patel (kp9583) – CW8 – Mackie – (20211)
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DEADLINE IS CENTRAL TIME
001
(part 1 of 2) 10.0 points
A light, inextensible cord passes over a light,
frictionless pulley with a radius of 15 cm. It
has a(n) 15 kg mass on the left and a(n)
5 kg mass on the right, both hanging freely.
Initially their center of masses are a vertical
distance 3
.
1 m apart.
The acceleration of gravity is 9
.
8 m
/
s
2
.
3
.
1 m
15 cm
ω
15 kg
5 kg
At what rate are the two masses accelerat
ing when they pass each other?
Correct answer: 4
.
9 m
/
s
2
.
Explanation:
Let :
R
= 15 cm
,
m
1
= 5 kg
,
m
2
= 15 kg
,
h
= 3
.
1 m
,
and
v
=
ω R .
Consider the free body diagrams
15 kg
5 kg
T
T
m
2
g
m
1
g
a
a
Since the larger mass will move down and
the smaller mass up, we can take motion
downward as positive for
m
2
and motion up
ward as positive for
m
1
.
Apply Newton’s
second law to
m
1
and
m
2
respectively and
then combine the results:
For mass 1:
summationdisplay
F
1
:
T

m
1
g
=
m
1
a
(1)
For mass 2:
summationdisplay
F
2
:
m
2
g

T
=
m
2
a
(2)
We can add Eqs. (1) and (2) above and obtain:
m
2
g

m
1
g
=
m
1
a
+
m
2
a
a
=
m
2

m
1
m
1
+
m
2
g
=
15 kg

5 kg
15 kg + 5 kg
(9
.
8 m
/
s
2
)
= 4
.
9 m
/
s
2
.
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