Exam 3 Energy Equations Physics Knowt

Main Kinematic equation

R2=R1+(vr,1)t+1/2at²

Use KE when

problems cares abt how the speed changes

Use PE when

the problems care abt going higher

Power can be

negative

Objects can have the same speed even if

they reach the ground at diff times

External work

energy added to or removed from your system by a force you are not treating as potential energy

if you are solving for thermal energy then friction is usually treated as…

internal work DEPENDING on siuation

You can use mgy in the equation Ei + Wext = Ef, but only if

Wext does not include Fg as force/work, Fg is now an internal force cuz u have Ug

How to find Kmax in U(J) (PE graph)

Kmax=Umax-Umin

what are some examples of internal forces

spring forces

What are usually external forces

Fg, friction, Fn

Work done by a variable force CALC EQ

W = ∫F·dr

Time, Acceleration, Velocty kinematics eq

Vr,2=Vr,1+at

Distance, acceleration, velocity kinematics eq

Vr²,2=vr²,1+2a(deltax)

Displacement, time, Velocity, acceleration kinematics eq

Deltax=Vit+1/2at²

if force and displacement are facing same direction

work is +

if force and displacement are facing opposite direction

work is -

if force and displacement are prependicular

work is 0

Work Equation

W=Magnitude of Force x Magnitude of Displacementcos(theta)

Work, kinetic energy calc equation

Work = Kinetic E = Integral of Force (USE RADIANS WHEN HAS TRIG IN THE FORCE)

work is a ____ quantity

scalar ("Scalar" doesn't mean "can never be negative." It means the quantity has only magnitude and no direction)

W total equation

Wext1 + Wext2 + …

in order for a force to work and have energy gained, force must be applied in

direction of motion

restoring force

force attempting to return a stretched bond to it unstretched (equilibrium) length

restoring force is opposite

displacement

as long as you dont stretch it too far, restoring will

return the object back to its og shape

plastic

object doesn’t return to og shape

all materials have

an elastic range

elastic range is followed by a

plastic range

deformation results in

permenant change

Hooke’s Law Equation

Fsp=-kx

Stretched spring force

Fsp < 0

stretched displacement

initial - final x

compressed displacement

final - inital x

compressed spring force

Fsp > 0

unstretched spring force

Fsp = 0

elastic

object returns to its og shape

forces that cause circular motion do

no work because motion is perpendicular to force

Dot product of i and j hats, component formula

A x B = AxBx + AyBy

Ki and Kf equation

K2/K1 = 1/2mv2²/1/2mv1²

Dot product magnitude form

A x B = |A| |B|cos(theta) - angle is between the 2 vectors

energy is not a

vector but uses vectors

if it doesn’t say specific thing has energy then

it doesn’t have energy for that situation

Hookes Law is

relationship between force/displacement for a spring

K cant be

negative

Calc Equation process for work of spring

Wsp= Integral Fsp → Integral -k*vector of x → -1/2k(x²f - x²i)

How to find Thermal energy

potential and kinetic energy

Thermal energy

motion of microscopic objects

Etherma, eq

K micro + U micro

Dissipative Forces

a force that causes the macroscopic kinetic energy to be transformed into thermal energy

example of dissipative force

kinetic friction, air drag

Eth dissipative force eq

Eth=Fkdeltas

Equation for power Esys eq

DeltaEsys/DetlaTime

Power

rate that energy is transferred

work

transfer of energy between system and enviornment

Power work eq

P=W/T

Power eq calc

Derivative of work w/ respect to time dw/dt

power force eq

P=F*FVcos(theta)

Work-Kinetic Energy Theorem?

ΔEsys= ΔK = Wₜₒₜ (Wa+Wb) - use a specific work IF the problem states

What is a restoring force?

A force that acts to return an object to equilibrium

What is Hooke's Law?

Fₛₚ = -kx

What does k represent?

Spring constant (stiffness of the spring)

Why is there a negative sign in Hooke's Law?

The spring force always opposes displacement

Formula for work done by a spring?

Wₛₚ = -½k(xf² - xi²)

Power from a force?

P = F·v = Fv cosθ = Fx/tcosθ

What is a dissipative force?

A force that converts mechanical energy into thermal energy.

Examples of dissipative forces?

Friction and air resistance.

Formula for nonconstant power

P = dE/dt

Relationship between potential energy and work?

ΔU = -Wᵢₙₜ

Change in gravitational potential energy?

ΔUg = mgΔy

What determines gravitational potential energy?

Vertical height only

Law of Conservation of Energy?

Total energy of an isolated system remains constant.

Mechanical energy eq

Emech = K + U

When is mechanical energy conserved?

When there are no dissipative forces.

Conservation of mechanical energy equation

Ki + Ui = Kf + Uf

Spring potential energy formula?

Usp = ½kx²

Change in spring potential energy?

ΔUsp = ½k(xf² - xi²)

What does the difference between total energy and potential energy represent?

Kinetic energy.

Can kinetic energy be negative?

No

What is stable equilibrium on an energy diagram?

A local minimum of potential energy

What is unstable equilibrium?

A local maximum of potential energy.

Relationship between force and potential energy

F = -ΔU/Δs

Calculus form of force-potential relationship

F = -dU/ds

What is a conservative force?

A force whose work depends only on starting and ending positions

Examples of conservative forces? Can be written with PE

Gravity and spring forces.

Examples of nonconservative forces? can’t be written with PE

Friction, drag, tension

Work conservative and PE eq

W conservative = -ΔU

Conservation of energy eq

Ei=Ef

Wext, Esys, Emech, Ethermal eq

Wext = ΔK + ΔU + ΔEthermal

work done by system

energy is transferred from system to surroundings

work done on the system

energy is transferred into the system by the surroundings

Conservation of energy with external work

Ei + Wext = Ef

Energy conservation with external work and thermal energy?

Ki + Ui + Wext = Kf + Uf + ΔEthermal