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Unformatted text preview: = lim
=
âˆ†tâ†’0 âˆ†t
dt
dW
P=
=
dt ï¿¿ ï¿¿
ï¿¿x
d F Â·ï¿¿
dt x
ï¿¿ Â· dï¿¿ = F Â· ï¿¿
ï¿¿v
=F
dt Figure 7.18 Conservation of Energy
Chapter # 8
Skier starts at the top of
the hill
â€¯On which run does her
gravitational energy
change the most (a), (b),
(c), (d) or are they all the
same?
Assume no friction Falling ball of mass m Conservative
and
NonConservative Forces Ball raised along a two dimensional path We call a force conservative if:
the work done by the force on an object
moving from one point to another depend only
on the initial and final positions of the object,
and independent of the particular path taken
WG = ï¿¿ 2 ï¿¿
Fg Â· dï¿¿
l 1 = ï¿¿ 2 mg cos Î¸dl 1 WG =âˆ’ ï¿¿ y2 mgdy y1 = âˆ’mg (y2 âˆ’ y1 ) Ï† = 180â—¦ âˆ’ Î¸ cos Î¸ = âˆ’ cos Ï† dy = dl cos Ï† continued
â€¯A force is conservative if the net
work done by the force on an object
moving around any closed path is
zero Potential Energy
âˆ’
â†’
âˆ’
â†’
Wext = F ext Â· d = mgh cos 0â—¦ = mgh = mg (y2 âˆ’ y1 )
â†’
âˆ’
â†’âˆ’
WG = F G Â· d = mgh cos 180â—¦ = âˆ’ mgh = âˆ’ mg (y2 âˆ’ y1 )
âˆ†U = U2 âˆ’ U1 = Wext = mg (y2 âˆ’ y1 ) âˆ†U = U2 âˆ’ U1 = âˆ...
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This note was uploaded on 02/03/2014 for the course PHYSICS 1061 taught by Professor Tsankov during the Fall '09 term at Temple.
 Fall '09
 tsankov
 Physics, Energy, Force, Work

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