Projectile Motion Horizontal Distance

Transcription

1 Projectile Motion Horizontal Distance

2 Biomechanical Model Projec1le Mo1on Horizontal Distance Projectile Horizontal Distance Time in the Air Projectile Motion Principle Linear Conservation of Momentum Principle Horizontal Linear Speed Projection Angle RPH Lift Force Linear Impulse- Momentum Principle 2 External Forces Principle External Forces Factors that slow the projectile down less Application Time of each External Force Slowing The Projectile Down Mass Fluid Density Coefficient of Lift Area of Lift Lift Force Principle Relative Velocity Drag Force Drag Force Principle Fluid Density Coefficient of Drag Area of Drag Relative Velocity

3 Biomechanical Model Projec1le Mo1on Horizontal Distance Projectile Horizontal Distance Projectile Motion Principle Horizontal Distance Time in the Air d = horiz ( s )( t ) horiz flight Horizontal Linear Speed Projection Angle RPH Lift Force

4 Biomechanical Model Projec1le Mo1on Horizontal Distance Lift Force Principle Speeding up side of the model F = L 1 2 ρ fluid C L A L ( v ) 2 rel Fluid Density Coefficient of Lift Lift Force Area of Lift Relative Velocity

5 Biomechanical Model Projec1le Mo1on Horizontal Distance Linear Conservation of Momentum Principle For projectiles, there are no factors that speed the projectile (once it is a projectile), therefore, we must only consider factors that slow the projectile down Linear Speed Factors that slow the projectile down less

6 Biomechanical Model Projec1le Mo1on Horizontal Distance Linear Impulse Momentum Principle 2 Factors that slow you down Δs = ΣFt m External Forces Application Time of each External Force Slowing The Projectile Down Mass

7 Biomechanical Model Projec1le Mo1on Horizontal Distance External Forces Principle External Forces Drag Force

8 Biomechanical Model Projec1le Mo1on Horizontal Distance Drag Force Principle Drag Force F = D 1 2 ρ fluid C D A D ( v ) 2 rel Fluid Density Coefficient of Drag Area of Drag Relative Velocity

9 Locomotion Minimum Movement Time Fundamental Biomechanical Principles

10 Linear Conserva1on of Momentum Principle Newton s First Law of Motion (Linear) This law explains what happens to a body if no net force acts on it There is no change in motion A body that is moving will continue to move in the same direction with the same speed A body at rest will stay at rest But, what does it mean when we say no net force? It simply means that any force that slows the body down must be matched by an equal force that speed the body up

11 Linear Conserva1on of Momentum Principle Real- World Application To maintain a constant state of motion, any factors that would slow the body down must be balanced by factors that speeds the body up. If the factors that slow the body down exceed the factors that speed the body up, the body slows down (i.e., the state of motion changes). If the factors that slow the body down are less than the factors that speed the body up, the body speeds up (i.e., the state of motion changes).

12 Linear Impulse- Momentum Principle Newton s 2 nd Law of Motion (Linear) If a net force is exerted on an object, the object will linearly accelerate in the direction of the net force, and its linear acceleration will be proportional to the net force and inversely proportional to its linear inertia (i.e., mass). The equation for Newton s 2 nd Law of Motion (Linear) is ΣF = ma

13 Linear Impulse- Momentum Principle The Linear Impulse- Momentum Principle is derived from Newton s 2 nd Law of Motion (Linear) ΣF = ma ΣF = m Δs t ΣFt = m( Δs)

14 Linear Impulse- Momentum Principle ΣFt is known as linear impulse Unit of measurement Newton- meter- sec (N- s) m(δs) is known as the change in linear momentum Unit of measurement kilogram meter per second (kg- m/s)

15 Linear Impulse- Momentum Principle Real- World Application A smaller decrease in linear speed of the body is caused by a smaller net force that slows you down, and/or a smaller application time of the net force that slows you down and/or an increase in the body segment s linear inertia (i.e., mass). Δs = ΣFt m

16 External Forces Principle This principle may be interpreted in several different ways. For slowing down, the principle is interpreted as follows: Whenever a projectile is moving through air, there is one one fluid force that can slow the body down (Drag Force)

17 Dynamic Fluid Forces Dynamic Fluid Forces When an object moves within a fluid (or when a fluid moves past an object immersed in it), dynamic fluid forces are exerted on the object by the fluid Two Types of Dynamic Fluid Force Drag Force Lift Force Unit of Measurement Newton (N)

18 Figure 8-5

19 Drag Force Principle Drag Force The dynamic fluid force that opposes motion of the body through a fluid (e.g., air or water; different densities, ρ) F = D 1 2 ρc D A D ( v ) 2 rel

20 Drag Force Principle Fluid Density (ρ) The ratio of mass to volume ρ = m/v The unit of measurement is a kilogram per meter cubed (kg/m3) The density of water is about 1000 kg/m3 The density of air is only about 1.2 kg/m3

21 Drag Force Principle Surface Drag (C D ) Surface drag represents the friction force between the fluid molecules and the surface of the object It is also called skin friction or viscous drag The coefficient of drag (C D ) is the measure of surface drag It is influenced by several factors associated with surface drag The roughness of the surface See Figure 8-6 The density (i.e., thickness) of the fluid (air vs. water)

22 Figure 8-6

23 Drag Force Principle Form Drag (A D ) Form drag represents the impact forces of the fluid colliding with the body It is also called shape drag, profile drag, or pressure drag Form Drag is influenced the two types of fluid movement Laminar Flow (higher pressure) Turbulent Flow (lower pressure) See Figure 8-7

24 Figure 8-7

25 Drag Force Principle Form Drag More collisions occur if the size of the turbulent flow region behind the body is large; thus, there is more drag force and opposition to movement Several factors influence the size of the turbulent flow region The shape of the object See Figure 8-8 Surface texture At lower velocities (less than 20 mph), an object with a smoother surface will have a smaller region of turbulent flow At higher velocities (greater than 20 mph), however, a rougher surface will actually result in a smaller region of turbulent flow See Figure 8-9

26 The Shape of the Object

27 Figure 8-9

28 Form Drag Principle Relative Velocity (v rel ) It is used to represent the relationship between the velocity of the object and the velocity of the fluid It is the difference between the object's absolute velocity and the fluid's absolute velocity See Figure 8-4

29 Figure 8-4

30 Drag Force Principle Strategies for Reducing Drag Force Reduce Fluid Density High- altitude Warm- weather Low humidity Reduce the Coefficient of Drag Make body surfaces and clothing (or equipment) smoother Wear tight- fitting clothes Reduce Cross- sectional Area for Drag Reduce the area being hit by the fluid Streamline the shape of the body or equipment

31 Drag Force Principle Strategies for Reducing Drag Force Reduce the Relative Velocity Because this term is squared, it has the greatest effect on drag force, so It is the most important variable that the athlete can control The method for reducing relative velocity is known as drafting

32 Drag Force Principle Strategies for Reducing Drag Force Additional Considerations Form drag accounts for most of the drag force at faster velocities, whereas Surface drag accounts for most of the drag force at slower velocities If you are moving through the fluid at speeds greater than 20 mi/hr, go for the streamlined shape which reduces the form drag Otherwise, try to reduce the surface drag.

33 LiO Force Principle The dynamic fluid force component that acts perpendicular to the relative motion of the object with respect to the fluid where, F = L 1 2 ρc L A L ( v ) 2 rel F L = lift force C L = coefficient of lift ρ = fluid density A L = surface area for lift v rel = relative velocity Some common examples (See Figure 8-11)

34 Figure 8-11

35 Characteris1cs of the Body or Body Segment to Create a LiO Force (C L ) Bernoulli s Principle Daniel Bernoulli ( ) Swiss Mathematician Faster- moving fluids exert less pressure laterally than do slower- moving fluids The airfoil The lateral pressure exerted by the faster- moving molecules is less than that exerted by the slower- moving molecules See Figure 8-12

36 Figure 8-12

37 Characteris1cs of the Body or Body Segment to Create a LiO Force (C L ) Spin The Magnus Effect Gustav Magnus, German Scientist Lift forces are also generated by spinning balls These lift forces are known as Magnus Forces See Figure 8-13

38 Figure 8-13 When molecules strike the lower surface of the ball, they don't slow down as much When the molecules strike the top surface of the ball, they are slowed down more According to Bernoulli's principle, then, less pressure will be exerted by the faster- moving molecules on the bottom surface of the ball

39 Characteris1cs of the Body or Body Segment to Create a LiO Force (C L ) Lift for Object Shapes other than Airfoils Lift is caused by the lateral deflection of fluid molecules as they pass the object The object exerts a force on the molecules that causes this lateral deflection According to Newton's third law, an equal but opposite lateral force is exerted by the molecules on the object This is the lift force See Figure 8-10 Angle of Attack

40 Figure 8-10