F08_Exam_2_v5

F08_Exam_2_v5 - Name 
 
 ME 270 – Fall 2008...

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 ME 270 – Fall 2008 Examination No. 2 
 INSTRUCTIONS Begin each problem in the space provided on the examination sheets. If additional space is required, use the yellow paper provided to you. Work on one side of each sheet only, with only one problem on a sheet. Each problem is worth 20 points. Please remember that for you to obtain maximum credit for a problem, it must be clearly presented, i.e. • • • • the coordinate system must be clearly identified. where appropriate, free body diagrams must be drawn. These should be drawn separately from the given figures. units must be clearly stated as part of the answer. you must carefully delineate vector and scalar quantities. If the solution does not follow a logical thought process, it will be assumed in error. When handing in the test, please make sure that all sheets are in the correct sequential order and make sure that your name is at the top of every page that you wish to have graded. Please circle your instructor’s name and section: Nauman 9:30-10:20 Nauman 11:30-12:20 Cook 2:30-3:20 Murphy 9:00-10:15 Problem 1 ________ Problem 2 ________ Problem 3 ________ Total ____________ Name 
 
 
 1.
Please
provide
your
answers
in
the
spaces
provided.

 
 1a.

(5
points)

Please
determine
the
centroid
in
the
y‐direction
 
for
the
region
under
the
 curve
given
by
the
equation:
 .


The
area
under
the
curve
is
given
as
A=
 Please
write
your
response
in
the
box
provided.


 y
 b
 a
 x
 Answer
1a:
 
 =





































units

 
 
 
 
 
 
 .

 Name 
 
 1b.
(5
points)

Please
determine
the
centroid
in
the
x‐direction,
 ,
for
the
shape
below.

 Please
put
your
response
in
the
box
provided.
 y
 4m
 2m
 3m
 x
 5m
 7m
 Answer
1b:
 
 =




































meters
 
 Name 
 
 1c.
(5
points)

A
100‐lb
weight
is
just
held
in
place
by
a
15‐lb
tension
in
the
direction
show.


 The
15‐lb
tension
makes
a
30º
angle
with
the
horizontal
axis.

Please
determine
the
static
 coefficient
of
friction, 
required
to
maintain
equilibrium
and
place
your
response
in
the
 box
provided.
 
 
 
 
 
 
 Name 
 
 1d.
(5
points)

A
100‐lb
load
is
applied
at
the
point
shown
is
used
to
keep
the
gate
shut.

The
 gate
has
a
width
of
one
foot
(1.00’)
out
of
the
page
and
a
pin
joint
at
point
A.

Determine
the
 maximum
height,
h,
that
the
water
can
fill
in
order
to
prevent
the
gate
from
opening
to
 within
three
significant
digits.

The
specific
weight
of
water
is
γwater=62.4
lb/ft3.
 
 γwater=62.4
 lb/ft3
 100­lb
 h?
 2
feet
 A
 
 
 
 
 Answer
1d:
 
 h
=
































feet
 
 
 Name 
 
 2.
Please
provide
your
answers
in
the
spaces
provided.
 
 Important:

Write
all
answers
in
these
boxes

 
























No
partial

credit
for
this
section,
and

 























no
credit

will
be
given
for
answers
in

 
























other
locations!
 
 

 Hint:






These
questions
are
designed
to
be
simple,
most
requiring
only

 














one
or
two
short
equations.

If
you
find
yourself
writing
pages

 















of
equations
you
are
almost
certainly
on
the
wrong
track.


 
 
 

 
 2a.
The
box
shown
here
is
about
to

 slide
down
a
ramp
of
ice
due
to
 its
own
weight.

 5.7˚
 
 
 Figure
for
Problem
2a.
 
 
 
 What
is
the
coefficient
of
friction
between
the
ice
and
the
box?

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Answer
2a:




































4
pts.
 
 




μ
=
_________
 Answer
2b:

 
 













4
pts.
 

 Answer
2c:

 
 













4
pts.
 



 Answer
2d:

 
 













4
pts.
 





θ
=
_________
 



 
Answer
2e:

 
 













4
pts.
 


P2
=
_________
 
 Name 
 
 Refer
the
figure
to
the
right

 

P
 for
problems
2b
and
2c:
 i
(2
m,
3
m)
 
 
 
 
 100
N
 
 
 
 y
 
 
 
 








x
 
 f
 
 2b.

For
P
=
25
N,
which
of
the
following
best
describes
the
values
of
μs
for
which
the
box


 




will
slip?


 
 A)

0
<

μs
<
0.1

 B)

0
<

μs
<
0.2
 C)

0
<

μs
<
0.3
 D)

0
<

μs
<
0.4
 E)

0
<

μs
<
0.5
 F)


all
of
the
above
 G)

none
of
the
above
 
 
 
 
 
 
 
 2c.

If
P
>
33.3
N,
which
of
the
following
best
describes
the
values
of
μs
for
which
the
box


 






will
tip?

 
 A)




0



<

μs
<
0.15

 B)

0.15
<

μs
<
0.25
 C)

0.25
<

μs
<
0.30
 D)

0.30
<

μs
<
0.35
 E)

0.35
<

μs
<
0.5
 F)

all
of
the
above
 G)
none
of
the
above
 
 
 
 
 
 
 Name 
 
 2d.

The
box
at
right
is
about
to
slip.

Selected
forces
are
provided.

 







If
the
normal
and
friction
forces
acting
on
the
above
box

 P1
 







were
summed
to
obtain
a
single
resultant
force
(R
=
N
+
f
),

 P2
 







what
would
be
the
direction
of
R
measured
clockwise
 







from
the
vertical
(see
diagram
in
box)?
 mg
 

 
 

y
 
 


















x
 






P1
=
200
N;


P2
=
120
N;


mg
=
75
N
 N
 






N
=
273.86
N
 10˚
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 P1
 2e.

Similar
problem,
different
parameters
and
angle
(see
fig.
at
right).


 







The
coefficient
of
friction
between
the
block
and
ramp
is
0.3.


 







For
what
value
of
P1
will
the
block
begin
to
slip?

 P2
 







Use
the
coordinate

system
of
the
figure.



 mg
 
 Hint:
notice
that
the
friction
force
required
to
 

y
 



























prevent
slip
is
independent
of
P1
and
is
 


















x
 f
 
 
 provided
below.
 15˚
 
 N
 f


=
1965
lbs;



P1
=
?
lbs
 P2
=
1500
lbs;

mg
=
1800
lbs
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Name Name 
 
 3.
An
airplane
wing
is
fixed
to
the
fuselage
with
a
pin
joint
at
point
A
and
a
support
strut,
 BC.
The
distributed
load
is
given
below.
It
is
30
lbs./in.
near
the
fuselage,
8
lbs./in.
near
the
 wing
tip
and
decreases
linearly.

 
 
 
 
 
 
 
 3a.
What
is
the
total
force
generated
by
the
distributed
load?
(3
points)
 
 
 
 
 
 
 
 
 
 
 Name 3b.
Draw
a
free
body
diagram
of
the
wing.
(7
points)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3c.
Calculate
the
magnitude
of
the
force
in
the
support
strut
BC.
(5
points)
 
 
 
 
 Name 3d.
Determine
the
reactions
at
point
A.

Write
the
total
force
at
point
A
as
a
vector.
(5
 points)
 
 
 
 Name ...
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