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Lets look at the equations of motion!
This shows that the quantity before free
fall is the equal to the same quantity
after the fall.
∆
y
2a
v
v
y
2
iy
2
fy
+
=
i
2
iy
f
2
fy
gy
2
v
gy
2
v
+
=
+
)
y
2g(y
v
i
f
2
iy
−
−
=
Energy – Ch 10
____________
Kinetic Energy & Potential Energy
mg
dt
dv
m
ma
F
y
net
−
=
=
=
dy
dv
v
dt
dy
dy
dv
dt
dv
y
y
y
y
=
=
mg
dy
dv
mv
y
y
−
=
Lets look the Newton’s second law in a freefall situation. F
net
= ____
Using the chain rule
Placing this into the above equation
Rearranging gives
mgdy
dv
mv
y
y
−
=
∫
∫
−
=
f
i
fy
iy
y
y
v
v
y
y
mgdy
dv
mv
____________
____________
Kinetic Energy & Potential Energy
mgdy
dv
mv
y
y
−
=
∫
∫
−
=
f
i
fy
iy
y
y
v
v
y
y
mgdy
dv
mv
f
i
fy
iy
y
y
v
v
2
y
mgy
mv
2
1
−
=
i
f
2
iy
2
fy
mgy
mgy
mv
2
1
mv
2
1
+
−
=
−
i
2
iy
f
2
fy
mgy
mv
2
1
mgy
mv
2
1
+
=
+
This is an equation that
shows the ___________ of
energy as an object falls.
It
shows that the initial energy
of the system is the same as
the final energy of the
____________
_______________
Kinetic Energy & Potential Energy
i
2
iy
f
2
fy
mgy
mv
2
1
mgy
mv
2
1
+
=
+
There quantities have specific names.
Kinetic Energy
Gravitational Potential Energy
Kinetic Energy is the energy of ______________.
Potential energy is the energy of ___________.
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View Full Document Kinetic Energy & Potential Energy
i
2
iy
f
2
fy
mgy
mv
2
1
mgy
mv
2
1
+
=
+
Note: This equation can now be written as
The total __________ of the system is not changed by freefall!
gi
i
gf
f
U
K
U
K
+
=
+
The unit of energy is called the Joule
1 joule = 1 J = 1 kgm
2
/s
2
Zero of Potential Energy
The zero of potential energy is __________.
You may set it to be
wherever you like.
We will typically take zero to be at the ______
point in the motion so that all of the height are positive.
This also
allows the potential energy of the object to be zero at the lowest
point.
Skiing down a Frictionless Hill
A skier on ski’s weights 500N.
They move down the slope a vertical
distance of 100m.
Find the speed of the skier at the bottom of the
slope assuming his initial velocity is 10.0 m/s.
10.0 m/s
100m
θ
Skiing down a Frictionless Hill
v
i
= 10.0 m/s
v
f
= ?
y
i
= 100m
y
f
= 0m
U
i
+ K
i
= _____________
mgy
i
+ ½ mv
i
2
= mgy
f
+ ½ mv
f
2
Cancellation of the masses yields:
______ + ½ v
i
2
= gy
f
+ _______
(9.80m/s
2
)(100m) + ½ (10.0m/s)
2
= ½ v
f
2
v
f
= [2[50m
2
/s
2
+ 980m
2
/s
2
]]
1/2
v
f
= 45 m/s
Note: does not
depend on
______ of
hill!!!
Whee
H
R
x
Roller Coaster of Death!!!
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This note was uploaded on 04/17/2008 for the course PHYSICS 122 taught by Professor Pope during the Spring '08 term at Clemson.
 Spring '08
 pope
 Energy, Kinetic Energy, Potential Energy

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