เนื้อหาบทที่ 4 : หัวข้อ 4.7[.pdf]

315 201 Physics of Matter
4 34
4.2 xy ก ( r ,θ )
:
5
⎜
⎝13
⎛ ⎞
ก r = 13 θ = arcsin ⎟ ก
⎠
ê
r
rɺ = 6 / ก ê
θ
r ɺ θ = 5
/
(ก) กก x ก y ( xɺ yɺ
)
() υ = rɺ
eˆ
r
+ r ɺ θeˆ
= xe ɺ ˆx
+ yɺ
eˆ
θ
y
ก…
2 2 2 2 2
x ɺ + yɺ
= rɺ
+ r ɺ θ
4.2
() ก υ = xɺ eˆ + yɺ
eˆ
…
x
y
(ก) ก…
υ = υ
sin β =
sin θ =
=
5
61
5
13
2
2
( 6m/s) + ( 5m/s) = 61 m/s
cos β =
cos θ =
6
61
12
13
∵ υ = xɺ
eˆ
x
+ ye ɺ ˆ y
= υ cos( β + θ ) eˆ
x
+ υ sin( β + θ ) eˆ
y
…
xɺ
yɺ
=
=
=
=
υ cos
( β + θ ) = υ( cos β cosθ
− sin β sinθ
)
⎛ 6 12 5 5 ⎞
61 ⎜ ⋅ − ⋅ ⎟ m/s =
⎝ 61 13 61 13 ⎠
47
13
m/s
( β + θ ) = υ( sin β cosθ
cos β sinθ
)
υ sin +
⎛ 5 12 6 5 ⎞
61 ⎜ ⋅ + ⋅ ⎟ m/s =
⎝ 61 13 61 13 ⎠
90
13
m/s
υ
2
2
2 2 ⎛ 47 ⎞ ⎛ 90 ⎞
2
x ɺ + yɺ
= + =
= rɺ
+
( r ɺ θ ) 2
= ⎜ ⎟ ⎜ ⎟ 61 m/s
...
⎝ 13 ⎠ ⎝ 13 ⎠
... .
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