PHY131 Final
Practice Exam Solutions
1)
A mass M = 2.00 kg is attached to a hanging mass m = 0.50 kg by a massless cord which hangs
over a massless and frictionless pulley.
M
m
a) If there is no firction between the mass M and the horizontal surface, draw free body
diagrams for the masses.
Mg
mg
T
T
N
b)
Using the free body diagrams, find the tension in the rope.
Newton’s second law:
g
m
m
m
a
a
)
m
M
(
mg
ma
T
mg
and
Ma
T
+
=
⇒
+
=
⇒
=
−
=
N
92
.
3
g
M
m
mM
Ma
T
=
+
=
=
⇒
c)
Find the acceleration of the masses.
2
s
m
96
.
1
5
g
g
5
.
2
5
.
0
g
m
m
m
a
:
above
see
=
=
=
+
=
d) If the masses move at constant speed, find the coefficient of friction between the mass
M and the horizontal surface.
25
.
0
M
m
Mg
N
F
mg
T
0
a
fr
=
=
µ
⇒
µ
=
µ
=
=
=
⇒
=
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2) In the picture below, the system is in equlibrium. The boom has mass m = 12.0 kg and length
l = 2.00 m. The point of attachment of the cord to the boom is at a distance 1.40 m (70 % of the
length of the boom). The angle
θ
is 37
o
. The suspended mass has m = 10.0 kg. Find the tension
T in the horizontal cord.
m
T
θ
base point
The system is in static equilibrium. Therefore, the sum of all torques about the base point (see
drawing) has to be zero:
N
168
12
.
1
mg
20
.
1
Mg
60
.
0
T
0
sin
l
mg
sin
2
l
Mg
cos
m
40
.
1
T
=
+
=
⇒
=
θ
×
×
−
θ
×
×
−
θ
×
×
=
τ
3)
A mass m = 0.500 kg oscillates on a frictionless horizontal surface with period T = 0.80 s.
a)
What is the spring constant k of the spring, which drives this motion?
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 Spring '03
 Rijssenbeek
 Physics, Friction, Kinetic Energy, Mass, kg, horizontal surface

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