physics chp 6/7

energy

Total amount of energy never changes. Conserved energy transfered from one system to another

isolated system

no external forces acting on it

closed system

does not allow any energy or matter to be transferred into or out of the system

conservative force

unconcerned of path taken, only final and initial positions. ex)gravity or spring constant

-if object returns to original position, net work is 0 and mechanical energy conserved

nonconservative force

concerned with path taken. ex) friction or air resistance because a longer path means more work

Work Energy Theorem

Wnet= change in KE

Wnet= Fnet x d x costheta or change in 1/2mv²

-only conservative work is gravity and spring constant

-the total net work done on an object equals the change in that object's kinetic energy.

work

way to transfer energy into or out of a system, product of the component of force along direction of displacement times the magnitude of distance

-work by force vector that is less than 90 degrees from displacement is +, if more than 90, -, if equal or 0 then no work done

-Same Direction (theta = 0)): If the force and the movement point in the exact same direction, work is Fxd

Kinetic Energy and work energy theorem

Wnet= change in KE= (1/2)mvf² - (1/2)mvi^2

potential energy

1. potential energy is stored

2. ability to do work or gain Kinetic Energy

3. Potential Energy defined only for conservative forces →gravitational PE or elastic PE

4. PE requires that 2 objects be apart of same system

5. Dependent on relative position of two objects

gravitational potential energy

Ug=mgy

elastic spring force

-when spring at equilibrium point, spring is stretched a certain distance of delta x from this equilibrium position. There is a restoring force (trying to bring string to equilibrium) proportioal to how far string is stretched. F=-kdeltax

elastic/spring potential energy

takes work to stretch spring and spring stores elastic PE. Ue=(1/2)kdelta x²

two potential energies

change in U=change in Ug + change in Ue (mgyf-mgyi)+(1/2kdelta xf² -1/2kdeltaxi²)

Mechanical Energy

E=K+U

Wnc=delta E

It represents the total energy an object has due to its motion and position, giving it the ability to do mechanical work.Total mechanical energy (\(E_{\text{mech}}\)) combines energy in motion with stored energy:

Conservation of Mechanical Energy

The conservation of mechanical energy states that the total mechanical energy in a closed system remains constant as long as only conservative forces (like gravity or springs) act on it.

-use when no friction
-delta E= deltak+ deltaU=0

-ki +Ugi + Uei = kf +Ugf + Uef

1/2mv²i + mgyi + 1/2kxi² = 1/2mv²f+ mgyf + 1/2kxf²

Friction

Wf=Ffdcostheta

Ff=Fn x friction coeffecient

Power

P=W/t or P=total E/t

-rate at which energy is transferred or transformed. Energy transfer into system done by external work so power defined as rate that work is done

linear momentum

p=mv

-Linear momentum is the product of an object's mass and its velocity. In physics, it measures how much "motion" an object has and how difficult it is to stop it from moving in a straight line.

-According to Newton's Second Law of Motion, applying a net external force to an object changes its momentum over time. A quick push over a short time or a gentle push over a long time can produce the same change in momentum, known as impulse.

linear momentum and force

F=ma → F=p/t

Impulse and collisions

I=Fext x time = linear momentum, if no external forces the Impulse and linear momentum=0

Collisions: classify a system as all objects colliding ex) fireworks exploding, collsion in midair, horz collision between two cars

conservation of momentum

-when system is isolated, momentum = 0 because external forces are 0

-can use if impluse very small

inelastic collisions

momentum conserved, most collisions do not conserve kinetic energy, occur when object stick together after collision

momentum and kinetic energy

K=p²/2m

elastic collisions

-during collision or explosion we can use conservation of momentum but most collisions do not conserve KE but if they do then use elastic

center of mass

moves in same way a single particle would given the same external forces

-if on symmetric object at the midpoint