01b Electric Force

8/13/2019 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

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01b Electric Force