This preview shows page 1. Sign up to view the full content.
Then, by the righthand rule, a downward component (
B
d
) of
G
B
will produce the
eastward
F
x
, and a westward component (
B
w
) will produce the upward
F
y
. Specifically,
,.
xd
yw
F
iLB
F
iLB
=
=
Considering forces along a vertical axis, we find
Ny
w
Fm
g
g
i
L
B
=
−=
−
so that
ff
m
g
i
L
B
ss
w
==
−
,
.
max
µ
b
g
It is on the verge of motion, so we set the horizontal acceleration to zero:
( )
0.
s
w
Ff
i
L
B
m
g
i
L
B
−= ⇒
=
−
The angle of the field components is adjustable, and we can minimize with respect to it.
Defining the angle by
B
w
= B
sin
θ
and
B
d
= B
cos
(which means
is being measured
from a vertical axis) and writing the above expression in these terms, we obtain
()
cos
sin
cos
sin
s
s
s
mg
iLB
mg
iLB
B
iL
θµ
µθ
=−
⇒
=
+
which we differentiate (with respect to
) and set the result equal to zero. This provides a
determination of the angle:
=
°
−−
tan
tan
.
.
11
060
31
s
bg
b g
Consequently,
( )
( )
(
)
( )
2
min
0.60 1.0kg 9.8m s
0.10T.
50A 1.0m cos31
0.60sin31
B
°+
°
(b) As shown above, the angle is
( ) ( )
tan
tan
0.60
31 .
s
=
°
45. (a) The magnetic force must push horizontally on the rod to overcome the force of
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Any
 Physics, Force, Friction

Click to edit the document details