Morgan, Mena – Homework 5 – Due: Oct 10 2007, 11:00 pm – Inst: Opyrchal, H
1
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time.
001
(part 1 of 1) 10 points
A hockey puck is given an initial speed of
24 m
/
s on a frozen pond. The puck remains
on the ice and slides 118 m before coming to
rest.
The acceleration of gravity is 9
.
8 m
/
s
2
.
What is the coefficient of friction between
the puck and the ice?
Correct answer: 0
.
249049 .
Explanation:
Basic Concept:
Newton’s Second Law:
F
net
=
ma
Solution:
From kinematics,
0 =
v
2
0
+ 2
ax
a
=

v
2
0
2
x
since the puck comes to a rest. Consider the
free body diagram for the situation:
μ
N
N
mg
Vertically, the puck is in equilibrium, so
F
net
=
N 
mg
= 0
⇒ N
=
mg
Horizontally, after the puck is given its initial
velocity, the friction force
f
k
=
μ
N
=
μmg
is
the only unbalanced force acting on it. Thus,
f
net
=
ma
= 0

f
k
=

μmg
μ
=

a
g
=
v
2
2
gx
=
(24 m
/
s)
2
2(9
.
8 m
/
s
2
)(118 m)
= 0
.
249049
keywords:
002
(part 1 of 1) 10 points
A 4
.
9 kg block slides down an inclined plane
that makes an angle of 25
◦
with the horizontal.
Starting from rest, the block slides a distance
of 2
.
2 m in 4
.
9 s.
The acceleration of gravity is 9
.
81 m
/
s
2
.
Find the coefficient of kinetic friction be
tween the block and plane.
Correct answer: 0
.
445696 .
Explanation:
Let :
m
= 4
.
9 kg
,
θ
= 25
◦
,
Δ
x
= 2
.
2 m
,
and
Δ
t
= 4
.
9 s
.
4
.
9 kg
μ
25
◦
Consider the forces acting on the block as
it slides down the incline:
~
N
~
f
k
m~g
From kinematics, since
v
0
= 0,
Δ
x
=
v
0
Δ
t
+
1
2
a
(Δ
t
)
2
=
1
2
a
(Δ
t
)
2
a
=
2 Δ
x
(Δ
t
)
2
=
2 (2
.
2 m)
(4
.
9 s)
2
= 0
.
183257 m
/
s
2
.
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Morgan, Mena – Homework 5 – Due: Oct 10 2007, 11:00 pm – Inst: Opyrchal, H
2
Applying
X
~
F
=
m~a
to the block,
X
F
y
=
N 
m g
cos
θ
= 0
m g
cos
θ
=
N
and
X
F
x
=
m g
sin
θ

f
k
=
m a
m g
sin
θ

μ
k
N
=
m a
m g
sin
θ

μ
k
m g
cos
θ
=
m a .
Thus
μ
k
=
g
sin
θ

a
g
cos
θ
=
(9
.
81 m
/
s
2
) sin 25
◦

(0
.
183257 m
/
s
2
)
(9
.
81 m
/
s
2
) cos 25
◦
=
0
.
445696
.
keywords:
003
(part 1 of 2) 10 points
A 8 kg block rests on a horizontal table, at
tached to a 7 kg block by a light string as
shown in the figure.
The acceleration of gravity is 9
.
81 m
/
s
2
.
8 kg
7 kg
~
T
What is the minimum coefficient of static
friction such that the objects remain at rest?
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 Spring '12
 James
 Physics, Force, Friction, Work, Correct Answer

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