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Version 018 – TEST03 – TSOI – (58160)
1
This printout should have 15 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001
10.0 points
The fgure below shows a rigid 3mass system
which can rotate about an axis perpendicular
to the system. The mass oF each connecting
rod is negligible. Treat the masses as parti
cles.
The
x
axis is along the horizontal direction
with the origin at the leFtmost mass 7 kg.
7 kg
7 kg
7 kg
4 m
4 m
x
The masses are separated by rods oF length
4 m, so that the entire length is 2 (4 m).
Determine the
x
coordinate oF the center oF
mass For the threemass system with respect
to the origin.
1. 3.07692
2. 5.06667
3. 5.0
4. 4.16667
5. 3.46154
6. 2.66667
7. 1.52941
8. 4.0
9. 4.28571
10. 2.35714
Correct answer: 4 m.
Explanation:
±irst fnd the center oF mass. Defne the
origin to coincide with the Far leFt mass
M
.
X
CM
=
∑
m
i
x
i
∑
m
i
=
(7 kg)(0 )
(7 kg) + (7 kg) + (7 kg)
+
(7 kg)(1 (4 m)
(7 kg) + (7 kg) + (7 kg)
+
(7 kg)(2 (4 m)
(7 kg) + (7 kg) + (7 kg)
=
21 kg
21 kg
(4 m)
= 4 m
.
002
10.0 points
A wheel starts From rest at
t
= 0 and rotates
with a constant angular acceleration about a
fxed axis. It completes the frst revolution in
6
.
5 s.
How long aFter
t
= 0 will the wheel com
plete the second revolution?
1. 6.08112
2. 9.89949
3. 9.61665
4. 7.9196
5. 7.21249
6. 2.82843
7. 11.8794
8. 8.76812
9. 9.19239
10. 3.67696
Correct answer: 9
.
19239 s.
Explanation:
Let :
t
1
= 6
.
5 s
,
θ
1
= 1 rev
,
and
θ
2
= 2 rev
.
The wheel starts From rest, so
θ
=
θ
0
+
1
2
αt
2
=
1
2
αt
2
∝
t
2
.
Thus
θ
2
θ
1
=
t
2
2
t
2
1
t
2
=
r
θ
2
θ
1
t
1
=
r
2 rev
1 rev
(6
.
5 s)
=
9
.
19239 s
.
003
10.0 points
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View Full DocumentVersion 018 – TEST03 – TSOI – (58160)
2
Two identical balls (labelled A and B) move
on a frictionless horizontal tabletop. Initially,
ball A moves at speed
v
A,
0
= 10 m
/
s while
ball B is at rest (
v
B,
0
= 0).
The two balls collide oFcenter, and after
the collision ball A moves at speed
v
A
= 6 m
/
s
in the direction
θ
A
= 53
◦
from its original
velocity vector:
10 m
/
s
A
before
B
after
6 m
/
s
A
0 m/s
b
b
53
◦
Which of the following diagrams best repre
sents the motion of ball B after the collision?
1.
after
8 m
/
s
B
53
◦
b
2.
after
4 m
/
s
B
37
◦
b
3.
0 m/s
B
b
after
4.
6 m
/
s
B
after
b
5.
after
6 m
/
s
B
53
◦
b
6.
after
4 m
/
s
B
53
◦
b
7.
4 m
/
s
B
after
b
8.
after
8 m
/
s
B
37
◦
b
correct
9.
after
6 m
/
s
B
37
◦
b
10.
8 m
/
s
B
after
b
Explanation:
Because we are given both the speed and
the direction of ball A after the collision, the
problem can be solved in terms of momentum
conservation only.
Indeed, there are no (horizontal) external
forces acting on the two balls, so their net
(horizontal) momentum vector is conserved
during the collision:
V
P
net
=
mV
v
A,
0
+
mV
v
B,
0
[before]
=
mV
v
A
+
mV
v
B
[after]
and since
V
v
B,
0
=
V
0
(ball B is initially at rest),
V
v
A
+
V
v
B
=
V
v
A,
0
.
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 Fall '10
 TSIO

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