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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