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FNT #7: Force, slope and the particle model
Damien Martin
November 27, 2006
Question 1: Throwing a ball
This questions asks about a ball that is thrown with the same initial speed
on the Earth and the moon. We are told that
g
Moon
≈
g
Earth
/
6.
a) Draw an energyinteraction diagram for both of these
situations
We know that KE
i
=
1
2
mv
2
i
for both situations, and that KE
f
=0
,asweare
interested in the highest point. We also know (either from conservation of
energy, or common sense) that
y
f
>y
i
. Finally we know that this is a closed
energy system. These considerations lead us to the following picture:
'
&
$
%
PE
y
↑
'
&
$
%
KE
v
↓
y
i
=0m
y
f
=??
v
i
>
0
v
f
∆PE + ∆KE = 0
mg
(
y
f
−
0) +
1
2
m
(0
2
−
v
2
i
)=0
Note that this diagram works for both the Earth and the moon.
b) Compare the maximum heights
In both cases,
all
the initial KE got converted into PE. As the initial amount
of KE in each case is the same, the ±nal amount of PE is the same. To show
1
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∆PE + ∆
KE
=0
(PE
f
−
0) + (0
−
KE
i
)=0
⇒
PE
f
=KE
i
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 Winter '08
 PARDINI
 Force

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