NAME
:
. . . . . . . . . . . . . . . . . . . . .
Massachusetts
Institute
of
Technology
16.07
Dynamics
Problem
Set
6
Out
date:
Oct
10,
2007
Due
date:
Oct
17,
2007
Time
Spent
[minutes]
Problem
1
Problem
2
Problem
3
Problem
4
Study
Time
Turn
in
each
problem
on
separate
sheets
so
that
grading
can
be
done
in
parallel
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Problem
1
(10
points)
The
geometry
of
a
”halfpipe”
as
used
in
skateboard
competition
is
a
ﬂat
horizontal
surface
separating
two
circular
arcs
of
radius
R
0
.
Pumping
is
the
process
by
which
the
skateboarder
does
work
and
gains
kinetic
energy
to
make
the
next
spectacular
move.
(This
really
works!!!!
But
maybe
I’ve
been
watching
too
much
TV.)
Consider
a
skateboarder
of
mass
m
in
the
halfpipe.
Assume
he
starts
from
height
h
0
with
zero
velocity.
He
is
standing
up
so
that
his
center
of
mass
is
R
1
from
the
center
of
curvature
of
the
circular
section
of
the
pipe.
As
he
goes
through
the
ﬂat
section,
the
height
of
his
center
of
mass
above
the
track
is
h
=
R
0
−
R
1
.
(Represent
the
skateboarder
as
a
point
mass
located
at
his
center
of
mass.
Assume
for
your
convenience
that
R
2
−
R
1
<<
R
0
.)
A1
1.
In
case
a,
he
traverses
the
pipe
without
change
of
stance.
Ignoring
wind
resistance
and
friction,
what
height
will
be
reach
on
the
other
side
of
the
pipe?
A2
What
normal
force
is
felt
on
his
feet
as
a
function
of
position
in
the
half
pipe?
In
the
round
section?
In
the
ﬂat
section?
Now
consider
case
b).
He
starts
with
the
same
initial
conditions.
However,
in
this
case,
when
he
reaches
the
ﬂat
section,
he
crouches
so
that
his
center
of
mass
is
now
at
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 Fall '09
 widnall
 Dynamics, Energy, Force, Kinetic Energy, Mass, maximum kinetic energy

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