fisica1-youn-e-freedman-exercicios-resolvidos

9.92: Energy conservation: Loss of PE of box equals gain in KE of system.
1 2 1 2
mboxgh
= mboxvbox
+ Ipulleyωpulley
2 2
1
2
+ Icylinderωcylinder
2
vBox
vBox
ωpulley
= and ωcylinder
=
r
r
1
mBgh
= m v
2
v
B
=
p
1
2
2
B B
1
mBgh
= m v
2
2
B B
m
B
1 ⎛ 1 2 ⎞ ⎛ v
+ ⎜ mCrC
⎟
2 2
⎜
⎝ ⎠ ⎝ r
1 2 1 2
+ mPvB
+ mCvB
4 4
m gh
+ m +
B
1
4
p
1
4
C
cylinder
1 ⎛ 1 2 ⎞ ⎛
⎜
v
+ ⎜ mPrp
⎟
2 ⎝ 2 ⎠
⎝ r
m
B
p
⎞
⎟
⎠
B
C
2
⎞
⎟
⎠
2
=
2
(3.00 kg)(9.80 m s )(1.50 m)
1
1.50 kg + (7.00 kg)
4
= 3.68 m s
1 2
9.93: a) The initial moment of inertia is I
0
= MR . The piece punched has a mass of
M
and a moment of inertia with respect to the axis of the original disk of
16
M ⎡1
⎛ R ⎞
⎢ ⎜ ⎟
16 ⎢⎣
2 ⎝ 4 ⎠
2
2
2
⎛ R ⎞ ⎤
+ ⎜ ⎟ ⎥ =
⎝ 2 ⎠ ⎥⎦
The moment of inertia of the remaining piece is then
9
512
MR
2 9 2 247
I = MR − MR = MR
2 512 512
1 2
2
2 1
2 383
b) I =
1 MR + M ( R / 2) − ( M /16)( R / 4) = MR
2
2
512
2
.
2
.
.