an object that is moving, they help to explain acceleration
motion diagram
focus's on a single point, assumes object is a single point (example: door handle)
particle model
any push or pull, ____ is a vector
force
quantity that has direction magnitude-size or length adds in a special way
vector
quantity in which direction is not important (example: takes me 5 seconds to walk to the end of the hallway)
scalar
an arrow from a reference point to a point of interest (maybe chosen everywhere)
postion vector
arrow is a vector symbol arrow always points to the right, for r1 the magnitude is 2m and the diection is 45 degrees
vector symbol
in a straight line path from an earler point to a later point
displacement vector
speed and direction
velocity
the result of adding together two or more vectors
resultant
pick a scale for the length of the arrows
draw an arrow representing one of the vectors
place another arrow representing on of the other vectors with its tail at the first arrows tips
contiued with step 3 until all the arrows tips are at the arrows tails
the resultant is the arrow from the tail of the first to the tip of the last
graphical method of adding vectors (tip to tail method)
put tails at same point
put tails at same point
complete the parallelagram draw in a side parallel, to a and b with the same length
the resultant goes from the point it started to the opposite side (A+B)
parallelogram method of adding vectors
a negative vector has the same magnitude but the exact opposite direction
vector subtracting
take the distance and divide by the time
average speed
speed at the moment in time
instantaneous speed
average velocity = displacement divived by time taken
velocity of average speed
____ points in the same direction as displacement, in motion diagrams displacement vectors will be used to represent average velocities
average velocity
the rate of change of velocity
1.) speed up
2.) slowing down
3.)changing direction
acceleration
_____ =change in velocity divided by the time taken
average acceleration
if the acceleration is facing the same direction of velocity it is ____
speeding up
if the acceleration is facing a different direction of velocity its ____
slowing down
one moment of time shorter than any mesasurement of time
an instant
_____ of time has zero length
a moment
only two possible directions of motions
horizontal
vertical
one dimension linear motion
amount of change in velocity in one unit (one second)
acceleration
if gravity is the only force acting on an object the objuect with have a downward acceleration of 9.8 m/s
the highest point of acceleration=
-9.8m/s
usually called normal forces perpendicualr forces symbol is n(with arrow above)
compression forces
force exerted by a stretched elastic object as it tries to return to its natural shape (bungie cord ropes steel cables) symbol: T-->)
pulls inwards at both ends
tension forces
force exterted by a spring symbol: fsp->
spring force
force exerted by a solid that always opposes mortion
friction
prevents an object from starting to slide
static friction
opposes a sliding object we will assume fk does not change with speed
kinetic friction
friction between a rolling object opposes a rolling object
rolling friction
force exerted by a liquid or gas that always opposes motion
drag
force exerted by expelling gas or liquid at high speeds
thrust
the net force of air pressure on most objects is close to zero so we will ignore air pressure
air pressure
net force is called
resultant force
picture showing all the forces acting on a certain object
for the particle model
free body diagram
the tendency of an object to resist changes in its velocity and all objects have inertia bowling ball has more inertia than a basketball
inertia
measure of an objects inertia the units of mass are kg, g, mg
mass
is the force of gravity on an object units of weight newtons
weight
an objects mass is the same everywhere, an objects weight depends on location
straightline through origin
direct proprtionality
every measureable quanity has only one unit
si units
interpenetration of hills and valleys on surfaces
surface roughness
chemical bond for only when they are touching, if you have two very smooth surfaces you can get alot of chemical bonds and large friction
chemical bonding
kinetic and rolling friction dont depend on speed
fsmas, fk, and fr are all proportional to the normal forces
object moving at constant speed
uniform circular motion
acceleration always points towars the middle of the circle
same direction speeding up, deals with speed
acceleration parallel
change of direction, if a perpendicular is opposite then it is slowing down, if direction of a perpendicular shows direction of object is curving
acceleration perpendicular
r axis is towards center of the circle
t axis tangetial to circle with positive t in counterclockwise direction
z axis perpendicular to the plane of motion
force towards the center of the circle would be static friction
rate of going in a circle most common unit rpm, symbol w-omega
angular velocity
direction of a force and where you apply the force makes a difference
torque
line around which an object is rotating
axis of rotation
a single point
pivot
turning effect of a force, radial forces cannot create torque only tangential forces can
torque
distance from axis to point where force is applied times the tangentail component of force
torque
+ for counterclock wise, - for clockwise
torque
angle between r axis and force
phi
___ is located at center of gravity from one point
force
all objects have a singel point called
center of gravity
to calculate torque due to gravity, the entire wieght of the object can be assumed to pull down at the cg for a symetic uniform object cg is at the objects geometric center
if an object is at rest and supported at a single point the cg must be either directly below the support point
is what changes an objects rotation(speeding up or slowing down)
torque
the net force equals zero
the net torque equals zero- cannot rotate
static equalibrium
pick an object to focus on
draw a free body diagram of this object
choose a pivot point
calculate torque about this pivot for all the forces
solve
applying sum of torque = zero
forces always occur in pairs, they are in opposite directions
forces always exerts a force back on one another
action reaction pair
states that every action has an equal and opposite direction reaction
whenever one object exerts a force on a second object the second object exerts an equal and opposite force back on the first object
newtons third law
____ are equal (at the bumpers)
contact forces
depends on acceleration, larger acceleration usually menas more internal damage (on the drivers)
internal forces
mass times velocity
momentum
the more force you have the bigger the impulse
impulse momentum theorum
one or more objects we consider as a unit, a group of objects we wish to study
system
everything else
enviornment
force one part of system exerts on another part of system
internal force
force enviornment exerts on a system
external force
equals the sum of momentum of a system
total momentum system
if the net external force on system equals zero a systems total momentum remains constant
internal forces cannot change total momentum of a system
choose a system
does net external force equal zero
choose inital and final times
then solve p^{}_{f = }p_{i}
using the law of conservation of momentum
if delta t is very small the impuse and delta p is very small
if there is firiction then they would be different, the net system would not equal zero
if delta t is small enough total momentum of the system is conderved even if they net external force doesnt equal zero
impulse approximation
can normally be used in
collisions
explosions-situations where internal forces cause an object to suddenly split apart into two or more parts
impuls approximations
objects stick together
inelastic collision
postive work means F is enhancing the motion
negative work means F is opposing motion
is one in which the work done by this force just depends on inital and final postion not depended on the path
conservative force
is the ability to do positive work
energy
is the ability to do work because of motion and speed
kinetic energy
ability to do work because of height
gravitational poetential energy
ability to do work because of the stretching or comressing of an elastic object
elastic potential energy
ability to do work because of temperature
thermal energy
ability to do work because of chemical reactions
are always associated with conservative forces
when the ball was thrown kinetic energy increased while chemical energy decreases
potential energies
work done by external forces
external work
choose a system to focus on when using Ug, earth must be part of the system
chooose initial and final times
calculate external forces Wext
calculate change in each system
solve the energy equation
steps in using energy equation
creates thermal energy
where delta s is the total distance traveled against Fdiss, it is not dissplacement
with _____ both objects must be included in the system bc they both gain thermal energy
dissipative forces
the random motion of the atoms of a substance
thermal motion
rate of doing work or the rate of gaining or using up energy
power
energy of a substance due to thermal potion two parts of Eth
kinetic energy of the atoms
a form of Us due to the stretching and compressing of chemical bonds
thermal energy
is a measure of the aberage random kinetic energy of the atoms of a substance
temperature
boiling point of water 100 degrees
freezing point 0 degrees
absolue zero -273
celsius scale
absolute zero- 0
freezing point- 273
boiling point - 373
kelvin scale
everything at same temperature
thermal equalibrium
transfers from hotter objects to the cooler objects because of atomic collisions or radiation
thermal energy
thermal energy that transfers froma hotter object to a cooler object
heat
amount of heat needed to increase 1kg of the material by 1 degrees celsius
can be thought of as thermal inertia
specific heat
the more atoms there are in a kg of material the more heat it requires to increase the temperature
force divided by area
pressure
average pressure at sea levelĀ atm
atmospheric pressure
when a gas expands Wext is negative with heat
when a gas compresses Wext is positive
first law of thermodynamics
thermally insulated heat =zero delta Eth is positive
adiabatic compression
heat = zero delta Eth is negative temperature decreases