# Physics roller coaster labels

-stored or hidden energy
-an objects capacity to do work
-height is the only variable that changes in its equation
-work done by conservative forces
potential energy
-where kinetic energy is zero
-at the highest point in the system
max potential energy
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all forms of energy and work are measured in
joules
equation for potential energy
mgh
potential energy increases as
kinetic energy decreases
potential energy is increased by an increase in
height
-energy of motion (whether horizontal or vertical motion)
-work needed to accelerate a body from rest to stated velocity
kinetic energy
the kinetic energy of an object is directly proportional to
the square of its speed
kinetic energy increases as
potential energy decreases
if there is an increase in speed, KE will
increase
equation for kinetic energy
1/2mv^2
-states that energy is never created or destroyed, only changes form
-total energy of an isolated system cannot change, but is only conserved over time
-total energy of isolated system is constant
Conservation of Energy
equation for conservation of energy
Ei=Ef (Ui+Ki+Wnc=Uf+Kf)
-measure of motion in a specific direction
-vector quantity
-when an object covers the largest amount of distance in the shortest amount of time
-also known as terminal velocity
max velocity
velocity is measured in
m/s
equation for velocity
delta x/t
if velocity is constant, the net force on an object is
zero
if velocity is increasing and there is an acceleration, the force on an object is
nonzero
if acceleration is decreasing velocity is
decreasing
as velocity decreases, the net force on an object is moving closer to
zero
-final KE must be less than initial KE
-force and distance in equation are magnitudes and never negative
-in order to be negative, cos@ must be negative
-occurs when vectors point in opposite directions, and angle between them is 180 (cos180= -1)
worknet negative
work is negative (because it’s gaining PE) when the marble is rolling
uphill
equation for worknet
delta K
equation for work
Fdcos@
-final KE must be more than initial KE
-force and distance in equation are magnitudes and never negative
-when force on object is same direction as displacement, the vectors have an angle of O (cos0=+1)
worknet positive
work is positive (because it’s gaining KE) when the marble is rolling
downhill
-scalar quantity equal to amount of force exerted over a certain distance
-transfer of energy into different forms
work
-when an object is in free-fall
-only work done on object is by gravity (pulling it back to the ground)
work due to gravity
equation for work due to gravity (change in PE)
Wg=-delta Ug
-due to gravity/acceleration of an object in the vertical direction during free-fall
9.8
acceleration is measured in
m/s/s
equation for acceleration
delta V/t
-force that makes an object go in a circle
-occurs along any curved path, always directed towards the center of the circle
-tighter the circle the more
-sum of forces pointing towards the middle of a circle
-perpendicular to tangential velocity (the straight path of an object)
-net force causing centripetal acceleration
centripetal force
centripetal force on top of a loop
force of gravity
centripetal force on bottom of loop
normal force
equation for centripetal force
mv^2/r
centripetal force is measured in
Newtons
-rate of change of tangential velocity
-if an object moves in a circular motion, tangential speed is constant, but direction of the tangential velocity vector changes as the object rotates (velocity is changing)
-direction is always towards center of circle
centripetal acceleration
equation for centripetal acceleration
v^2/r
centripetal acceleration is measured in
m/s/s
-change in momentum over a certain amount of time in the positive direction (down)
-final momentum is larger than initial momentum
-vector quantity
positive impulse
the marble has positive impulse when it travels
downhill
equation for impulse
J=deltaP
J=Ft
impulse is measured in
N-S
-change in momentum in a certain amount of time in the direction established as negative (up)
-vector quantity
-the longer a resultant force is applied the bigger the change in linear momentum
negative impulse
the marble has negative impulse when it travels
uphill
-states for a collision in an isolated system the momentum of the two objects before the collision equals the momentum of the two objects after the collision
-the loss of momentum of one object equals the gain of the other
Conservation of Momentum
KE is conserved in a collision
elastic
KE is not conserved in a collision
inelastic
objects stick together (velocity is same) in a collision
perfectly inelastic
momentum is measured in
N-S
equation for momentum
P=mv
Pi=Pf
-two dimensional motion
-object falls in parabolic path only under influence of gravity
-constant acceleration in x and y directions
-horizontal and vertical motions completely independent of each other
-horizontal has no acceleration, velocity is constant
-vertical component of acceleration is 9.8
-time in both directions is the same
-at peak of parabola the velocity in vertical direction is zero
projectile motion
-occurs where total work in system is zero
-must have no acceleration, but could be at constant velocity
mechanical equilibrium
type of mechanical equilibrium when an object cannot return to its original position after being moved from rest
unstable
type of mechanical equilibrium when an object returns to its original position after being moved from rest
stable
type of mechanical equilibrium when the object is moving at a constant velocity
dynamic
dynamic mechanical equilibrium occurs during straight but slightly sloped track because the force that the marble is moving at (mgsin@) equals (going in the opposite direction) the
force of friction
stable mechanical equilibrium occurs at the bottom of hills because if the marble is moved it will
unstable mechanical equilibrium occurs at the top of hills because if the marble is moved it will
during mechanical equilibrium equations for force and acceleration would equal
zero
-Law of Inertia
-states an object in motion will stay in motion at a constant velocity if the net force is zero
-an object at rest remains at rest unless a net force acts on it
-an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a nonzero force
Newton’s First Law of Motion
Newton’s first law applies to the marble whenever the marble has a
constant velocity
during Newton’s first law, equations for force and acceleration would equal
zero
-states the acceleration of an object is directly proportional to the force applied to the object and inversely proportional to the mass of the object
Newton’s Second Law of Motion
in Newton’s second law, a larger mass requires a ______ amount of force to be moved
larger
in Newton’s second law, a smaller mass requires the same amount of force but more
acceleration
equation for Newton’s Second Law of Motion
F=ma
-states that for every action force, there is a equal but opposite reaction force
-the forces cannot cancel each other out or acceleration would be zero
-always comes in a pair, but always on two different objects
Newton’s Third Law of Motion
Newton’s Third Law of Motion allows for the marble to travel through the roller coaster (its contact forces) and also for energy to be
conserved
equation for Newton’s third law
F=ma
Fa=-Fb
-friction force for an object in motion
-lower than static friction
-more force is required to set the objects in motion than to keep them in motion
kinetic friction
force that fights the intended motion and is opposite the intended direction of motion of an object
friction
kinetic friction decreases with a _______ in the speed of sliding objects and _____ with an increase in the speed of sliding objects
decreases, increases
if the force vector decreases, kinetic friction ____ and if the force vector increases, kinetic friction _____
decreases, increases
equation for friction is
Ff=uFn
kinetic friction is measured in
Newtons
-states that the force needed displace a spring is inversely proportional to the displacement times the strength of the spring
-only for ideal springs
Hooke’s Law
in Hooke’s Law, when a spring is stretched, it opposes the stretching with a force known as the
spring force
in Hooke’s Law, the magnitude of the spring force is _____ to the displacement from the spring’s equilibrium position
proportional
in Hooke’s Law, a spring with a larger spring constant produces larger forces at the same
displacement
in Hooke’s Law, the direction of the spring force is _____ the displacement
opposite
in Hooke’s Law, the proportionally constant k is the force of spring constant and is the property of a
particular spring
in Hooke’s Law, the force that will always try to restore the spring to its relaxed state, whether it has been stretched or compressed is known as the
restoring force
equation for Hooke’s Law
Fx=-kx
equation for potential energy of an ideal spring (Hooke’s Law)
U=1/2kx^2
Hooke’s Law is measured in
N/m

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