128k views
1 vote
QUESTION 1

Determine the work done by the force
F=31+] + k in moving an object through
displacement T = 7 -7 -K​

1 Answer

3 votes

It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.

Let θ be the angle between the force vector F and the displacement vector r. The work W done by F in the direction of r is

W = Fr cos(θ)

The cosine of the angle between the vectors can be obtained from the dot product identity,

ab = ||a|| ||b|| cos(θ) ==> cos(θ) = (ab) / (||a|| ||b||)

so that

W = (Fr)² / (||F|| ||r||)

For instance, if F = 3i + j + k and r = 7i - 7j - k (which is my closest guess to the given vectors' components), then the work done by F along r is

W = ((3i + j + k) • (7i - 7j - k))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))

==> W ≈ 5.12 J

(assuming F and r are measured in Newtons (N) and meters (m), respectively).

User Shrewd
by
4.2k points