01b Electric Force
Transcript of 01b Electric Force
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Review: Three Dimensional Coordinate System
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(Negative)
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Directed line segment:
21
_________
PP
Magnitude
2122122122_________
21 zzyyxxrPP
Directionfrom P1 to P2
initial coordinates = (x1, y1, z1)
final coordinates = (x2, y2, z2 )
Direction cosines:
cos x where xis angle with respect to positive x direction
cos y where yis angle with respect to positive y direction
cos z where zis angle with respect to positive z direction
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Direction
from P1 to P2
initial coordinates = (x1, y1, z1)
final coordinates = (x2, y2, z2 )
r
xxx
12cos
ryy
y12cos
r
zzz
12
cos
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Example 1
A particle of mass m1is attracted to another
mass m2. Calculate the magnitude and
direction of the gravitational force ofattraction exerted on m1by m2.
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magnitude Coordinates (cm)
m1 250 gms P1 (-3, 4, 1)
m2 375 gms P2 ( 2, - 5, - 6 )
Direction is P1to P2since m1is attracted towards m2
222
222
222
2
12
2
12
2
12
2
m1055.1cm155795
164532
x
zzyyxxr
m1245.0m1055.1:Check
m0.1245cm45.12cm155
22
2
xr
r
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01-x 32.66
45.12
32cosso
45.12
32cos
x
01-x 29.136
45.12
45cosso
45.12
45cos
y
01-x 21.124
45.12
16cosso
45.12
16cos
z
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pNnNNxmx
kgkg
kg
mNx
r
mmGF
403403.01003.41055.1
)375.0)(250.0(1067.6
10
222
211
2
2112
Magnitude
Components
N1027.221.124cos1003.4cos
N1091.229.136cos1003.4cos
N1062.132.66cos1003.4cos
10010
1212
10010
1212
100101212
xxFF
xxFF
xxFF
zz
yy
xx
kji
kjiF
N1027.2N109.2N1062.1
N1027.2N109.2N1062.1
101010
101010
12
xxx
xxx
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Example 2. Given are the following
charges and their respective locations:
Calculate the resultant force exerted on q1
by q2and q3
Charge Magnitude Location (in cm)
q1 +2.5 C P1(-2, 4, -3)
q2 -3.6 C P2( 5, -1, -2)
q3 +1.8 C P3( 3, 2, 6)
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Solution: from superposition principle:
Solve for F12
q1will be attracted to q2(opposite signs)so direction of F12is P1to P2
kjiFFFF
....1413121
zyx FFF
q1 +2.5 C P1(-2, 4, -3)
q2 -3.6 C P2( 5, -1, -2)
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q1 +2.5 C P1(-2, 4, -3)
q2 -3.6 C P2( 5, -1, -2)
23242222
222
2
12
2
12
2
12
2
12
m105.7m1075cm75157
324125
xx
zzyyxxr
01-x 07.36
66.8
25cosso
66.8
25cos
x
m0.0866cm66.8cm75 212 r
01-y 27.125
66.8
41cosso
66.8
41cos y
01-z 37.83
66.8
32cosso
66.8
32cos
z
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Nmx
CxCx
C
mNx
r
qqkF
79.10105.7
)106.3)(105.2(1099.8
23
66
2
29
2
12
21
12
Magnitude
Components
N25.137.83cos79.10cos
N23.627.125cos79.10cos
N72.807.36cos79.10cos
0
1212
0
1212
01212
zz
yy
xx
FF
FF
FF
kjiF N25.1N23.6N72.812
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Nmx
CxCx
C
mNx
r
qqkF
68.31010.1
)108.1)(105.2(1099.8
22
66
2
29
2
12
21
13
Magnitude
Components
N16.309.149cos68.3cos
N70.001.79cos68.3cos
N75.147.118cos68.3cos
0
1313
0
1313
01313
zz
yy
xx
FF
FF
FF
kjiF N16.3N70.0N75.112
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Fx Fy Fz
F12 8.75 -6.23 1.25F13 -1.75 0.70 -3.16
Sum 7.00 -5.53 -1.91
kjiF N91.1N53.5N00.7 net
N12.991.153.57.00F2/1222