Muraj, Hamza – Homework 19 – Due: Mar 8 2006, 4:00 am – Inst: Florin
1
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The due time is Central
time.
001
(part 1 of 1) 10 points
An object attached to the end of a string
swings in a vertical circle of radius 2
.
4 m as
shown. At an instant when
θ
= 36
◦
, the speed
of the object is 10 m
/
s and the tension in the
string is 29 N.
The acceleration of gravity is 9
.
8 m
/
s
2
.
10 m
/
s
29 N
2
.
4 m
36
◦
9
.
8 m
/
s
2
What is the mass
m
of the object?
Correct answer: 0
.
807656 kg.
Explanation:
Let :
θ
= 36
◦
,
v
= 10 m
/
s
,
r
= 2
.
4 m
,
and
g
= 9
.
8 m
/
s
2
.
θ
v
T
mg
R
θ
g
Basic Concepts:
F
r
=
m a
r
=
m v
2
r
Solution:
The centripetal acceleration is
a
r
=
v
2
r
. According to Newton’s second law,
the total force in the radial direction should
be equal to
F
r
=
m a
r
.
The forces acting on the mass are the ten
sion
T
on the string, directed radially inward,
and the weight force, whose component in the
radial direction is
m g
sin
θ
. The radial com
ponent of the resultant force is then
F
r
=
m a
r
=
T
+
m g
sin
θ ,
or
m
v
2
R

g
sin
θ
¶
=
T .
Finally,
m
=
T
v
2
R

g
sin
θ
=
(29 N)
(10 m
/
s)
2
(2
.
4 m)

(
9
.
8 m
/
s
2
)
sin(36
◦
)
=
0
.
807656 kg
.
002
(part 1 of 1) 10 points
A block of mass 2
.
88 kg is kept at rest as
it compresses a horizontal massless spring
(
k
= 59
.
8 N
/
m) by 11
.
4 cm.
As the block
is released, it travels 0
.
537 m on a rough hori
zontal surface before stopping.
The acceleration of gravity is 9
.
8 m
/
s
2
.
Calculate the coefficient of kinetic friction
between surface and block.
Correct answer: 0
.
0256382 .
Explanation:
Using the workenergy theorem, we have
k x
2
2
=
μ mg ‘ .
Therefore
μ
=
k x
2
2
m g ‘
=
(59
.
8 N
/
m) [(11
.
4 cm) (0
.
01 m
/
cm)]
2
2 (2
.
88 kg) (9
.
8 m
/
s
2
) (0
.
537 m)
= 0
.
0256382
.
003
(part 1 of 1) 10 points
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Muraj, Hamza – Homework 19 – Due: Mar 8 2006, 4:00 am – Inst: Florin
2
The two blocks are connected by a light
string that passes over a frictionless pulley
with a negligible mass.
The 5 kg block lies
on a rough horizontal surface with a constant
coefficient of kinetic friction 0
.
2. The hanging
block has a mass of 7 kg.
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 Spring '09
 Turner
 Energy, Force, Kinetic Energy, Mass, Momentum, kg

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