A few days ago
vector components?
23. Three forces, each of which is perpendicular to the
other two, act on an object. If the magnitudes of
these forces are 6 N, 15 N, and 10 N, respectively,
find the magnitude and direction of the resultant.
(State the angles that the resultant makes with the
two larger forces.)
please show me step by step
Top 1 Answers
A few days ago
Favorite Answer
Let the forces be 6N in the direction of unit vector i, 10N in the direction of unit vector j, and 15N in the direction of unit vector k.
The individual forces are then 6i, 15j and 10k, and their resultant is:
6i + 15j + 10k.
The magnitude of the resultant v is:
|v| = sqrt(6^2 + 15^2 + 10^2)
= sqrt(36 + 225 + 100)
= sqrt(361)
= 19N.
If y is the angle between the resultant and the 15N force, then:
cos(y) = v.j / |v|
= |6i + 15j + 10k| . j / 19
cos(y) = 15 / 19.
If z is the angle between the resultant and the 10N force, then:
cos(z) = v.k / |k|
= |6i + 15j + 10k| .k / 19
cos(z) = 10 / 19.
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