30
o
M
m
w
1
=Mg
N
T
1
f
s
a
1
=0
w
2
=mg
T
2
a
2
=0
w
1
=Mg
N
T
1
f
k
a
1
w
2
=mg
T
2
a
2
x
1
y
1
x
2
y
2
30
o
w
1
w
y
w
x
30
o
w
1
=Mg
N
T
1
a
1
w
2
=mg
T
2
a
2
=0
Towards the hole
45°
45°
#1
#2
#3
#4
P
R
Q
Answers
PHYS116A.01
Midterm Exam 1
Version 2
(Version 1 answers are a permutation of Version 2 answers)
Problem 1
At the top of an inclined plane that is at a 30
o
angle with the horizontal, there is a
frictionless pulley. Two wooden blocks, one of mass M= 1 kg that lies on the plane and
another of mass m=0.30 kg that hangs from the pulley are connected with a thin massless
string. Initially the blocks are not moving. Then at t=0 we push the first block so that it
gets velocity v
0
=0.5 m/s upwards along the plane. The coefficient of kinetic friction
between the block and the plane is
μ
k
=0.2 .
Assume that the string is long enough and
the ground far enough, so that the second block never reaches the pulley or the ground
while the first block lies on the inclined plane.
( sin(30
o
) = 1/2,
cos(30
o
) = /2 )
Show your work!
1.
Draw the free body diagrams of the two blocks before they start moving
2.
Draw the free body diagrams of the two blocks after they start moving
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3.
The static friction force before the blocks start moving is
We choose coordinate systems as follows (the components of w
1
are shown):
This value is positive. If we have started with the f
s
pointing in the negative direction,
we would get a negative value, which will tell us that f
s
is pointing in the opposite.
a.
f
s
= M g cos(30
o
) + m g
b.
f
s
= M g + m g
sin(30
o
)
c.
f
s
= M g cos(30
o
)  m g
d.
*** f
s
= M g sin(30
o
)  m g
e.
f
s
= M g sin(30
o
) + m g
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 Fall '09
 Velkovsky
 Physics, Force, 1 kg, 2 m, 5.7 m

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