Understanding Newton's Laws in Biomechanics

[MUSIC PLAYING] We have previously covered Newton's laws of motion and their relevance to biomechanics. Now we're going to take a moment to review these laws and break them down further to gain a deeper understanding of how they apply to biomechanical concepts and human movement. A body will maintain a state of rest or constant velocity unless acted upon by an external force that changes the state. Inertia describes an object's resistance to change in motion. It is directly related to the object's mass. The greater the mass, the greater the inertia, and therefore, the more difficult it is to either start movement or to change the object's current motion. For an object to begin moving or to change its motion, its inertia must be overcome. This requires a net external force that is greater than the object's inertia, which, in turn, causes the object to accelerate. Law number two, or the law of acceleration, states that the change in motion is proportional to the force impressed and occurs in the direction of the straight line in which that force is applied. This law forms the foundation for the equation that relates all forces acting on an object, with force being equal to the mass times the acceleration. From this, we can state that acceleration of an object is determined by both the magnitude of the forces applied, both internal or external, and the object's mass. The greater the net force acting on an object, the greater its acceleration will be and always in the direction of the net force. For example, if a baseball pitcher applies the same amount of force to a 16-pound shot put and a 5-ounce baseball, which one would accelerate more? Certainly, the baseball because it has less mass, and therefore, less inertia, allowing it to reach a higher acceleration when the same force is applied. By understanding Newton's second law, we can break down this equation even further by expressing acceleration as the change in velocity over the change in time. Then, by rearranging the equation and moving the change in time to the other side, we arrive to a new concept. This is known as impulse. Impulse is defined as the product of force and the time during which the force acts. If the force is not constant, impulse is calculated using the average force multiplied by the duration of that average force. Impulse is important because it describes how momentum changes and helps explain how we initiate or stop motion during physical activity. Impulse is essentially a measure of the effect of a force acting over time. You may sometimes see impulse represented with the letter J. But for the purpose of our class, we'll simply refer to it as impulse to avoid any confusion with other variables like joules, which are used for energy. If you recall from earlier content, the longer we interact with an object, the more opportunity we have to apply force to it. Impulse is one way to represent and quantify this relationship. Since impulse is the product of force and time, we can graph these values, placing force on the y-axis and time on the x-axis. The area under this curve, it represents the impulse. The longer an object applies force to another, the greater the effect that force will have on the object. To produce a similar effect over a shorter period of time, a greater amount of force is applied. For example, this figure shows the vertical ground reaction force over time for one step during walking, skipping, and running. All three activities produce similar impulse values, but running occurs over a much shorter contact time, and therefore, requires a much greater peak force applied into the ground. As you look at the figure, try to identify which curve corresponds to which activity based on the shape, duration, and peak magnitude of the force curves. Also, through the re-arrangement of Newton's second law, we can identify a key component of the equation known as momentum. Momentum is the quantity of motion an object has, and it's calculated as the product of mass and velocity. Based on our understanding of Newton's second law and the relationship between impulse and momentum, we can state the following. The impulse produced by a net force acting over a period of time causes a change in momentum of the object upon which that force is applied. To change the momentum of an object, either the mass or the velocity must change. Since in biomechanics we typically assume that mass stays constant, a change in momentum generally implies a change in velocity. A simple way to understand momentum is through an example. Getting hit by a football lineman hurts a whole lot more than getting hit by a toddler. How come? Well, because the lineman has more mass and typically moves with a greater velocity, resulting in much more momentum, and consequently, a greater transfer of force when contact is made. Newton's laws form the foundation for the principles of the conservation of momentum, particularly when we are considering objects with constant mass. Linear momentum is defined as the product of an object's mass and its linear velocity. The faster an object moves, the more momentum it has. Likewise, the greater the mass of a moving object, the more momentum it carries. This principle is key to understanding how forces are transferred and managed during collisions, impact, and movement within biomechanics. When two objects collide in a head-on collision, their combined momentum is conserved as long as no external forces act on the system. This principle allows us to predict post-collision movement if we know the object's objects masses and their velocities before collision. Although these collisions typically occur over a very short time interval, they involve the exchange of relatively large forces between the objects. Understanding this concept is especially important in biomechanics and sports science, where collisions, such as in tackling, blocking, or jumping into another player, can have significant implications for performance and also with injury risk. In a perfectly elastic impact between two objects in a head-on collision with equal masses, the pre-collision momentum of each object is completely transferred to the other after the collision. In other words, the relative velocities after the impact are the same as before, just in opposite directions. However, even in a perfect elastic situation where the masses are not equal, the principle of conservation of momentum still holds. In these cases, the post-collision velocities of the two objects will not be the same as their initial velocities. Because although momentum is conserved, the differing masses affect how the momentum is distributed. Since mass remains constant, any change in momentum from one object must be balanced by the opposite change in the other, resulting in different velocity outcomes based on the mass ratio between the two objects. A perfectly inelastic or plastic collision is the opposite of a perfectly elastic collision. In a perfectly inelastic collision, momentum is still conserved. But instead of bouncing off one another, the colliding objects stick together and move as a single combined mass after the impact. This means they will share the same velocity post-collision, which is determined by the combined mass and the total momentum prior to the collision. Most collisions are neither perfectly elastic nor perfectly inelastic, but fall somewhere in between. These types of collisions are considered elastic, but not perfectly elastic. The coefficient of restitution is used to describe these collisions. It is defined as the ratio of the velocity of separation to the velocity of approach. The velocity of separation refers to the difference between the velocities of the two objects just after the collision, describing how quickly they move apart. The velocity of approach refers to the difference between the velocities of the two objects just before the collision, describing how quickly they move towards each other. Essentially, the coefficient of restitution tells us the relative elasticity of an impact-- how much energy is conserved versus lost in the collision. A perfectly elastic collision has a coefficient of restitution of 1.0, its maximum value. A perfectly inelastic collision has a coefficient of restitution of 0.0, its minimum value. The coefficient of restitution is a critical measure in most ball sports, as the bounciness of the ball and the nature of the surface or implemented strikes can significantly impact the outcome of performance or competition. One common method for determining the coefficient of restitution is to drop a ball from a specified height onto a fixed impact surface. By measuring both the height of the drop and the height of the rebound, we can calculate the coefficient of restitution, which provides insight into how much energy is retained or lost during the impact. Let's look at an example of a football player tackling. If our player is 70 kilograms and is running in a positive x direction at a constant 1.5 meters per second, his momentum can be calculated by multiplying his mass by his velocity, which gives us 105 kilogram meters per second. Let's say our football player contacts a 10-kilogram static tackling popup. Let's then calculate the combined new horizontal velocity of the athlete plus the popup. We can calculate the combined mass which gives us 80 kilograms and plug it into our momentum equation and solve for velocity. Since momentum is conserved, our momentum stays at 105 kilogram meters per second. Solving for velocity with our new mass gives 1.31 meters per second, which means that as soon as the football player made contact with the tackling popup, they slowed down due to that particular contact. This interpretation of Newton's second law is particularly useful when studying human movement. If we want to change the velocity of an object, we can do so by increasing the net force acting on the object, increasing the duration over which the force is applied, or using a combination of both. In some situations, our goal may be to decrease overall momentum. For example, during landing from a jump, when landing, we often flex or bend multiple joints, such as the hips, the knees, the ankles. And knowing the relationship between impulse and momentum, think about why this would occur. Similar to landing from a jump, we can apply the impulse momentum relationship to another common movement-- catching a ball. For example, when a baseball player catches a ball, they often make contact with the ball in the glove and then draw it in towards their body. You may have heard a coach refer to this as being soft when catching. This technique directly reflects the impulse momentum relationship. By increasing the amount of time over which the ball's velocity is reduced to zero, the player is effectively spreading the force out over a longer duration. As a result, there is less discomfort or strain from the impact because the same change in momentum occurs over a lower peak force. The same principle helps explain why we flex at multiple joints and aim to land softly after jumping. By increasing the time over which we land, we reduce the peak forces experienced at the joints, which can protect the musculoskeletal system and improve movement efficiency. Here's an example of two vertical jumps performed by the same individual, one resulting in a higher jump, and the other resulting in a lower jump. Using a force platform, we can measure the vertical ground reaction forces displayed on the y-axis in relation to time displayed on the x-axis for each jump. Since impulse is the product of force and time, the shaded areas under the force-time curve represents the impulse. When the impulse is greater, there is more shaded area, indicating a greater change in momentum. This greater omentum results in higher vertical jumps, demonstrating the direct relationship between impulse and jump performance. However, it's important to note that during a vertical jump, an individual must maximize impulse by carefully balancing the trade-off between the magnitude of the applied force and the duration of that force. While increasing the time of force of application, can increase the impulse, there's a point at which it becomes less effective. Because when the force is applied over a longer duration, the magnitude of the force can be generated often decreases pretty significantly. Therefore, an effective vertical jump requires the athlete to find an optimal balance, applying a high enough force within an efficient amount of time to maximize the impulse and achieve a peak jump height. Here's an example of a counter-movement jump, where the jumper begins from an upright standing position, makes a preliminary downward movement by flexing at the knees and at the hips, and then immediately extends the knees and hips to jump vertically off the ground. In the figure, the horizontal dashed line represents the magnitude of body weight. At the beginning of the movement, you can see a decrease in vertical ground reaction forces. This occurs during the initial downward motion when the person is dropping into knee and hip flexion. Then, there's a large increase in vertical ground reaction force as the jumper begins the upward phase, powerfully engaging the muscles concentrically but has not yet left the ground. At this point, the person is in the air, and you'll notice that there's no ground reaction force since they're no longer in contact with the ground. Finally, the landing phase begins, marked by a large spike in ground reaction forces as the feet contact the ground again. You might also notice a wave-like undulation, a rise and fall in force after landing. This is due to eccentric activation of the hip and the knee flexors, which helps the person absorb the landing force more gradually and land softly. Had the jumper landed with straight legs, you would see a massive, sharp spike in force, followed by a sudden drop-off, indicating less absorption and greater stress on the body. The eccentric muscle action during landing is critical, as it increases the time interval over which the force is applied, reducing the peak impact in helping to protect the joints and soft tissue. Here's an example from a classic 1992 study that explored vertical ground reaction force during soft and rigid landings. The study found that rigid landings resulted in a larger peak force, while the duration of force application was roughly the same for both landing styles. If we recall, that impulse is represented by the area under the force-time curve. This means that the stiff landing produced a greater linear impulse, nearly 23% higher compared to that of a soft landing. This increased impulse, coupled with a larger peak force, suggests greater mechanical loading on the body during stiff landings, which may have implications for injury risk and joint stress. To every action, there is always an equal and opposite reaction. This is Newton's third law of motion, and it illustrates a fundamental concept that forces never act in isolation but always occur in pairs. When two objects interact, the force exerted by object A on object B is always matched by a force of equal magnitude in opposite direction exerted by object B on object A. This principle is crucial in understanding how we move from walking to jumping to throwing. Because every action we perform relies on the reaction forces from the surfaces or the objects we interact with. In almost any real-world situation, there are multiple forces acting simultaneously on an object. To fully understand what causes or inhibits movement, we must consider all of the forces involved. For example, when interacting with a static object, like the floor or a wall, there's a normal reaction force, a force that acts perpendicular to the surface and in the opposite direction of our weight. This force helps to support the body and prevents it from passing through the surface, as illustrated here. Now that we've looked at normal forces, we'll move on to examine frictional forces, which play a crucial role in movement, stability, and performance. Friction is a force that acts parallel to the interface of two surfaces that are in contact during the motion. Impending motion of one surface occurs as it moves over the other. Here, we can see two scenarios involving friction. The person on the left still has friction between the skis and the snow, but the static and kinetic friction are both much less than shoes on grass, even though the hill is the same slope. While it may seem that the area of contact influences the force of friction, this is not actually the case. The force of friction is determined by the normal reaction force, or often simply called the normal force, and the coefficient of friction between the two surfaces, where mu is the coefficient of friction, and F subscript n is the normal force which acts perpendicular to the surface. The coefficient of friction is a dimensionless number that depends on the nature and condition of the interacting surfaces. The greater the coefficient of friction, the stronger the molecular interactions between the two surfaces. And thus, the greater the frictional force resisting motion If we consider this example, here of pulling a block on a table, there will be a static frictional force between the block and the table. If we steadily increase the pulling force on the block, the table also applies an increasing opposite force resisting the movement. At the point where the pulling force is at its maximum and no movement results, the resisting force is called the maximum static friction force. Once the applied force is greater than the maximum static friction force, movement will occur. As the block slides along the surface of the table, molecular bonds are continually made and broken. After two surfaces start moving relative to each other, it becomes somewhat easier to maintain that motion. The result is a force of sliding friction that opposes the motion. Sliding friction and rolling friction are types of kinetic friction noted by the equation here. Let's take a look at this example using frictional force. The first items to determine are the horizontal and vertical components of the movement. We know that Dave is pulling Dana with 300 newtons of force at a 30-degree angle. This 300 newtons is associated with the hypotenuse of the triangle that we can make from the horizontal and vertical components. Knowing this information, we can determine the vertical component by using the equation for sine. Therefore, the sine of 30 degrees is equal to the opposite side or the vertical component divided by the hypotenuse. Based on this calculation, we can determine the vertical component is equal to 150 newtons. Now we must find the horizontal component. We can find the horizontal component by using the equation for cosine. Therefore, the cosine of 30 degrees is equal to the adjacent side, or the horizontal component, divided by the hypotenuse. Based on this calculation, we can determine that the horizontal component is equal to 260 newtons. We now know the vertical and horizontal forces associated with Dave pulling the sled at a 30-degree angle with 300 newtons. In order to determine whether or not Dave can actually pull the sled, we need to next determine the frictional force. In order to determine the frictional force, we need the coefficient of static friction and the normal force. We know the coefficient of static friction is 0.10. So we can insert this value into the equation. To find the normal force, we need to know the mass and acceleration. Due to the situation, the acceleration will be the acceleration of gravity of 9.81 meters per second squared. To assess the mass, we must include the mass of the entire system. This includes the mass of both Dana and the mass of the sled. The total mass would be 58 kilograms. We can now enter the 58 kilograms into the normal force calculation. Ultimately, we get a normal force of 570 newtons of downward force. We now know there's 570 newtons for the normal force. However, there's 150 newtons of upward force as Dave tries to pull the sled. This upward force must be accounted for. We need to take our calculated normal force and subtract the upward force due to Dave trying to pull the sled, and we can get a net downward force of 420 newtons. We can now take the total net normal force of 420 newtons and insert this into the frictional force equation. And there is a total frictional force of 42 newtons. The ultimate question is, does Dave provide enough force to break static friction and pull Dana? We know that the frictional force is 42 newtons. We also know that Dave is pulling at a 30-degree angle with 300 newtons. This means that there's 260 newtons of horizontal force. Based on the amount of horizontal force, we know that Dave can pull Dana because he exerts 218 newtons more than what's required to overcome the frictional force.

[MUSIC PLAYING]  We have previously covered Newton's laws of motion and their relevance to biomechanics. Now we're going to take a moment to review these laws and break them down further to gain a deeper understanding of how they apply to biomechanical concepts and human movement. A body will maintain a state of rest or constant velocity unless acted upon by an external force that changes the state. Inertia describes an object's resistance to change in motion. It is directly related to the object's mass. The greater the mass, the greater the inertia, and therefore, the more difficult it is to either start movement or to change the object's current motion. For an object to begin moving or to change its motion, its inertia must be overcome. This requires a net external force that is greater than the object's inertia, which, in turn, causes the object to accelerate. Law number two, or the law of acceleration, states that the change in motion is proportional to the force impressed and occurs in the direction of the straight line in which that force is applied. This law forms the foundation for the equation that relates all forces acting on an object, with force being equal to the mass times the acceleration. From this, we can state that acceleration of an object is determined by both the magnitude of the forces applied, both internal or external, and the object's mass. The greater the net force acting on an object, the greater its acceleration will be and always in the direction of the net force. For example, if a baseball pitcher applies the same amount of force to a 16-pound shot put and a 5-ounce baseball, which one would accelerate more? Certainly, the baseball because it has less mass, and therefore, less inertia, allowing it to reach a higher acceleration when the same force is applied. By understanding Newton's second law, we can break down this equation even further by expressing acceleration as the change in velocity over the change in time. Then, by rearranging the equation and moving the change in time to the other side, we arrive to a new concept. This is known as impulse. Impulse is defined as the product of force and the time during which the force acts. If the force is not constant, impulse is calculated using the average force multiplied by the duration of that average force. Impulse is important because it describes how momentum changes and helps explain how we initiate or stop motion during physical activity. Impulse is essentially a measure of the effect of a force acting over time. You may sometimes see impulse represented with the letter J. But for the purpose of our class, we'll simply refer to it as impulse to avoid any confusion with other variables like joules, which are used for energy. If you recall from earlier content, the longer we interact with an object, the more opportunity we have to apply force to it. Impulse is one way to represent and quantify this relationship. Since impulse is the product of force and time, we can graph these values, placing force on the y-axis and time on the x-axis. The area under this curve, it represents the impulse. The longer an object applies force to another, the greater the effect that force will have on the object. To produce a similar effect over a shorter period of time, a greater amount of force is applied. For example, this figure shows the vertical ground reaction force over time for one step during walking, skipping, and running. All three activities produce similar impulse values, but running occurs over a much shorter contact time, and therefore, requires a much greater peak force applied into the ground. As you look at the figure, try to identify which curve corresponds to which activity based on the shape, duration, and peak magnitude of the force curves.  Also, through the re-arrangement of Newton's second law, we can identify a key component of the equation known as momentum. Momentum is the quantity of motion an object has, and it's calculated as the product of mass and velocity. Based on our understanding of Newton's second law and the relationship between impulse and momentum, we can state the following. The impulse produced by a net force acting over a period of time causes a change in momentum of the object upon which that force is applied. To change the momentum of an object, either the mass or the velocity must change. Since in biomechanics we typically assume that mass stays constant, a change in momentum generally implies a change in velocity. A simple way to understand momentum is through an example. Getting hit by a football lineman hurts a whole lot more than getting hit by a toddler. How come? Well, because the lineman has more mass and typically moves with a greater velocity, resulting in much more momentum, and consequently, a greater transfer of force when contact is made. Newton's laws form the foundation for the principles of the conservation of momentum, particularly when we are considering objects with constant mass. Linear momentum is defined as the product of an object's mass and its linear velocity. The faster an object moves, the more momentum it has. Likewise, the greater the mass of a moving object, the more momentum it carries. This principle is key to understanding how forces are transferred and managed during collisions, impact, and movement within biomechanics. When two objects collide in a head-on collision, their combined momentum is conserved as long as no external forces act on the system. This principle allows us to predict post-collision movement if we know the object's objects masses and their velocities before collision. Although these collisions typically occur over a very short time interval, they involve the exchange of relatively large forces between the objects. Understanding this concept is especially important in biomechanics and sports science, where collisions, such as in tackling, blocking, or jumping into another player, can have significant implications for performance and also with injury risk. In a perfectly elastic impact between two objects in a head-on collision with equal masses, the pre-collision momentum of each object is completely transferred to the other after the collision. In other words, the relative velocities after the impact are the same as before, just in opposite directions. However, even in a perfect elastic situation where the masses are not equal, the principle of conservation of momentum still holds. In these cases, the post-collision velocities of the two objects will not be the same as their initial velocities. Because although momentum is conserved, the differing masses affect how the momentum is distributed. Since mass remains constant, any change in momentum from one object must be balanced by the opposite change in the other, resulting in different velocity outcomes based on the mass ratio between the two objects. A perfectly inelastic or plastic collision is the opposite of a perfectly elastic collision. In a perfectly inelastic collision, momentum is still conserved. But instead of bouncing off one another, the colliding objects stick together and move as a single combined mass after the impact. This means they will share the same velocity post-collision, which is determined by the combined mass and the total momentum prior to the collision. Most collisions are neither perfectly elastic nor perfectly inelastic, but fall somewhere in between. These types of collisions are considered elastic, but not perfectly elastic. The coefficient of restitution is used to describe these collisions. It is defined as the ratio of the velocity of separation to the velocity of approach. The velocity of separation refers to the difference between the velocities of the two objects just after the collision, describing how quickly they move apart. The velocity of approach refers to the difference between the velocities of the two objects just before the collision, describing how quickly they move towards each other. Essentially, the coefficient of restitution tells us the relative elasticity of an impact-- how much energy is conserved versus lost in the collision. A perfectly elastic collision has a coefficient of restitution of 1.0, its maximum value. A perfectly inelastic collision has a coefficient of restitution of 0.0, its minimum value. The coefficient of restitution is a critical measure in most ball sports, as the bounciness of the ball and the nature of the surface or implemented strikes can significantly impact the outcome of performance or competition. One common method for determining the coefficient of restitution is to drop a ball from a specified height onto a fixed impact surface. By measuring both the height of the drop and the height of the rebound, we can calculate the coefficient of restitution, which provides insight into how much energy is retained or lost during the impact.  Let's look at an example of a football player tackling. If our player is 70 kilograms and is running in a positive x direction at a constant 1.5 meters per second, his momentum can be calculated by multiplying his mass by his velocity, which gives us 105 kilogram meters per second. Let's say our football player contacts a 10-kilogram static tackling popup. Let's then calculate the combined new horizontal velocity of the athlete plus the popup. We can calculate the combined mass which gives us 80 kilograms and plug it into our momentum equation and solve for velocity. Since momentum is conserved, our momentum stays at 105 kilogram meters per second. Solving for velocity with our new mass gives 1.31 meters per second, which means that as soon as the football player made contact with the tackling popup, they slowed down due to that particular contact.  This interpretation of Newton's second law is particularly useful when studying human movement. If we want to change the velocity of an object, we can do so by increasing the net force acting on the object, increasing the duration over which the force is applied, or using a combination of both. In some situations, our goal may be to decrease overall momentum. For example, during landing from a jump, when landing, we often flex or bend multiple joints, such as the hips, the knees, the ankles. And knowing the relationship between impulse and momentum, think about why this would occur.  Similar to landing from a jump, we can apply the impulse momentum relationship to another common movement-- catching a ball. For example, when a baseball player catches a ball, they often make contact with the ball in the glove and then draw it in towards their body. You may have heard a coach refer to this as being soft when catching. This technique directly reflects the impulse momentum relationship. By increasing the amount of time over which the ball's velocity is reduced to zero, the player is effectively spreading the force out over a longer duration. As a result, there is less discomfort or strain from the impact because the same change in momentum occurs over a lower peak force. The same principle helps explain why we flex at multiple joints and aim to land softly after jumping. By increasing the time over which we land, we reduce the peak forces experienced at the joints, which can protect the musculoskeletal system and improve movement efficiency. Here's an example of two vertical jumps performed by the same individual, one resulting in a higher jump, and the other resulting in a lower jump. Using a force platform, we can measure the vertical ground reaction forces displayed on the y-axis in relation to time displayed on the x-axis for each jump. Since impulse is the product of force and time, the shaded areas under the force-time curve represents the impulse. When the impulse is greater, there is more shaded area, indicating a greater change in momentum. This greater omentum results in higher vertical jumps, demonstrating the direct relationship between impulse and jump performance. However, it's important to note that during a vertical jump, an individual must maximize impulse by carefully balancing the trade-off between the magnitude of the applied force and the duration of that force. While increasing the time of force of application, can increase the impulse, there's a point at which it becomes less effective. Because when the force is applied over a longer duration, the magnitude of the force can be generated often decreases pretty significantly. Therefore, an effective vertical jump requires the athlete to find an optimal balance, applying a high enough force within an efficient amount of time to maximize the impulse and achieve a peak jump height. Here's an example of a counter-movement jump, where the jumper begins from an upright standing position, makes a preliminary downward movement by flexing at the knees and at the hips, and then immediately extends the knees and hips to jump vertically off the ground. In the figure, the horizontal dashed line represents the magnitude of body weight. At the beginning of the movement, you can see a decrease in vertical ground reaction forces. This occurs during the initial downward motion when the person is dropping into knee and hip flexion. Then, there's a large increase in vertical ground reaction force as the jumper begins the upward phase, powerfully engaging the muscles concentrically but has not yet left the ground. At this point, the person is in the air, and you'll notice that there's no ground reaction force since they're no longer in contact with the ground. Finally, the landing phase begins, marked by a large spike in ground reaction forces as the feet contact the ground again. You might also notice a wave-like undulation, a rise and fall in force after landing. This is due to eccentric activation of the hip and the knee flexors, which helps the person absorb the landing force more gradually and land softly. Had the jumper landed with straight legs, you would see a massive, sharp spike in force, followed by a sudden drop-off, indicating less absorption and greater stress on the body. The eccentric muscle action during landing is critical, as it increases the time interval over which the force is applied, reducing the peak impact in helping to protect the joints and soft tissue. Here's an example from a classic 1992 study that explored vertical ground reaction force during soft and rigid landings. The study found that rigid landings resulted in a larger peak force, while the duration of force application was roughly the same for both landing styles. If we recall, that impulse is represented by the area under the force-time curve. This means that the stiff landing produced a greater linear impulse, nearly 23% higher compared to that of a soft landing. This increased impulse, coupled with a larger peak force, suggests greater mechanical loading on the body during stiff landings, which may have implications for injury risk and joint stress. To every action, there is always an equal and opposite reaction. This is Newton's third law of motion, and it illustrates a fundamental concept that forces never act in isolation but always occur in pairs. When two objects interact, the force exerted by object A on object B is always matched by a force of equal magnitude in opposite direction exerted by object B on object A. This principle is crucial in understanding how we move from walking to jumping to throwing. Because every action we perform relies on the reaction forces from the surfaces or the objects we interact with. In almost any real-world situation, there are multiple forces acting simultaneously on an object. To fully understand what causes or inhibits movement, we must consider all of the forces involved. For example, when interacting with a static object, like the floor or a wall, there's a normal reaction force, a force that acts perpendicular to the surface and in the opposite direction of our weight. This force helps to support the body and prevents it from passing through the surface, as illustrated here. Now that we've looked at normal forces, we'll move on to examine frictional forces, which play a crucial role in movement, stability, and performance. Friction is a force that acts parallel to the interface of two surfaces that are in contact during the motion. Impending motion of one surface occurs as it moves over the other. Here, we can see two scenarios involving friction. The person on the left still has friction between the skis and the snow, but the static and kinetic friction are both much less than shoes on grass, even though the hill is the same slope. While it may seem that the area of contact influences the force of friction, this is not actually the case. The force of friction is determined by the normal reaction force, or often simply called the normal force, and the coefficient of friction between the two surfaces, where mu is the coefficient of friction, and F subscript n is the normal force which acts perpendicular to the surface. The coefficient of friction is a dimensionless number that depends on the nature and condition of the interacting surfaces. The greater the coefficient of friction, the stronger the molecular interactions between the two surfaces. And thus, the greater the frictional force resisting motion If we consider this example, here of pulling a block on a table, there will be a static frictional force between the block and the table. If we steadily increase the pulling force on the block, the table also applies an increasing opposite force resisting the movement. At the point where the pulling force is at its maximum and no movement results, the resisting force is called the maximum static friction force. Once the applied force is greater than the maximum static friction force, movement will occur. As the block slides along the surface of the table, molecular bonds are continually made and broken. After two surfaces start moving relative to each other, it becomes somewhat easier to maintain that motion. The result is a force of sliding friction that opposes the motion. Sliding friction and rolling friction are types of kinetic friction noted by the equation here.  Let's take a look at this example using frictional force. The first items to determine are the horizontal and vertical components of the movement. We know that Dave is pulling Dana with 300 newtons of force at a 30-degree angle. This 300 newtons is associated with the hypotenuse of the triangle that we can make from the horizontal and vertical components. Knowing this information, we can determine the vertical component by using the equation for sine. Therefore, the sine of 30 degrees is equal to the opposite side or the vertical component divided by the hypotenuse. Based on this calculation, we can determine the vertical component is equal to 150 newtons.  Now we must find the horizontal component. We can find the horizontal component by using the equation for cosine. Therefore, the cosine of 30 degrees is equal to the adjacent side, or the horizontal component, divided by the hypotenuse. Based on this calculation, we can determine that the horizontal component is equal to 260 newtons.  We now know the vertical and horizontal forces associated with Dave pulling the sled at a 30-degree angle with 300 newtons. In order to determine whether or not Dave can actually pull the sled, we need to next determine the frictional force. In order to determine the frictional force, we need the coefficient of static friction and the normal force. We know the coefficient of static friction is 0.10. So we can insert this value into the equation.  To find the normal force, we need to know the mass and acceleration. Due to the situation, the acceleration will be the acceleration of gravity of 9.81 meters per second squared. To assess the mass, we must include the mass of the entire system. This includes the mass of both Dana and the mass of the sled. The total mass would be 58 kilograms. We can now enter the 58 kilograms into the normal force calculation. Ultimately, we get a normal force of 570 newtons of downward force.  We now know there's 570 newtons for the normal force. However, there's 150 newtons of upward force as Dave tries to pull the sled. This upward force must be accounted for. We need to take our calculated normal force and subtract the upward force due to Dave trying to pull the sled, and we can get a net downward force of 420 newtons. We can now take the total net normal force of 420 newtons and insert this into the frictional force equation. And there is a total frictional force of 42 newtons.  The ultimate question is, does Dave provide enough force to break static friction and pull Dana? We know that the frictional force is 42 newtons. We also know that Dave is pulling at a 30-degree angle with 300 newtons. This means that there's 260 newtons of horizontal force. Based on the amount of horizontal force, we know that Dave can pull Dana because he exerts 218 newtons more than what's required to overcome the frictional force.

Transcript for:Understanding Newton's Laws in Biomechanics

Transcript for:
Understanding Newton's Laws in Biomechanics