Question

A constant force F = −4i + 1j − 10k moves an object along a straight line from point (4, -3, 7) to point (-10, 9, 7).

Find the work done if the distance is measured in meters and the magnitude of the force is measured in newtons.

Work: ??? Nm

Answer 1

you have to parameterize the line first the do the line integral from [0,1] if you parameterize the line right then it will be [0,1] *r'(t)dt
onece you parametrize you take derivitve d/dt and take the magnitude. that will turn the ds=dt
the dot F with r'(t) and your ||r'(t)|| will be a constant so pull that to the front , the integrate.

Answer 2

wow ! that's a hard one to do ! do u mind showing more detail please ! perhaps numerical please

Answer 3

W=F*distance or ds which from calc 1 or 2 =sqrt(i component squared+....+z component squared)

Answer 4

i am going to the gym right now, when i come back if someone has not yet answered it i will do it. go to this website in the mean time.... http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsPtI.aspx

Answer 5

so sqrt of 117 ! times what then !?

Answer 6

http://www.ltcconline.net/greenl/courses/202/vectorIntegration/lineIntegrals.htm

then go half way done they do an excellent job of explaining Work=F*r'(t)dt

Answer 7

but i got lost half way it explains very good though ! too much computation

Answer 8

(-10-4)it+(9--3)jt+(7-7)kt
x=4-14t
y=-3+12t
z=7 tE[0,1]
r(t)=-14t,12t,0 r'(t)=-14,12,0
||r'(t)||=sqrt(196+144)=sqrt(340)
Line Integral [0,1]=(-4,1,-10)*(-14,12,0)sqrt(340)dt
Line integral [0,1]56+12=68(sqrt(340))dt
which to me looks like 68sqrt(340)
340=34*10=17*2*2*5
2sqrt(85)*68=136sqrt(85) Tell me if thats what you see in your book

Answer 9

Do you know how to parameterize a line?

Answer 10

no !

Answer 11

if p=(a,b,c) and Q=(x,y,z)
PQ=(x-a)it+(y-b)jt+(z-c)kt this is also your r(t)
equation =P+PQ
so x=a+(x-a)t
y=b+(y-b)t
z=c+(z-c)t

Answer 12

i tried 136sqrt(85) its not correct !

Answer 13

that's why i hate online homework ! grrrr....

Answer 14

ok lemme go to the gym, if anyone else answer im sorry i just did this all on the comp no scratch work. Ill be back less than 2 hrs ill search for you

Answer 15

oh online HW ios horrible im sorry

Answer 16

have fun man and thanks again

Answer 17

your welcome.

Answer 18

Try your answer with out the SQRT(340)

Answer 19

nope !

Answer 20

ok ill do it i swear add me on Facebook too ill send you a step by step thing of how to do it. names brett cory and facebook pic is orange

Answer 21

its due in 2 hours though !

Answer 22

new port beach !?

Answer 23

yeah. F=-4i+1j-10k
r'(t)=-14i,12j,0k
F*r'(t)=56+12+0=68dt
INT[0,1]68dt=68mN stil;l no?

Answer 24

it is 68 :D thanks man

Answer 25

just added u on fb too name is Ehsan Rahimzadegan

Answer 26

AWWW ok glad to help you can still ad me n ask calc 3 questions if you would like

Answer 27

yeah man thanks i will !