if a motion is angular apply this simple test: Identify two points on the object. When the object moves do the two points move in a circular pattern around the same axis of rotation? If they do, then you have an example of angular motion. Thus you can see that human movement perhaps involves more examples of angular motion versus any other form of motion and while this is true the net outcome of human movement can really be defined as a complex interaction of both linear and angular motion, which we refer to as general motion (or combination motion).

General Motion

So we now know that general motion is a combination of linear and angular motion. It is the most common form of motion in sports and activities. We often employ rotary motion in order to move linearly, bike riding is a nice example. The movement patterns of other objects, like projectiles, usually display general motion. For example the flight path of a soccer ball may initially be linear progressing to curvilinear, unlike the ball itself is actually is actually rotating (angular). Being able to visualize and analyze movements in this way will help you to gain a better understanding of the type of movement pattern involved in any situation.

Practice Problems

Newtonian Laws

Define the (4) Newtonian Laws we discussed and then present three examples of how each is applicable in a sporting environment.

1. Law 1. Inertia:

2. Law 2. Acceleration:

3. Law 3. Reaction:

4. Law 4. Gravity:

2. Identify & Explain the Newtonian Law(s) applying to the following examples:

a. Apple falling to the ground:

b. Forces created during a heel strike:

c. Two hockey players colliding on the ice:

d. A skater gliding on the ice:

e. A softball toss:

f. A chair sitting in a room:

A 105kg hockey player collides with a 95kg player. The 105kg player exerts a force of 450N on the 95kg player. How much force does the 95kg player exert on the 105kg player?

A boy drops a ball from a 2nd floor apartment window. It takes the ball 2.4 secs to reach another boy who catches it standing on the ground. Approximately, what speed does the ball hit the ground?

Approximately what speed must the boy on the ground release the ball in order to make sure the boy on the 2nd floor can catch it?

Center of Gravity

We have spent some time in this chapter talking about gravity and its effects on accelerating and decelerating objects. This discussion of gravity is different from center of gravity (COG) which is also of vital importance and understanding in sports. You will remember back in Chapter 5 that we provided a brief description of COG in our initial discussion of planes and axes. While COG is an ever changing and complex phenomenon, here COG is essentially that point where all three cardinal axes cross (i.e. sagittal, frontal and transverse). And because we change our body height, shape, etc. our COG is constantly changing. As a simple guide we often estimate our COG as lying somewhere around our “belly button” during normal upright walking and running. However, given the complexities of human movements, especially during sports, the COG can move dramatically and can in many circumstances exist outside of our bodies. A more scientific definition of COG is that “point in an object around which its mass (or weight) is evenly distributed and balanced.” It is also the point through which the face of gravity exists (usually without causing rotation). Now, COG and center of mass (COM) are different, even though most of the time on earth they are the same. COM can be defined as that point in a body where the entire mass is assumed to be concentrated. For the most part, we can assume COM and COG to be the same and many will use the terms interchangeably. It is also important to remember that COG and COM are imaginary lines and points that are in constant movement as an object changes position, height, etc. In sports, correct movement necessitates we rotate in a controlled manner around our COG. If we do not then we tend to fall. Therefore it is of value to be able to identify, locate or estimate our COG. This can be done mathematically in a simple form. While the mathematics are straightforward for a simple object our body is a series of objects, i.e. legs, arms, head, torso, etc. Therefore calculation of total body COG often requires multiple calculations. In order to do the calculation one must know the weights (masses) of each component. There are some estimates for segmental body part weig