Final_F08_v6

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(First)
 ME 270 – Fall 2008 
 Final Examination 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 ________ Problem 4 ________ Problem 5 ________ Total ____________ Name 
 


























































































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(First)
 1a.
 A
massless
wedge
(B)
is
used
to
lift
Block
A
(which
has
a
mass
of
100
kg.)
by
applying
force
 P.

 The
coefficient
of
static
friction
is
 µs
=
0.20
between
the
Block
A
and
the
wedge.

The
coefficient
of
 static
 friction
 is
 µs
 =
 0.20
 between
 the
 wedge
 and
 the
 fixed
 bottom.
 
 Rollers
 are
 located
 between
 Block
A
and
the
vertical
wall. 
 a. Denote
the
coordinate
system
and
draw
the
free‐body
diagrams
for
the
wedge
and
the
block
 (please
use
the
figures
provided).


(6
points)
 b. Determine
the
force
P
that
will
begin
to
lift
the
block
(show
all
your
work).

Please
place
 your
response
in
the
box
provided.

(6
points)
 
 
 
 
 
 Block
A
 100
kg
 P
 Massless
wedge
B
 20°
 Answer:

P
=
 
 Name 
 


























































































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(First)
 1b.
What
is
the
angle
between
line
segments
CD
and
CE?
(8
points).

 
 
 
 
 
 
 
 
 
 
 
 
 
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(First)
 2a.
By
inspection,
determine
all
the
zero‐force
membersin
the
truss
below
and
list
them
in
the
box
 provided
(4
points)
 
 Zero‐force
members:
 
 
 2b.
A
60‐lb
triangular
block
with
a
thickness
of
1‐ft
out
of
the
page
is
used
retain
water.

The
block
 will
not
slide.
 
 a. Please
determine
the
center
of
mass
(xc
and
yc)
for
the
triangular
block
relative
to
point
O.

 The
block
is
3‐ft
wide
and
5‐ft
tall
(4
points)
 b. If
 the
 specific
 weight
 of
 the
 water
 is
 given
 as
 γ=62.4
 lb/ft3
 please
 determine
 the
 height
 of
 water,
h,
that
will
place
the
triangular
block
in
a
state
of
impending
tipping
about
point
O
(6
 points)
 2a.
 xc
=















ft.
 yc
=















ft.
 
 
 
 2b.

 h=

















ft.
 y
 5‐ft
 O
 
 
 
 
 
 h
 3‐ft
 x
 
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(First)
 2c.


Please
state
Newton’s
Three
Laws
in
order
(6
points)
 
 1st
Law
 
 
 
 
 
 
 2nd
Law
 
 
 
 
 
 
 3rd
Law
 
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(First)
 3.
A
small‐rocket
launch
is
being
tracked.

At
the
instant
shown
the
tracker
is
rotating
at
2rad/s
in
 the
CCW
direction.
Please
indicate
responses
to
the
following
in
the
answer
space
provided:
 
 A. Determine
the
radius,
r
(2points)
 B. Draw
 the
 cylindrical
 and
 rectangular
 basis
 vectors
 on
 the
 rocket
 at
 the
 instant
 shown
 (4
 points)
 C. Determine
the
velocity
of
the
rocket
(4points)
 D. Determine
the
value
of
dr/dt
for
the
rocket
at
this
instant.
(2
points)
 6000
meters
 1500
meters
 3a.

r
=

 
 3b.
Place
the
coordinates
on
 the
rocket
 
 
 3c.

vrocket
=

 
 
 3d.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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(First)
 3e.
An
ME
270
student
pushes
a
50
kg
cart
with
frictionless
wheels
along
the
top
of
an
 accelerating
train.

The
train
has
a
constant
acceleration
of
1.25
m/s2
to
the
right,
and
the
 student
pushes
with
a
constant
force
of
200
N.

 
 
 
 
 50
kg
 
 
 1.25
m/s2
 
 
 
 
 
 Draw
a
free
body
diagram
of
the
cart
(2
points).
 
 
 
 
 
 Sum
forces
to
find
the
acceleration
of
the
cart
(3
points).
 
 
 
 
 
 
 
 
 
 
 
 
 
 What
is
the
acceleration
of
the
cart
with
respect
to
the
train?

(3
points)
 
 
 
 
 
 
 
 
 Name 
 


























































































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(First)
 4.
The
foot
pedal
is
used
to
support
the
mass
(m
=
100
kg).
Note
that
the
foot
pedal
is
an
 angled
bracket
that
consists
of
points
B,
C,
and
the
point
at
which
the
load
is
applied.

 
 4a.
Draw
a
free
body
diagram
(with
an
appropriate
coordinate
system)
of
the
foot
pedal
(B‐ C‐load
application
point).
Note
that
the
interior
shaft
(denoted
by
hidden
lines)
is
a
 frictionless
surface
that
provides
a
negligible
force
to
keep
the
system
aligned.
(6
points)
 
 4b.
Determine
the
force,
P,
required
to
support
the
100
kg
load.

(5
points)
 
 
 4c.
Calculate
the
force
in
link
AB.
Is
it
in
tension
or
compression?
(3
points)
 
 
 
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(First)
 4d.
Write
out
each
vector
in
component
form
and
determine
the
resultant
force
in
 Cartesian
coordinates
for
the
figure
illustrated
below.

 
 
 
 Name 
 


























































































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(First)
 5.

A
1500
kg
car
travels
clockwise
without
slipping
around
a
circular
path
of
 radius
100
m.

A
graph
of
the
car’s
speed
is
shown
below.


 
 A) At

t
=
12
sec,
what
distance
has
the
car
travelled?


 (1
point)
 B) What
is
the
maximum
value
(irrespective
of
sign)
of
 the
car’s
rate
of
change
of
speed?
(1
point)
 C) Using
path
coordinates,
what
are
the
velocity
and
 acceleration
vectors
of
the
car
at

t
=
3
sec?
(8
points)
 

 Parts
D­F
on
next
page…..
 
 
 
 
 
 
 5a.


distance
=
___________________
 
 
 
 
 
 5b.

________________________________
 
 
 
 
 
 5c.

v
=
___________en

+
_________et
 
 
 
 






 
 






a
=
___________en

+
_________et
 
 
 
 
 
 
 
 5d.
FBD:
 
 
 
 
 
 
 
 
 



















 
 
 
 
 
 
 
 
 
 
 5e.

Fnet
=
__________en

+
________et

 
 
 
 
 
 5f.


v
=

___________

i

+

_________
j
 
 
 
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(First)
 Problem
5
(continued)
 
 Suppose
at
the
position
shown,
the
car
has
a
speed
of
23
m/s
and
rate
 of
change
of
speed
of
‐17
m/s2
as
it
travels
clockwise
around
the
track.
 

 D) Draw
a
free
body
diagram
of
the
car.

Include
a
normal/tangential
 coordinate
system.
(4
points)
 E) Calculate
the
net
force
in
the
tangential
direction
and
the
net
force
in
the
normal
 direction
acting
on
the
car.
(4
points)
 F) At
the
same
instant,
a
cell
phone
placed
on
the
dashboard
of
the
car
is
observed
to
slip
 across
the
dashboard
at
a
rate
of
3
m/s.

If
the
direction
of
the
cell
phone’s
path
is
 perpendicular
to
the
path
of
the
car,
what
is
the
velocity
of
the
phone
with
respect
to
a
 person
standing
at
the
middle
of
the
track?
(2
points)
 
 Name 
 


























































































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(First)
 
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This note was uploaded on 12/21/2011 for the course ME 270 taught by Professor Murphy during the Fall '08 term at Purdue.

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