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# Forces KIN 330

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This 26 page Class Notes was uploaded by Courtney Notetaker on Wednesday February 25, 2015. The Class Notes belongs to KIN 330 at Michigan State University taught by in Winter2015. Since its upload, it has received 87 views.

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Date Created: 02/25/15

Mechanical Work 02092015 How are coefficients of friction and restitution similar How are they different Both of unit less Both can not have negative values the lowest they can be is zero Both can not have values over one COF deals with the materials that two things are made out of COR deals with the two surfaces of the material Work The product of force and the amount of displacement in the direction of the force WFd displacement The means by which energy is transferred from one object to another UFd U work done on object F force applied to the object D displacement of an object along the line of action of the force Unites Nm orJ joule Because the force will likely vary we will use the average force for the equation Concentric positive work Isometric no work Eccentric negative work 0 Work can be positive or negative o It is positive when the object is displaced in the same direction of the force o It is negative when the object is displaced in the opposite direction of the force Where Do We See Negative Work Catching a football 0 Lowering from a pull up Gymnast landing and absorbing body weight and gravity 0 Person getting tackled in football 0 Generally dispassion of forces 0 Downhill skiing Energy 0 Energy is a term that has many meaning In mechanics energy is de ned as the capacity to do work 0 Many forms of energy including heat light sound chemical and so on Only focus on mechanical energy Mechanical Energy 0 The sum of kinetic energy energy due to motion and potential energy energy due to position Depends on frame of reference Kinetic Energy KE 12mvquot2 Units kg msquot2m Nm J Velocity will have a larger effect on KE Potential Energy The energy capacity to do work that an object has due to its position Gravitational potential energy which is energy due to an object s position relative to Earth Strain energy which is due to the deformation of an object Gravitational PE Due to an object s position relative to Earth PE Wh PE mgh h is height Same units Strain Energy Due to an object s deformation SE 12kdeltaxquot2 k stiffness or spring constant of material Delta x change in length or deformation from its un deformed position 0 Same units 0 Examples 0 Spring board 0 Diving board 0 Ligaments and tendons Generally be the lowest value out of the three How do Energy and Work Relate Work done Change in KE change in PE change in SE W KE 0 0 600 12mvfquot2 Vf SROOT 1200 2kg Vf 245 ms Remember Delta nal initial Doing Work to Increase Energy 0 Impulse o Impulse change in momentum 0 From this we should know that a large change in kinetic energy requires that a large force be applied over a long distance Doing Work to Decrease or Absorb Energy Catching Landing Running shoes Boxing gloves Air bag in a car Landing mats in track and eld Glove in baseball and softball Shock absorbing energy absorbing Conservation of Mechanical Energy The total mechanical energy of an object is constant if no external force other than gravity acts on the object U deltaE U 0 Delta KE Delta PE Delta SE Kei Pei Sei Kef PEf SEf Plug your various formulas for E in here and solve for unknowns Power Power is the rate of doing work P worktime Units js or watts 1 js 1 W What else do we measure in watts 0 Electricity What is the other unit for power 0 Horsepower How do we increase Power Shorten the duration of the activity Increase U which is F d For the same duration of time apply the force for a longer distance lncrease F which is m a If you increase any of these while keeping the others the same will power go up 0 Yes Power curve downward trend Where do we use Power in the Real World Vertical jump Biking use a power tap to nd the right gears Running nd the best stride length Still applies if sprinting or marathoning What are Common Power Tests Vertical jump Bench rep test Shuttle run 40 yard dash Step test Work in joules is calculated as body weight handheld weight x step height Cycle ergometer pedaling at a speci c cadence against a known resistance Newton s Laws 02042015 Newton s Laws of Motion 0 Newton s laws of motion are three physical laws that together laid the foundation for classical mechanics 0 They describe the relationship between a body and the forces acting upon it and its motion in response to said forces 0 They have been expressed in several different ways over nearly three centuries First Law when viewed in an inertial reference frame an object either is at rest or moves at a constant velocity unless acted upon by an external force 0 Second law the acceleration of a body is directly proportional to and in the same direction as the net force acting on the body and inversely proportional to its mass Thus Fma where F is the net force acting on the object m is the mass of the object and a is the acceleration of the object 0 Third law when one body exerts a force on a second body the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the rst body Newton s First Law of Motion Law of Inertia Objects at rest remain at rest and objects traveling at a steady rate in a straight line continue that way until a force acts on them 0 How this applies to human movement in sport 0 O O O O This is difficult gravity is an external force that acts on all objects close to the Earth Not on Earthbut if air resistance is negligible then yes for horizontal displacement of a projectile Also if the sum of the forces is zero the object is in a state of static equilibrium If something is moving in a straight line at a constant velocity Static equilibrium the sum of all the external forces acting on an object is zero if the object is in static equilibrium Says that if the net external force acting on an object is zero then there will be no change in motion of the object If it is already moving it will continue to move in a straight line If it is at rest it will stay at rest 0 SLIDES Conservation of Momentum o Newton s rst law of motion provides the basis for the principle of conservation of momentum Linear momentum is the product of an object s mass and its linear velocity The faster an object moves the more momentum it has The larger a moving object s mass the more momentum it has L mv kg ms Where do we see this Ball with bat Ball with racket Ball with feet Person with person Linear Momentum is de ned by L mv 0 Mass and velocity Velocity of an object is constant if the net force acting on the object is zero In sports and human movement most objects we deal with have a constant mass lf velocity is constant so is momentum meaning the constant net force is equal to zero Velocity is a vector quantity momentum is also a vector quantity SLIDES For a system made up of a number of objects the sum of the momenta of all the objects oat some initial time is equal to the sum of the momenta of all the objects at some later or nal time is no external forces act on the system A perfectly elastic collision is de ned as one in which there is no loss of kinetic energy in the collision Top equation is for objects that hit and bounce off one another Bottom equation is for objects that hit and stick together Perfectly Elastic Collisions When momentum is transferred from one object to another MaUa MbUb MaVa Mbe Books solves for Va and Vb Can solve for any of these variables What will happen if the objects are the same size 0 Equal effect 0 Different sizes 0 One with the bigger mass will have the affect on the other object 0 Moving in opposite direction 0 Hit each other and depending on size determines how they recoH 0 One velocity has to be negative and one velocity has to be positive 0 Moving in the same direction 0 Speed up the object in front transfer momentum Perfectly Plastic Collision A and B adhere and remain together after their impact The velocity of their common center of mass after the impact is given by 0 SLIDES inelastic collision Perfectly lnelastic Collision When objects stay together and move together at the same speed after a collision Can solve for any of these variables 0 Examples 0 Most collisions in the real world are not perfectly inelastic or perfectly elastic Coefficient of Restitution o SLIDES Will always be a value between zero and one o Is affected by the nature of both objects in the collision o SLIDES Where is it used in rules and regulations 0 Coefficient of restitution of tennis balls footballs basketballs etc Newton s 2nCI Law Anytime an object starts stops speeds up slows down or changes direction it is accelerating and a net external force is acting to cause this acceleration Sum of forces ma This applies to all 3 planes of movement Think about riding an elevator and how it effects how your weight feels Used to determine vertical acceleration and deceleration due to gravity with projectiles Lower something you exert less force than raising an object What does this men when it comes to vertically lifting a stationary object o The more force you apply the acceleration will be higher lmpulse and Momentum lmpulse is the product of force and time during which the force acts SLIDES Restating the 2nCI law the average net force acting over some interval of time will cause a change in momentum of an object The force we apply is important but how long we apply the force is also important Using lmpulse to Decrease Momentum Want to slow something down 0 Example trying to catch a ball or stop a pass lncrease delta t Spreading force out over a longer period of time will help to diffuse it better Newton s Third Law of Motion If an object exerts a force on another object the other object exerts the same force on the rst object but in the opposite direction Think about pushing on a wall or standing on the oor Newton s Law of Universal Gravitation States that all objects attract each other with a gravitational force that is inversely proportional to the square of the distance between the objects Also stated that this force of gravity is proportional to the mass of each of the two bodies being attracted to each other SLIDES R is distance On Earth this becomes F mg or Wmg Real World Examples Seat belts 0 Second law How does the counter movement in a vertical jump help 0 Third law How would swing through the ball help performance in a striking sport 0 First keeps velocity constant with your body 0 Second increase in acceleration 0 Third increase in equal and opposite Linear Kinematics Describing Objects in Linear Motion 01212015 What is Kinematics o The branch of dynamics concerned with the description of motion 0 Dynamics deal with motion Statics deal with no motion Branches of Rigid Body Mechanics Diagram What is Linear Kinematics o Kinematics the topic of this chapter is the branch of dynamics concerned with the description of motion o It is the description of movements without getting into what causes those movements 0 The outcomes of many sporting events are kinematic measures speed acceleration and so forth What is Motion 0 Change of position 0 Need time and space Motion o In physics motions is a change in position of an object with respect to time and its reference point 0 We classify motion as linear angular or both general Linear Motion 0 Also referred to as translation It occurs when all points on a body or object move the same distance in the same direction and at the same time o This can happen in two ways rectilinear translation or curvilinear translation Rectilinear translation occurs when all points on a body or object move in a straight line so that the direction of motion does not the change the orientation of the object does not change and all points on the object move the same distance 0 Curvilinear translation all points of the object follow curved paths o No axis Angular Motion 0 Angular motion is also referred to as rotary motion or rotation It occurs when all points on a body or object move in circles or parts of circles about the same xed central line or axis 0 Can occur inside or outside the body 0 Most of our joint movements 0 Bicycle wheel or tire wheel o If you are not sure if something is angular or linear try to nd an axis and see if all points move about it General Motion 0 Combination of linear and angular motions o It is the most common type of motion exhibited in sports and human movement 0 Running and walking are good examples of general motion So What Classifying motion as linear angular or general motion makes the mechanical analysis of movement easier Position 0 The rst kinematic characteristic we might describe out an object is position 0 Our de nition of motion the action or process of change in position refers to position Mechanically position is de ned as location in space 0 Can be at the beginning middle or end of a movement 0 Usually the Earth s surface 0 Real world examples include track and hockey We can use Cartesian coordinates for 2 dimensional movement 0 We need to add an axis for each dimension added 0 Units of length used to describe position 0 Meters Distance Traveled and Displacement Distance traveled is a measure of the length of the path whose motion is being described from the starting initial position to ending nal position DIRECTION OF TRAVEL IS NO CONSIDERED 0 Displacement is the straight line distance in a speci c direction from the starting initial position to ending nal position Resultant displacement is the distance measured in a straight line from the initial position to the nal position 0 Displacement is a vector quantity 0 It has a distance magnitude and direction Distance Traveled Simply a measure of the length of the path followed by the object whose motion is being described from its starting initial position to its ending nal position Distance will always be greater than or equal to displacement Computing Distance Net Displacement Find distance by summing magnitudes of the displacements for a series of rectilinear movements 0 Find overall displacement by adding individual displacements Formulas Triangle means change 0 d means distance 0 x amp y are the direction we are moving in o f subscript is nal 0 i subscript is initial Velocity and Speed 0 Velocity is rate of motion in a speci c direction 0 More speci cally it is the rate of displacement Since displacement is a vector quantity so is velocity 0 Velocity has a magnitude number and a direction associated with it 0 Has units of lengthtime or ms 0 Velocity change in positionchange in time 0 Velocity displacementtime Speed is just rate of motion it is the rate of distance traveled It is described by a single number on thus it is a scalar quantity 0 Speed distancetime Speed and velocity are the same when you are moving in a straight line Instantaneous Speed or velocity at a speci c instance in time 0 Or distance traveled divided by the time it took to travel that distance if the time interval used is very small relative to activity Example 0 Velocity vs speed as I move around the room 0 Speed can be constant but velocity changes if you change direction Acceleration 0 Rate change of velocity 0 A vector quantity because velocity is a vector quantity 0 Change in velocitywhat that means is speeding up slowing down stopping changing direction are all acceleration Acceleration change in velocitychange in time 0 Units msquot2 Can also be instantaneous o The direction of motion does not indicate the direction of acceleration Uniform Acceleration and Projectile Motion 0 When acceleration of an object is constant it is considered uniform This will occur when the next external force acting upon on an object is constant and unchanging This allows us to describe the motion of the object with equation and predict or know things about the object Ball Toss Describe the motion of the ball 0 Curvilinear Horizontal Motion of a Projectile o The horizontal velocity of a projectile is constant and its horizontal motion is a straight line Optimal Angle for Release 0 If you want to maximize the time of ight or the height reached by a projectile the vertical component of release velocity should be maximized and the projection angle should be about 45 degrees 0 If you want to minimize the time of ight of a projectile the upward component of released velocity should be minimized Chapter 5 Torque s and Moments of Force What are Torques A turning effect produced by a force Angular or rotary force A torque produced by a force may also be called a moment of force or a moment for short Example when we spin a book by applying force outside its COG Torque An external force directed through the COG of an object is called a centric force The effect of a centric force is linear movement An external force not directed through the COG of an object is called an eccentric force note force not contraction The effect of an eccentric force is to change both the linear and angular motions of an object A force couple is a pair of forces which are equal in size but opposite in direction and non collinear The effect of a force couple is to cause a change in only the angular motion of an object No linear change based on Newton s 1st law T Fxr o T torque moment of force 0 F force 0 r moment arm of perpendicular distance 0 Units Nm Work KE PE SE ls considered a vector Usually positive counter clockwise and negative is clockwise Where do we use Torque in the real world Opening doors What 0 Getting bolts off an object Swinging a golf club baseball bat tennis racquet etc Rowing Wrestling Muscular Torque Most muscular contractions produce torque about our different joints 0 Size of moment arm changes as we move this is partially why our muscles are stronger in some joint positions than others 0 A muscle s moment arm is maximal at 90 degree angle of pull Strength Training Devices and Torque How could we better design weight equipment to take into account changes in the size of the moment arm 0 Change the pulley system Forces and Torques in Equilibrium 0 Linear for an object to be at static equilibrium the external forces acting on it must sum to zero 0 Angular for an object to be at static equilibrium the external torques acting on it must sum to zero 0 For an object to be at equilibrium the external forces must sum to zero and the external torques about any axis must sum to zero is Center of Gravity o The center of gravity is the point at which the entire mass or weight of the body is maybe considered to be concentrated 0 Sum erSumercg o W weight of one element 0 r moment arm of that element 0 Sum w the total weight of the object o ch the movement arm of the entire weight of the object o The location of the COG of the object relative of the axis about which the moments of force are being measured COG of the Human body 0 ln anatomical position 12 inches below the belly button 55 of height for adult females 57 of height for adult males Where would a child s COG be Higher or lower 0 Higher because their upper body is bigger than their lower body Higher your COG the more unstable you are COG and Performance 0 Think about volleyball and basketball players 0 Think about vertical jump test 0 How do some athletes appear to hang in the air 0 Manipulating body while in the air so it looks like the individual is at the same height COG and Stability 0 Stability is the capacity of an object to return to equilibrium or to its original position after it has been displaced When we want to be stable 0 Alignment 0 Hockey players running into the boards and other individuals 0 Gymnastics 0 When we want to resist movement 0 When do we want to be unstable able to move quickly 0 Sprinter down on the blocks Receiving a serve Swimming Downhill skier Goalie 0000 Factors Affecting Stability The stability of an object is affected by the height of the COG the size of the base of support and the weight of the object Base of support is the area within the lines connecting the outer perimeter of each of the points of support P x h W x b P toppling force h moment arm of toppling force W weight of object B moment arm of the book Stability and Potential Energy The most stable stance or position that an object or person can be in is the one that minimizes potential energy 0 The lower the PE the more stable a person is PE mgh Lower h COG Stability and Human Movement Stability is maintained only as long as the line of gravity falls within the base of support Walking is a series of falls and catches Some times you want to maximize stability in a certain direction Examples 0 Walking 0 Running 0 Hopping o Skipping When do you want to minimize stability increase mobility 0 When you are pushing on an object Forces Maintaining Equilibrium or Changing Motion 01262015 Facts About Forces 0 Are acting upon us at every instant of our lives 0 Important for motion because they allow us to start moving stop moving change direction 0 Important even if we are not moving 0 We are manipulating forces just to stay sitting or standing So What is A Force 0 A push or a pull 0 EX muscles can pull and use joints to create a pushing motion 0 We know them as pounds but for this class we should know them as Newton 0 Sir Isaac Newton laws of motion 0 English scientist and mathematician 1N the force required to accelerate a 1 kg mass 1mss Force 0 1 N 225 pounds 0 1 pound 4448 N 1 N is roughly the force of the apple that fell on Newton s head quotIt s a mathematical term represented by an arrow with both direction and magnitude Vector o It has size and direction What is a Force A force is any in uence that causes a free body to undergo a change in speed a change in direction or a change in shape Force can also be described as a push or pull that can cause an object with mass to change its velocity A force has both magnitude and direction making it a vector quantity Classifying Forces lnternal Forces 0 Pulling tensile forces putting the structure under tension 0 Pushing compressive forces Hold thing together but can also be greater than the structure can withstand bad news 0 Pulls ruptures tears and breaks lnternal forces are important for studying the nature and causes of injuries Muscles can only change our motion if they can apply force against some external object Examples 0 Kicking a ball 0 Walking running biking skipping etc o Diving off a diving board External Forces Forces that act on an object as a result of its interaction with the environment surrounding it External forces are either contact forces or noncontact forces Touching versus nontouching Examples 0 Gravity o Magnetism 0 Nuclear forces at the atomic level Acceleration due to gravity is 981 mss Roughly 10 Fma Wmg W 10kg 981mss 981 kgmss 981 N Contact Forces Solids of uids 0 Sliding a desk across a surface 0 Swimming 0 Sailing or driving a power boat Friction horizontal Normal contact force vertical Friction is important when 0 Locomotion so we need to understand it EX car wheel a Smooth enough to move but sticky enough to not slip We Will Focus on Dry Friction Happens between non lubricated surfaces of solid objects or rigid bodies in contact and acts parallel to the contact surface Between two surfaces that are not moving the friction is called static of limiting friction Between two surfaces that are moving it is called dynamic sliding or kinetic 0 Dynamic will be the greatest Fs usR subscripts Fd udR subscript d F is a friction force u is coefficient of friction and R is normal contact force Does surface area have an effect on friction o No it is not part of the equation Does the weight of an object have an effect on friction 0 Yes due to the R in the equation Does the material type have an effect on friction 0 Yes due to the u in the equation Addition of Forces Force Composition The net force acting upon an object is the sum of all the external forces acting upon it This is not just found by adding up all of the forces Why not 0 They are not always going in the same direction o If they are going in the same direction it is made much more simple Forces are vectors and we need a direction to go with it The resultant force is found by adding two or more forces The net force is all of the external forces acting upon an object It is also referred to as the resultant force because it results from the addition of all the external forces Colinear Forces Easiest to deal with All have the same line of action Pushes are generally positive and pulls are usually negative Real world examples of collinear forces 0 Tug of war 0 Anything in the weight room Concurrent Forces Do not act along the same line but do act through the same point Ways to calculate 0 Use a free body diagram and a graphical representation of all forces 0 Use Pythagorean s theorem 0 Use trig SOH CAH TOA Where theta is the angle we are using in a right triangle Resolution of Forces What if the external forces are not collinear and do not act in a vertical or horizontal direction Find the components of each and break down Examples look in book Graphics will get you a good estimate but we need to be able to calculate We need to remember that these are vectors so we need to use the head to tail method Direction is important Static Equilibrium If it is at rest the forces are in equilibrium and the object is described as being in a state of static equilibrium This means that the net forces are equal to zero There is a branch of mechanics dealing with this called statistics This is useful in calculating how strong you have to be to hold a certain position or to stop or withstand a certain force Example 0 Doing planks Sum of a static force will equal zero Steps in Determining Resultant Forces Draw a free body diagram and don t forget to include gravity If the forces are collinear then you only have to use one formula otherwise separate into vertical and horizontal components Make sure the signs are correct Use Pythagoreans theorem and arctangent to determine the size and direction of the resultant force EXAMPLES ON SLIDES Do the problems from the book pages 4650

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