Work done by Forces, Work & KE, Conservation of KE, Work-Energy Theorem, Linear Momentum, Constant angular acceleration

Work done by force when force is constant

W = F(r)cos0

work unit

Joule (J)

1 J = 1 N\*m

work can be

positive negative or zero

if there is no displacement

there is no work no matter how large the force is

if F and r are perpendicular (90)

then the force does no work

positive work

theta less than 90 degrees

zero work

theta is 90 degrees

negative work

theta is greater than 90 and less than 270 degrees

if multiple forces are acting on an object, the total work can be found by

adding up with individual works (Wtot=W1+W2+W3)

OR

using work equation using total force

Wtot = Ftot\*r\*cos0

kinetic energy

the capacity of an object to do work based on its motion

KE=(1/2)mv^2

work-energy theorem

Wtot = delta KE = (1/2mvf^2)-(1/2mvi^2)

force not constant

Us or Ug

finding work graphically

area under a force vs displacement graph

Hookes law

Fsp = -kx

|Fsp| = k|x|

units of spring constant

N/m

work done by springs

Wsp = -(1/2kxf^2)-(1/2kxi^2)

conservative force

work done depends on the initial and final positions and does not depend on the path taken

conservative force examples

gravitational force

elastic force

nonconservative force examples

friction

applied force

push & pull action

tension force

the work done by gravity depends only on

the height of the starting and ending points (delta y)

for conservative forces it is always

possible to define a potential energy

the change in potential energy is equal

to the negative of the work done by a conservative force

delta U

\-Wcons

Ug

mgy

Us

(1/2)kx^2

if only conservative forces do work

the total mechanical energy remains constant

Emech before = Emech after

Emech = K + U = 0

conservation of mechanical energy

if only conservative forces do work, then the total mechanical energy is constant (zero)

work when friction is involved

Wtot= Wcons + Wnoncons

if non-conservative forces do work on the system

Emech = K + U = Wnoncons

power

the rate at which work is being done on a system

power unit

1 J/s = 1 Watt (W)

power formulas

P = dw/dt

Pavg = work/ time

two types of momentum

linear momentum and angular momentum

linear momentum

p =mv

units: kg\*m/s

momentum

vector quantity

\-multiple nonzero can add up to zero

kinetic energy

non-negative scalar quantity

K > 0

momentum and KE

K = p^2/2m

momentum and newtons second law

Fnet = dp/dt

I net

delta p (change in momentum)

impulse momentum theorem

F(delta t) = mvf - mvi

law of conservation of momentum

the total momentum of an isolated system is constant

impulse approximation

collisions and explosions are so brief they impart a comparatively insignificant impulse

perfectly elastic

two objects bounce after the collision

move separately

momentum & KE conserved

inelastic collision

two objects deform during collision so KE decreases

move separately after the collision

momentum conserved

perfectly inelastic

two objects stick together after collision

finals velocities are the same

momentum conserved

explosions

one big object becomes multiple smaller ones

KE not conserved

momentum conserved

elastic collision equation

m1v1 + m2v2 = m1v1 + m2v2

inelastic collision equation

m1v1 + m2v2 = (m1+m2)v3