Consider the physical quantities m , s , v , a , and t with dimensions [ m ] = M , [ s ] = L , [ v ] = LT − 1 and [ a ] = LT − 2 . Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation: ( a ) F = m a ; ( b ) K = 0.5 m v 2 ; ( c ) p = m v ; ( d ) W = m a s ; ( e ) L = m v r
Consider the physical quantities m , s , v , a , and t with dimensions [ m ] = M , [ s ] = L , [ v ] = LT − 1 and [ a ] = LT − 2 . Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation: ( a ) F = m a ; ( b ) K = 0.5 m v 2 ; ( c ) p = m v ; ( d ) W = m a s ; ( e ) L = m v r
Consider the physical quantities
m
,
s
,
v
,
a
,
and
t
with dimensions
[
m
]
=
M
,
[
s
]
=
L
,
[
v
]
=
LT
−
1
and
[
a
]
=
LT
−
2
. Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation:
(
a
)
F
=
m
a
;
(
b
)
K
=
0.5
m
v
2
;
(
c
)
p
=
m
v
;
(
d
)
W
=
m
a
s
;
(
e
)
L
=
m
v
r
Consider the physical quantities m, s, v, a, and t with dimensions [m] = M, [s] = L, [v] = LT–1, [a] = LT–2, and [t] = T. Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation: (a) F = ma; (b) K = 0.5mv2; (c) p = mv; (d) W = mas; (e) L = mvr.
A traditional unit of length in Japan is the ken (1 ken 1.97 m).What are the ratios of (a) square kens to square meters and (b) cubic kens to cubic meters? What is the volume of a cylindrical water tank of height 5.50 kens and radius 3.00 kens in (c) cubic kens and (d) cubic meters?
In a situation in which data are known to three significant digits, we write 6.379 m = 6.38 m and 6.374 m = 6.37 m. When a number ends in 5, we arbitrarily choose to write 6.375 m = 6.38 m. We could equally well write 6.375 m = 6.37 m, “rounding down” instead of “rounding up,” because we would change the number 6.375 by equal increments in both cases. Now consider an order-of-magnitude estimate, in which factors of change rather than increments are important. We write 500 m ~ 103 m because 500 differs from 100 by a factor of 5 while it differs from 1 000 by only a factor of 2. We write 437 m ~ 103 m and 305 m ~ 102 m. What distance differs from 100 m and from 1 000 m by equal factors so that we could equally well choose to represent its order of magnitude as ~ 102 m or as ~ 103 m?
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