E-61
No. 15
Cycle of Simple Pendulum
Determines the cycle (
T
) of a simple pendulum with a string of length .
T
= 2
π
g
(
g
: gravitational acceleration, > 0
)
T
= 2
π
g
(
g
: gravitational acceleration, > 0
)
Units: : m,
T
: seconds
No. 16
Cycle of Spring Pendulum
Determines the cycle of simple oscillation (
T
) of a spring pendulum when the mass of the
weight (
m
) and the spring constant of the spring (
k
) are known.
T
= 2
π
k
m
(
m
,
k
> 0)
T
= 2
π
k
m
(
m
,
k
> 0)
Units:
m
: kg,
k
: N/m,
T
: seconds
No. 17
Doppler Effect
Determines the oscillation frequency (
f
) heard by an observer when both the sound source
and observer are moving, when the sound source oscillation frequency (
f
1
), acoustic velocity
(
v
), sound source movement speed (
v
1
) and observer movement speed (
u
) are known.
Units:
v
,
v
1
and
u
: m/s,
f
1
and
f
: Hz
No. 18
Equation of State of Ideal Gas
Determines the pressure (
P
) of a gas when the number of mols (
n
), absolute temperature (
T
),
and volume (
V
) are known.
f
=
f
1
(
v
≠
v
1
,
f
1
>
0, (
v
−
u
)/(
v
−
v
1
)
>
0
)
v
−
v
1
v
−
u
f
=
f
1
(
v
≠
v
1
,
f
1
>
0, (
v
−
u
)/(
v
−
v
1
)
>
0
)
v
−
v
1
v
−
u
P
=
V
n
RT
(
R
: gas constant,
n
,
T
,
V
> 0
)
P
=
V
n
RT
(
R
: gas constant,
n
,
T
,
V
> 0
)
Units:
n
: mol,
T
: K,
V
: m
3
,
P
: N/m
3
No. 19
Centrifugal Force
Determines the centrifugal force (
F
) for an object of mass
m
moving at velocity
v
in a circular
pattern of radius
r
.
F
=
r
v
2
m
(
m
,
v
,
r
> 0)
F
=
r
v
2
m
(
m
,
v
,
r
> 0)
Units:
m
: kg,
v
: m/s,
r
: m,
F
: N
No. 20
Elastic Energy
Determines the elastic energy (
U
) of an object when its elastic constant (
K
) and elongated
length (
x
) are known.
U
=
K
x
2
2
1
(
K
,
x
> 0)
U
=
K
x
2
2
1
(
K
,
x
> 0)
Units:
K
: N/m,
x
: m,
U
: J
