LO2 for PHYS 101

1. LO:
Simple
Pendulum
You
are
swinging
a
coin
suspended
from
a
string
of
length
0.5m
from
side
to
side
(on
a
2-­‐dimensional
plane).
You
are
in
a
lab
and
measure
with
some
instruments
that
the
net
tangential
force
at
a
certain
point
in
time
is
20N
and
the
tension
force
in
the
string
at
that
point
in
time
is
10N.
Before
you
do
anything
else,
Joss
“The
Boss”
Ives
(your
Physics
101
professor)
jumps
in
to
help
you
measure
the
mass
of
the
coin,
but
manages
to
tip
over
a
water-­‐filled
graduated
cylinder
and
break
the
scale.
He
quickly
apologizes,
but
you
don’t
worry
because
you
know
how
to
find
the
mass
using
the
whiz-­‐kid
physics
powers
Joss
taught
you
in
your
lectures
(which
you
happen
to
attend
with
the
greatest
enthusiasm!).
Part
a)
Find
the
mass
of
the
coin
that
was
suspended
from
the
string.
Part
b)
Out
of
curiosity,
you
also
want
to
find
the
displacement
at
that
point.
In
other
words,
find
s
(hint:
arc
distance).
Part
c)
Find
the
frequency
and
the
angular
frequency
of
oscillation
of
the
pendulum.
Length = 0.5m
s = ?
m = ?
T = 10N
Fnet,t = 20N

2.
Solution:
Given
Information:
FT
=
10N
Fnet,t
=
20N
Relevant
Equations:
T
=
mgcos
θ
Fnet,t
=
-­‐mgsin
θ
s
=
Lθ
f
=
ω/2π
=
(1/2π)*sqrt(g/L)
Part
a)
|
𝐹!"#,!
𝑇
| = |
−mgsin 𝜃
mgcos 𝜃
| = | −
sin 𝜃
cos 𝜃
| = tan 𝜃
𝜃 = tan!!
𝐹!"#,!
𝑇
𝐹!"#,! = −𝑚𝑔 sin 𝜃
𝑚 = −
𝐹!"#,!
𝑔 sin 𝜃
𝜃 = tan!!
20𝑁
10𝑁
≅ 1.11°
𝑚 =
20𝑁
(9.8)(sin 1.11°)
≅ 2.29𝑘𝑔
Part
b)
𝑠 = 𝐿𝜃
𝑠 = 0.5𝑚 1.11° ≅ 0.56𝑚
Part
c)
𝑓 =
1
2𝜋
𝑔
𝐿
=
1
2𝜋
9.8
0.5𝑚
≅ 0.71 𝐻𝑧
𝜔 = 2𝜋𝑓 ≅ 4.46
𝑟𝑎𝑑
𝑠