concept 4a Flashcards
translation
motion through space without rotation
vectors
are numbers that have magnitude and direction
displacement, velocity, acceleration, and force
scalars
numbers that have only magnitude and no direction
distance, speed, energy, pressure, and mass
resultant of vectors
the sum or difference of 2 or more vectors
always add tip-to-tail
place the tail of vector B at the tip of vector A without changing either the length to direction of arrow
tip-to-tail method
place the tail of vector B at the tip of vector A without changing either the length to direction of arrow
lengths of the arrow must be proportional to the magnitudes of the vectors
for vector addition
vector subtraction
subtraction is accomplished by adding a vector with equal magnitude but opposite direction to the first vector
simply flipping the direction of the vector being subtracted and then following the tip-to-tail method
right hand rule for vector direction
point thumb in direction of vector A
extend fingers in direction of vector B
palm/curl fingers to establish plane b/w the 2 vectors. this is the direction of the resultant
displacement (x or d)
change in position of an object in motion
vector quantity
connects in a straight line from the starting position to final position
independent of path
distance (d)
the path traveled
dependent on the path taken
scalar quantity
velocity (v)
the speed of an object displacement divided by time vector quantity unit m/s direction of velocity is necessarily the same as direction of displacement
speed (v)
rate of actual distance traveled in a given unit of time
scalar
force (F)
vector quantity experienced as pushing or pulling on objects
can exist b/w objects that aren’t touching
unit newton (N=kg*m/s^2)
gravity
an attractive force that is felt by all forms of matter
between 2 objects that depends on their masses and the distance between them
acceleration due to gravity (g)
g=10m/s (9.8)
gravitational force (Fg)
Fg=Gm1m2/r^2
G=6.67e-11
friction
type of force that opposes the movement of objects
causes objects to slow down or become stationary
2 types: static and kinetic
static friction (fs)
exists b/w a stationary object and the surface upon which it rests
0<(mu sub s)N
(mu sub s) is the coefficient of static friction and N is the magnitude of the normal force
normal force
is the component of the force b/w 2 objects in contact that is perpendicular to the plane of contact b/w the object and the surface upon which it rests
kinetic friction (fk)
exists b/w a sliding object and the surface over which the object slides
fk=(mu sub k)N
is a constant value (bc of the =)
static and kinetic friction
the value of (mu sub s) is always larger the (mu sub k)
the max value for static friction will be greater than the constant value for kinetic friction
objects will “stick” until they start moving, then will slide more easily over one another
mass (m)
a measure of a body’s inertia-the amount of matter in the object
scalar quantity
unit kg
independent of gravity
weight (Fg)
is a measure of gravitational force on an objects mass
is a force, is a vector quantity with unit N
Fg=mg
center of mass
or center of gravity
the weight of object can be applied at a single point in the object
for a uniform object it is at the geometric center of the object
acceleration (a)
rate of change of velocity that an object experiences as a result of some applied force
vector quantity
unit m/s^2
a=v/t
deceleration
acceleration in the direction opposite the initial velocity
graph of velocity vs. time
the tangent to the graph at any time, t, which corresponds to the slope of the graph, indicates the instantaneous acceleration
slope=acceleration
positive slope, postive acceleration, same direction as velocity
negative slope, decelertion, opposite direction of velocity
Newton’s first law
a body either at rest or in motion with constant velocity will remain that way unless a net force acts upon it
Fnet=ma=0
aka law of inertia
thought of as a special case of second law
Newton’s second law
an object of mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector
Fnet=ma
no acceleration occurs if the forces cancel out
Newton’s third law
to every action, there is always an equal but opposite reaction
law of action and reaction
Fab=-Fba
for every force exerted on object A by B there is an equal but opposite force exerted on B by A
linear motion
object’s velocity and acceleration along the line of motion
the pathway of a moving object continues along a straight line
one-dimentional motion
linear motion equations
v=v0+at x=v0t+1/2at^2 v^2=v0^2+2ax x=(v avg)t kinematics equations
free fall
object falls with a constant acceleration-accel. due to gravity (9.8)-and will not reach terminal velocity
solve using kinematics equations
air resistance
opposes the motion of an object, like friction
increases as the speed of the object increases
object in free fall will experience a growing drag as the velocity increases, will eventually equal the weight of object, and will fall at constant velocity
terminal velocity
velocity at which air resistance is equal to gravitational force and no acceleration occurs for an object in free fall
projectile motion
motion that follows a path along 2 dimensions
velocities and accelerations have 2 directions (usually horizontal and vertical) and are independent of each other
*for MCAT vy will change at rate of g but will be able to assume the vx is constant bc air resistance is negligible
inclined planes
motion in 2 dimensions
best to divide force vectors into components that are parallel and perpendicular to the plane
circular motion
occurs when forces cause an object to move in a circular path
uniform circular motion
the instantaneous velocity vector is always tangent to the circular path
object is kept in the circular path by a centripetal force
centripetal force
force that points radically inward, toward the center of the circle
keeps the object moving in a circular pathway
generates a centripetal acceleration
Fc=mv^2/r
dynamics
the study of forces and torques
translational equilibrium
exists only when the vector sum of all the forces acting on an object is zero
called the first condition of equilibrium, and is a reiteration of Newton’s first law
rotational motion
occurs when forces are applied against an object in such a way as to cause the object to rotate around a fixed pivot point, aka fulcrum
torque
moment of force
application of force at some distance from the fulcrum generates this
primary motivator for rotational motion that combines force, lever arm, and the angle b/w them
units Nm
T=rF=rFsin(theta)
lever arm
the distance b/w the applied force and the fulcrum
rotational equilibrium
exists only when the vector sum of all the torques action on an object is zero
called second condition of equilibrium
torque directions
torque that generates clockwise motion are considered negative
torque that generates counterclockwise motion are considered positive
energy
refers to a systems ability to do work or to make something happen
kinetic and potential
kinetic energy
the energy of motion
KE=1/2mv^2
unit joule (J=kg*m^2/s^2)
related to speed not velocity, object has KE regardless of direction of velocity
any object with mass that is moving with some speed has KE
potential energy
energy that is associated with a given object’s position in space or other intrinsic qualities of the system
stored energy, the potential to do work
gravitational and elastic
gravitational potential energy
depends on an object’s position with respect to some level of datum (“ground” or zero potential energy position)
PE=U=mgh
if any of the variables increase so does the potential energy
elastic potential energy
energy stored in springs and other elastic systems
when it is stretched or compressed from equilibrium length it has spring potential energy
U=1/2kx^2
k is the spring constant, x is magnitude of displacement from equilibrium
spring constant
k
measure of the stiffness of the spring
total mechanical energy
sum of an object’s potential and kinetic energies
E=U+K
first law of thermodynamics
accounts for the conservation of mechanical energy
energy can never be created nor destroyed-it is merely transferred from one from to another
does not mean that the total mechanical energy is held constant
conservative forces
force that does not cause energy to be dissipated from a system
such as gravity, electrostatic forces, and springs
pathway independent and associated with a potential energy function
conserve mechanical energy
nonconservative forces
dissipate mechanical energy as thermal or chemical energy
frication and air resistance
determining if a force is conservative
- if the change in energy around any round-trip path is zero
- if the change in energy is equal despite taking any path b/w 2 points
work
function of the applied force and the distance through which it is applied or the pressure and volume changes in a gas system
the use of energy to accomplish something
unit joules
measure of energy transfer
W=Fd=Fdcos(theta)=forcedisplacement
power
rate at which energy is transferred from one system to another
rate at which work is accomplished, energy expenditure per unit time
unit watts (W=J/s)
work-energy theorem
states that net work is equal to the change in energy (usually kinetic) of an object
Wnet=delta K=Kf-Ki
allows us to calculate work without knowing the magnitude of forces or displacement
mechanical advantage
the reduction in input force required to accomplish a desired around of output work using a simple machine
=Fout/Fin
ratio of magnitudes of the force exerted on an object by a simple machine (Fout) to the force actually applied on the simple machine (Fin)
simple machines
inclined plane wedge (2 merged inclined planes) wheel and axle lever pulley screw (rotating inclined plane)
pulleys
use same paradigm as incline planes: reduction of necessary force at the cost of increased distance to achieve3 a given value of work
allow heavy objects to be lifted using a reduced force
efficiency
=Wout/Win=(load)(load distance)/(effort)(effort distance)
load determines output force
effort determines input force
from output force and mechanical advantage we can determine necessary input force
load
the weight of an object balanced by tension of ropes
load distance is the certain height in air that the object is lifted
load is a force
effort
the force required to life the object
effort distance is equal to the total distance moved by all ropes/pulleys
