-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

-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

-at the highest point in the system

max potential energy

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

-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

-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

-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)

-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)

-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

-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)

-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

-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

-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

-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

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

-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

-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

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

-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

-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

return to its original position

unstable mechanical equilibrium occurs at the top of hills because if the marble is moved it will

not return to its original position

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

-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

-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

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

-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

-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