Chapter A  Problems
Blinn College  Physics 2425  Terry Honan
Problem A.1
Suppose that
x
is a length,
t
is a time and
a
is an acceleration. To get a general expression for
x
as a function of both
t
and
a,
we
choose the general form:
x
= k
a
m
t
n
where
k
is a dimensionless constant. For this expression to be dimensionally correct what must
m
and
n
be?
Problem A.2
Three fundamental constants G, c and
—
have dimensions:
[
G
] =
L
3
M
ÿ
T
2
, [
c
] =
L
T
and [
—
] =
M
L
2
T
.
(a) What must
m
,
n
and
p
be to make
L
0
a length, when
L
0
=
G
m
ÿ
c
n
ÿ
—
p
.
(b)
—
, called "h bar", is a rescaled version of Plank's constant
h
; it is usually also called Plank's constant.
—
=
h
2
p
=
1.054
μ
10

34
J
ÿ
s
Using this and the values of
G
and
c
given in the book evaluate
L
0
.
Comment:
G
is
Newton's Gravitational constant
,
c
is the
speed of light
which plays a central role in Relativity and
—
is called
Plank's
constant
, which appears in Quantum theory.
L
0
is known as the
Plank length
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 Spring '09
 Acceleration, General Relativity, Plank

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