work  is done on an object by a constant force. 

This force is constant in both magnitutiude & direction.

the joule (J) 

= 1 N • m

If motion and force are in the same direction so that :

θ = 0

cos θ = 0

what will work be? 

W= Fd

For ex you push a cart 50 m with 30 N of force your work will be

W= 30 x 50

=1500 J

True,

ex you carry a grocery bag at rest 

OR

if you carry it horizontally across the room at a constant velocity

(this b/c there is horzontial force required to MOVE the bag at a constant velocity)

therefore theta is 90 and cos 90 =0

b/c displacment is perpendicular to force

Energy is a (conserved/nonconserved) quantity

KE= 1/2mv²

aka work is force x displacment

W_{net= ΔKE}

OR

W_{net= KE2 - KE1}

4x times greater

=

is capable of doing 4x more work

If the net work  (W) is positive then KE ___

If the net work (W) is negative then KE ___-

If the net work is (W) is zero then KE

1. Increases

2. Decreases

3.same

energy associated with forces that depend on the position or configuration of an object/s

REALTIVE to

surroundings

wound-up spring(waiting to be released)

stretched elastic band (waiting to be released)

an object at some height above the ground

(like a cup on a counter)

-F_frd = 1/2mv_2² - 1/2mv₁² -mgy2-mgy1

friction= (KE2-KE1)-(PE2-PE1)

 Recall the previous example:

 object at some height above the ground

(like a cup on a counter)

is an example of what specific potential energy?

potential gravitational energy 

(b/c of its position realtive to Earth)

W_ext= F_ext d cos 0

= mgh

W_ext=mg (y2-y1)

W_{ext =} PE₂-PE₁

=ΔPE

PE_grav= mgy

m= object mass in kg

g= 9.8 m/s

y= height in m

W_G= -mg (y₂- y₁)

W_{G= -} (PE₂ - PE₁)

W_{G= - Δ PE}

therefore the work done by gravity on an object is NEGATIVE

F_s = - kx

where

k= spring constant

x= distance

Give the formula to find the potential energy in a stretched/compressed string measured from its equilibrium positon

elastic PE= 1/2 kx²

scalar value

where x is the amount of spring stretched/compressed (meters)

units: N

no, it depends on the force involved.

note: kinetic energy does,

1/2mv²

work that is done by a force that depends on :

path

start point

end point

ex: friction

work  depends on intial + end position NOT PATH

ex. gravity

W_NC = ΔKE +ΔPE

1/2mv_1² + mgy_{1 =} 1/2mv₂² +mgy₂

* remember friction, tension are ex

When can

ΔKE +ΔPE =0 ?

when there are NO nonconservative forces

* the kinetic & potential energy changes are equal but opposite in sign 

(-5 and + 5)

if onlt conservative forces are acting, the total mechanical energy of a system neither decreases or increases in ANY process .

(aka it is conserved).

E= KE + PE

E= 1/2 mv² + mgy

recall this is  energy is constant

E1 =E2 

energy before=

energy after

The rollercoaster problem:

If there is no friction, then the speed of the rollercoaster will depend on

if there is a nonconservative force like friction, where does the KE +PE go?

unit for power (P)

capital P

W (watts)

1W= 1 J/s

P (average power) = (in words)

work/time

=

energy transformed

P (average power) = 

in terms of force & average velocity

P  

= W /t

= Fd/t

= F v

P  = W /t

give another formula for average power in terms of potential energy

= mg_yf-mg_yi

t

elastic PE energy formula :

where there is kinetic energy

such as firing  a spring loaded gun