Version 045/AACDB – quiz1031 – Demkov – (59910)
1
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001
10.0 points
A cylindrical pulley with a mass oF 5
.
1 kg, ra
dius oF 0
.
883 m and moment oF inertia
1
2
M r
2
is used to lower a bucket with a mass oF 2 kg
into a well. The bucket starts From rest and
Falls For 3
.
6 s.
r
M
m
How Far does it drop? The acceleration oF
gravity is 9
.
8 m
/
s
2
.
1. 24.5
2. 25.6517
3. 41.2571
4. 19.6951
5. 13.1116
6. 27.9138
7. 30.2565
8. 17.8025
9. 13.4742
10. 36.0624
Correct answer: 27
.
9138 m.
Explanation:
Let :
M
= 5
.
1 kg
,
r
= 0
.
883 m
,
m
= 2 kg
,
and
g
= 9
.
8 m
/
s
2
.
Let
T
be the tension in the cord and
α
the
angular acceleration oF the wheel. Newton’s
equation For the mass
m
is
mg

T
=
ma
T
=
m
(
g

a
)
and For the disk
T r
=
I α
(

)
rh
=
p
1
2
M r
2
P
±
a
r
²
2

2
=
M a
2
= (
M
+ 2
m
)
a
a
=
2
M
+ 2
m
±rom kinematics, since
v
0
= 0 ,
y
=
v
0
t
+
1
2
a t
2
=
1
2
a t
2
=
1
2
p
2
M
+ 2
m
P
t
2
=
mg t
2
M
+ 2
m
=
(2 kg) (9
.
8 m
/
s
2
) (3
.
6 s)
2
5
.
1 kg + 2 (2 kg)
=
27
.
9138 m
.
002
10.0 points
A(n) 7 kg object moving at 9 m
/
s in the posi
tive
x
direction has a onedimensional elastic
collision with an object initially at rest. AFter
the collision the object oF unknown mass has
a velocity oF 8 m
/
s in the positive
x
direction.
What is the unknown mass?
1. 8.75
2. 10.6667
3. 5.0
4. 2.1
5. 3.2
6. 1.4
7. 3.6
8. 6.3
9. 2.13333
10. 4.0
Correct answer: 8
.
75 kg.
Explanation:
Given:
v
2
i
= 0.
±rom conservation oF
momentum, we have
m
1
v
1
i
=
m
1
v
1
f
+
m
2
v
2
f
m
1
(
v
1
i

v
1
f
) =
m
2
v
2
f
.
(1)
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View Full DocumentVersion 045/AACDB – quiz1031 – Demkov – (59910)
2
Because of elastic collision, energy is con
served. Therefore
1
2
m
1
v
2
1
i
=
1
2
m
1
v
2
1
f
+
1
2
m
2
v
2
2
f
m
1
(
v
2
1
i

v
2
1
f
) =
m
2
v
2
2
f
m
1
(
v
1
i

v
1
f
) (
v
1
i
+
v
1
f
) =
m
2
v
2
2
f
(2)
Dividing Eq. (2) by Eq. (1) we have
v
1
i
+
v
1
f
=
v
2
f
v
1
f
=
v
2
f

v
1
i
(3)
Substituting Eq. (3) in Eq. (1) we have
m
1
v
1
i
=
m
1
(
v
2
f

v
1
i
) +
m
2
v
2
f
m
2
v
2
f
=
m
1
v
1
i

m
2
(
v
2
f

v
1
i
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 Spring '07
 Swinney
 mechanics, Acceleration, Angular Momentum, Mass, Angular velocity, Angular Acceleration, kg

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