Biomechanics Exam 3

Force

A mechanical disturbance or load that may deform a body or change its state of motion

Is force a vector or scalar quantity?

Vector

• Has: 

  • Magnitude  

  • Direction  

  • Point of application 

  • Line of action (line of application) 

Point of application

• Where to the tendon attaches to the bone for internal forces

• For external forces, point of application is where body is in contact with some external body (ex: ground reaction force)

Examples of contact forces

• Ground reaction forces 

• Joint reaction force 

• Friction 

• Fluid resistance 

• Muscle force 

Examples of non-contact forces

• Gravity 

• Centripetal 

Newton’s First Law

• Law of Inertia 

• A body will maintain a state of rest or constant velocity unless acted on by an external force that changes the state 

• In absence of net force, the state of motion of an object will not change 

Inertia depends on ______

mass of object

What is inertia

Inertia is the resistance of an object to changes in its state of motion

Newton’s Second Law

• Law of Acceleration 

  • Acceleration of an object is: 

    • Directly proportional to the net force 

    • Inversely proportional to the mass 

    • In the same direction as net force 

    • Defined by the equation: F=ma 

If net force is increased, what happens to acceleration?

It increases (F= ma)

Newton’s Third Law

• Law of reaction

• For every action, there is an equal and opposite reaction

Law of Gravitation

All bodies are attracted to one another with a force proportional to the product of their masses and inversely proportional to the distance between them 

Ex: weight (W = mg) 

Ground Reaction Force (GRF)

The equal and opposite reaction force the ground exerts on the body during stance  (stance phase of walking)

How do you measure GRF 

• Force plate used to measure GRF 

• GRF is assumed to act on the center of
  mass of the individual

If a person is standing still on a force plate, what would their GRF read?

It would be equal to their weight (need acceleration to change the GRF)

Center of mass (COM)

object's mass is equally distributed in all directions

When acceleration is negative = vertical GRF is….

less than a person’s bodyweight

When calculating GRF, is gravity negative or positive?

Positive

Describe vertical GRF in walking 

• Highest in stance phases 

• Highest in the pre-swing phase, specifically

When acceleration is positive = vertical GRF is….

greater than a person’s bodyweight

Speed impact on GRF

• Stance phase is shortened with greater speeds 

• Max GRF is higher in running than in walking

• Steeper slope with greater speed

• With running, one defined peak whereas walking has two peaks

Why is there only one peak in the vertical ground reaction force graph of running?

Heel does not hit ground

How does mass affect GRF?

• Larger mass means higher max values for VGRF 

• Shape of graph does not change with mass 

Joint Reaction Force 

• Equal and opposite force between two articulating bones (ie joint) caused by the weight and inertial force on the bones 

• From compressive force and shear force, we can calculate joint reaction force (resultant joint reaction force) 

Muscle Force

Resultant of all forces generated by muscle force

Friction

force acting at the area of contact between two surfaces in the direction opposite that of motion or motion tendency

What kind of force is friction?

contact

Factors affecting friction

• Force acting perpendicular to the surface

  • Ground reaction force

• Properties of the surface

  • coefficient of friction

Order these from lowest to highest coefficient of friction: ice, gravel, concrete

ice < gravel < concrete

Smaller coefficient of friction is easier or harder to move across?

easier

Static friction

When applied force is exerted on object/body, but no movement occurs; static friction resists the applied force 

Maximal static friction

• Eventually, you get to a point where you have applied enough force to overcome the static friction and make the object/body movement — this is the max static friction

• Static friction just before applied force exceeds friction

For static bodies, friction is equal to ______

applied force

Kinetic friction

• AKA dynamic friction

• Applied force exceeds friction force, creating movement 

• The friction that is experienced by a moving object/body 

For kinetic bodies, friction is ______ applied force

less than 

Is it easier to get an object to start moving or to keep it moving? Explain.

• Static friction coefficient is greater than dynamic friction

• Molecular bonds form between surfaces that are static

  • When in movement, these bonds can’t form as well

  • Harder to break the initial bonds

Translational Friction

• Object that occurs when there is sliding of an object/body 

Rolling friction 

• Object rolls on surface and point of contact between object and surface changes 

• Ex: bike wheels

Rotational Friction 

• Resistance between rotating bodies 

• The resistance to motion that a rotating body experiences due to friction

Rotational Friction vs Rolling Friction

Rolling friction acts on the point of contact, while rotational friction is a twisting force that affects the object's spin. 

Artifical grass vs natural grass

• Theory is that artificial turf exerts higher frictional forces on people moving on it than natual grass

• Injury risk is higher

• Literature is inconclusive

What kind of force is fluid resistance?

contact force

What kind of force is air resistance?

Fluid force (a contact force)

Fluid force

Types of force exerted on object in fluid

Two main types of fluid force

Drag and lift

Drag

Force that resists the movement of object/body 

Coefficient of drag

An index of how smooth and streamlined the object/body is

What affects drag?

• Coefficient of drag

• Projected frontal area of object/body (area facing flow, A)

• Fluid densitu (or viscosity)

• Velocity of the body/object relative to the fluid

What does the magnitude of C_d depend on?

• Shape of object

• Orientation of object relative to flow 

• Streamlining reduces C_d 

How to calculate relative velocity?

Relative velocity = velocity of object/body + velocity of fluid 

Types of drag force

• Surface drag: friction of fluid on object’s surface

• Pressure drag: caused by pressure differential between the front and back of the object

Surface Drag

The friction of fluid on an object’s surface

Pressure Drag

• Caused by pressure differential between the front and back of the object

• Dominant form of drag in human movement

• Creates a turbulent wake

• Pressure differential = pressure in front of object/body

Turbulent Wake

Non-uniform flow of fluid around an object

What happens when you increase pressure differential?

Increase in resistance and pressure drag

Describe the pressure differenial and turbulent flow of the highest pressure drage

Highest pressure drag has highest pressure differential and largest turbulent flow

Why do golf balls have dimples 

They reduce the turbulent wake which in turn reduces pressure drag 

Free body diagrams (FBD) 

• Sketches of a defined system in isolation with all force vectors acting on the system 

• Which forces you draw depend on how you define the system

Centripetal force a non-contact or contact force?

non-contact

Centripetal force definition

the net force that causes an object to move in a circular path by constantly pulling it towards the center of the circle; line of application is towards the center of the circle 

Momentum definition

effect of force applied over time 

Momentum and collision relationship

• Momentum is particularly useful in collision analysis  

• Increases in momentum increases resulting effect of collision

Perfectly inelastic collision definition

• collision resulting in the total loss of system velocity 

• AKA plastic collision

Inelastic collisions 

• Momentum is conserved and objects stick/move together instead of bouncing apart 

• Momentum before collision = momentum after the collision 

Impulse Definition

Change of momentum over time 

How can we maximize jump height

• By increasing impulse

  • I = force * change in time

  • Can increase force

  • Can increase time interval

Impulse-momentum relationship 

The impulse applied to an object/body is equal to the change in its momentum

How do you decrease an object's force when catching a baseball or softball?  

Increase contact time (cushioning or dampening)

Think about impulse formula

How do you minimize forces acting on your body when landing from a jump? 

Flexing the hips, knees, and dorsiflexing the ankle allows for more time (greater range of motion) 

Think about impulse formula

Kinetics

forces that cause motion

Angular motion

all parts of the body or object do not move through the same distance during the same amount of time

Torque

Tendency of a force to cause rotation about an axis 

What directions can act torque be in?

• Counterclockwise  

• Clockwise

Gravitational Torque (in human movement)

A rotational movement that a person experiences due to gravity

Muscle torque 

• Using muscle force to produce a rotational movement 

• Ex: trunk flexion

Ground Reaction Force Torque 

• When ground reaction force acts on a person causes them to have a rotational movement  

• A person doing a backflip 

Line of action/pull (torque)

Straight line in the direction of which the force is acting  

Moment arm

• perpendicular distance from the line of action of a force to the axis 

• In other words: the distance from the application of the forces to the center of mass of the segment

Relationship between moment arm and joint angle

• Moment arm is a function of joint angle 

• Changes non-linear with joint angle 

• Also affected by angle of attachment

• This is the same relationship for muscular and gravitational torque

Center of mass

• The point at which the sum of torques is equal to zero 

• The point at which a body’s mass (weight) is evenly distributed (balanced)

• Think: seesaw

Center of gravity

The projected position of the center of mass vertically on the ground

Is the center of mass always inside the body/object? Explain.

The calculated center of mass might not always be inside the body 

• Eg. The Fosbury flop (jump used in high jump) 

• Curved body makes center of mass below the cross bar 

• Requires less force in jumping 

Center of mass relationship with gravitational torque

force acts on center of mass

Muscular torque and center of gravity relationship

Muscular torque is counteracting the center of gravity

Calculating muscular torque vs gravitational

Do not need to use the sin function in gravitational torque because line of pull of gravitational force is likely perpendicular to moment arm so sin(theta) is not needed (sin(90) =1) 

Do need sin function to calculate muscular

Why are the center of masses of humans hard to calculate? How do we overcome this?

• Difficult to compute COM for human bodies because the various material of the human body have different densities  

• Also changes from instant to instant 

• Segmental method is how we overcome this 

  • We break down body into segments  

  • Calculate the center of mass of each segment using literature values that tell you what percent of the bone from the proximal end the COM is  

  • Can use all the centers of masses of the segments to find the COM of the entire body 

How can you use center of mass to calculate moment arm?

Moment arm = horizontal distance between COM and axis of rotation

If net force = 0, then change in velocity =

0

Weight needs to be in what units when calculating gravitational torque

Newtons (N)

Lever definition

simple machines consisting of a relatively rigid bar-like body that may be made to rotate about an axis 

What are the parts of a lever

effort/force arm, resistance arm, fulcrum

Force arm

perpendicular distance from line of action to effort force

Resistance arm

perpendicular distance from the line of action to resistance (or load) force 

Fulcrum

the point of support or axis about which a lever may be made to rotate 

Describe the biceps brachii as parts of a lever

• Fulcrum = axis of rotation at the elbow 

• Effort force = muscle force of biceps 

• Resistance force = gravitational force on the forearm 

What is mechanical advantage?

mechanical effectiveness of a lever calculated by taking the effort arm/resistance arm 

What affects mechanical advantage

• Muscle length 

• Cross-sectional area of muscle 

• Moment arm 

• Angle of attachment of muscle 

• Shortening velocity of muscle 

• Training  

• Fatigue 

Mechanical advantage > 1 means…

• It’s easier to lift something 

• Can generate more force with less effort 

Mechanical advantage < 1 means…

• It’s harder to lift something

• Requires more effort to produce force 

• Can be advantageous when you need to have greater speed or distance/endurance rather than greater force 

1^st class lever

Effort force and resistance force are on opposite sides of the fulcrum