Kinetic Energy is associated with the state of motion

Different energies:

? Kinetic/translation

? Gravitational potential

? Heat energy

? Electromagnetic energy

? Strain or elastic energy

Each energy is associated with a

¡°scalar¡± which defines a state of a

system at a given time.

Kinetic Energy

Kinetic Energy is associated with the state of motion

1 2

KE = mv

2

Units of Joules: 1 J = kg¡¤m2/s2

? KE depends on speed (v) not v ( here v = v ? v = v )

? KE doesn¡¯t depend on which way something is moving

or even if it¡¯s

i ¡¯ changing

h i direction

di i

? KE is ALWAYS a positive scalar

2

2

How much is ¡°Kinetic Energy¡±

Kinetic Energy is associated with the state of motion

2

? KE depends on speed not v ( here v 2 = v )

? KE doesn

doesn¡¯tt depend on which way something is moving

or even if it¡¯s changing direction

1)

Electron (e-) moving in Copper

me = 9.11¡Á10-31 kg and v ~ 1¡Á106 m/s KE = 7¡Á10-19 J ( ~ 4 eV)

2))

Bullet traveling

g at 950 m/s (3100

(

ft/s).

)

m = 4.2 g and v ~ 950 m/s (3100 ft/s)

KE = 2000 J

3)

Football Linebacker

m = 240 lbs and v ~ 18 mph

p ((7 m/s)) KE = 2800 J

4)

Aircraft Carrier Nimitz

m = 91,400 tons and v ~ 1 knot

KE = 10 MJ

Work

If you apply a net force ((~a¡ü

a¡ü ¡ú v¡ü), KE ¡ü

and

if you decelerate (a¡ý ¡ú v ¡ý), KE ¡ý

Somehow force is related to KE energy¡­

If we transfer energy via a force, this is work.

¡°Doing work¡± is the act of transferring energy.

Work (W) is said to be done on an object by a force.

Energy transferred to an object is positive work.

work

gy transferred from an object

j is negative

g

work.

Energy

Work and Kinetic Energy

How to find an ¡°alternate

alternate form

form¡± of Newton¡¯s

Newton s 2nd Law that relates position and velocity.??

Start in 1-D (e.g. Bead along wire x? ), we know ¡­

Fx,net

dv

= max = m

dt

? dx ? ? dv?? dx ?

dv

(Fx,net

)?? ?? = ?? m ???? ?? = mv

,

dt

dt dt

dt

Fx,net

dx

=

dt

d (12 mv2 )

dt

Fx,net dx = d ( mv

1

2

2

)

2

1

dx

=

d

mv

KE1

¡Ò

(

) = KE 2?KE

x,net

2

¡ÒF

Wnet ¡Ô ¡Ò Fx,net dx = KE 2 ?KE 1= ¦¤KE

Wnet = ¦¤KE

Work--Kinetic Energy Theorem

Work

Work-Kinetic

Energy Theorem

(

change in the kinetic

energy of an object

)=(

net work done on

the particle

If Fnet is not a function of x , then

Wnet ¡Ô Fnet ? d = ¦¤KE

No work is done on an object by a force unless there is a

component of the force along the objects line of motion.

)

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