Biomechanics Lecture 6 (Linear Kinematics)

Newton's 1st law

Law of Inertia

Law of inertia

A body in motion will stay in motion, a body at rest will stay at rest unless acted upon by and external force, rest is a constant state.

What is inertia

the ability to resist a change in motion, has no unit.

mass is a property of...

intertia

Newton's second law

law of acceleration

Law of acceleration

Force = Mass x acceleration, also a=F/m

acceleration is directly proportional to _____ and inversely proportional to ____

force, mass

In the law of acceleration, if mass is cut in half,

acceleration doubles, and vice versa. Heavier objects (more mass) require more acceleration to move with the same velocity than lighter objects (less mass)

Newton's third law

Law of reaction

What is the law of reaction

for every action, there is an equal and opposite reaction, when one body exerts a force on a second, the second body exerts an equal reaction force in magnitude and opposite in direction

law of reaction equation

sum of a unit is constant

what is weight

product of mass and the acceleration caused by the attractive force between it and the earth : 9.81

Newtons 3rd law of motion introduces

friction

What is friction

a force that acts parallel to surfaces in contact and opposite to the direction of motion

What is a resultant force?

The overall force on a point or object

friction is dependent on

reaction force and coefficient of friction

starting friction

greater than moving friction, the effort to start an objects motion is greater than starting friction. You must break the barrier of friction

magnitude of Kinetic friction remains

constant, it is the friction that occurs between an object and a surface when it is in motion

The coefficient of friction serves as an

index

different surfaces have different

coefficients of friction

Friction equation

Ff = μFn (R)

Fn or R

normal perpendicular reaction force, inversely proportional to the force you are applying

what is frictional force? (F sub f)

A force that resists motion between two surfaces that are pressed together

Momentum is the quantity of

MOTION that the body possesses

Momentum is

mass, and the quantity that that mass has, is velocity

Linear momentum equation

M = mass x velocity

If you are able to possess more motion by running at someone who is standing still who has more mass...

you have more momentum than they do and can therefore knock them down

Momentum equation (with entanglement/elasticity)

mass1 (initial) + mass2 (initial) = (mass 1 +mass 2)Velocity (final [given or explicitly stated])

momentum equation for perfectly plastic objects

Newton's first law may be restated as the

principle of conservation of momentum

Principle of convervation of momentum

in the absence of external forces, the total momentum of a given system remains constant (M1=M2)

Coefficient of Restitution

number that serves as an index of elasticity for colliding bodies

equation for coefficient of restitution

-e = relative velocity after impact/relative velocity before impact

-e = v1-v2/u1-u2

Equation for coefficient of restitution with a moving body and a stationary one (with no velocity)

Impulse

change in momentum, or Ft (force x time)

Equation for force

Force = mass x acceleration

elasticity

an objects ability to return to its original size and shape when outside forces are removed

factors that affect coefficient of resitution

1) velocities

2) Temperature

3) Material

4) Spin

Work

force x displacement (force over a distance) (Measured in JOULES)

Power

amount of speed in that amount of time, amount of work per unit of time

Power equation

P=W/t (measured in WATTS) or P=Fxdisplacement/time

What is mechanical energy?

the capacity to do work, units of energy are Joules, thera are three forms of energy: kinetic, potential, thermal

What is kinetic energy

the energy an object has due to its motion (by virtue of motion)

Kinetic energy equation

KE=1/2mv^2 (THE [MV] PART CAN ALSO BE SUBSTITUTED FOR MOMENTUM) Also if theres no velocity then theres no motion and KE is zero

What is potential energy?

Energy by virtue of a body's position or configuration, (energy that is stored) by virtue of the object's height

Potential energy equation

PE = m x 9.81 x h (mg is weight)

What is the law of conservation of mechanical energy

when gravity is only acting external force, a body's mechanical energy remains constant

Law of conservation of mechanical energy equation

KE + PE = C (TE is negligible here)

What is the principle of work and energy

the work of a force is equal to the change in energy it produces in the object acted upon (W= change in KE +change in PE)

What is torque?

the rotary effect of a force about an axis of rotation, measured as the product of force and a force's moment arm

What is torque, more simply explained?

effect of force and perpendicular distance (where sine and cosine come in)

What is a moment arm

distance between a force's line of action and an axis of rotation

torque is the angular equivalent of

Force

in equilibrium, you cannot necessarily change the weight of a person, but the...

moment arm can change

When you're working with levers, what kind of equilibrium are you working with

static

conditions of static equilibrium

Third class lever

the input force is between the fulcrum and the load

third class body lever

First class lever

The fulcrum is positioned between the effort and resistance

first class body lever

Second class lever

the load is between the fulcrum and the effort (calf muscle)

second class body lever

What is mechanical advantage?

ratio of moment arm of the force to the moment arm of the resistance for a given lever

torque equilibrium equation

F(a) x distance (a) = F (b) x distance (b)

equations of dynamic equilibrium

concept indicating a balance between applied forces and inertial forces for a body in motion

center of gravity

point around which a body's weight is equally balanced in all directions, also center of mass

stability (mass, friction, CG, base of support)

resistance to DISRUPTION of equilibrium

balance (foot position)

ability to CONTROL equilibrium

What increases a body's stability?

increasing body mass, increasing friction between the body and the surfaces of contact