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Projectiles Using Energy

Conservative System: Ei = initial mechanical energy = KEi + PEi

Ef = KEf + PEf

=

mvi2 + mgh

=

mvi2

Conservation: Ef = Ei

mvi2 =

mvi2 + mgh

Conservative Systems with Springs:

Hooke’s Law =

spring = -k

Wsp

sp

Fext = -Fsp

= kx

Wsp =

kx2 = PE stored by spring

Non-Conservative Systems (Friction):

Wext =

ext ∆ = Fext ∆x

Frictionless: Wext = ∆KE + ∆PE

Add Friction: Wext = ∆KE + ∆PE + ∆TE

∆TE: thermal energy dissipated by the system

Alternatively, Wext - |Wf| = ∆PE + ∆KE

∆TE = |Wf| Wf = Fk∆x

Power:

- the rate at which energy is transferred from one system to another

Wext = Fext∆x

Power =

IF an external force is applied giving external work Wext over a time interval, then

the average power is Pavg =

If Wext = Fext∆x, Pavg =

= Fext

= Fext Vavg

Instantaneous Power: Pinst =

ext

inst =

ext

Momentum & Impulse:

- collisions between objects involve complex forces that act over short time

scales and are typically not constant

- consider a large force exerted over a small interval of time

o impulse force

o parameterized by the area under the force-time graph = Impulse

Impulse =

=

avg∆t = area under force-time graph

Momentum: p = mV

I = Favg∆t

=

∆t

I = Pf – Pi = ∆P

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