Posted by **Anonymous** on Sunday, February 24, 2008 at 6:41pm.

I forgot how to do the following, so I'm not sure if they're correct or not:

Find the work done by a force "F" that causes a displacement "d".

i and j = unit vectors

a)

F = 4i + j

d = 3i + 10j

W = (4i + j)(3i + 10j)

W = 12|i|^2 + 40ij + 3ij + 10|j|^2

W = 12(1) + 40(0) + 3(0) + 10(1)

W = 22

b)

F = 2i

d = 5i + 6j

W = (2i)(5i + 6j)

W = 10|i|^2 + 12ij

W = 10(1) + 12(0)

W = 10

- Math: Vectors -
**Damon**, Sunday, February 24, 2008 at 7:29pm
You want F DOT D (I am using capital for vector) = |F||D| cos T

where T is the angle between them.

dot product = scalar product = FxDx + FyDy

= 4*3 + 1*10 = 12+10 = 22

Now do that one other way

|F| = sqrt(4^2+1^2) = sqrt(17)

|D| = sqrt(3^2+10^2) = sqrt (109)

angle F to x axis = tan^-1 (1/4) =14 deg

angle D to x axis = tan^-1 (10/3)=73.3 deg

so T = 73.3 - 14 = 59.3

cosT = .5105

so

W = |F||D| cos T = 21.97 = 22 to our sig figs

check

- Math: Vectors -
**Damon**, Sunday, February 24, 2008 at 7:31pm
b)

F = 2i

d = 5i + 6j

W = 2*5 + 0*6

W = 10

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