Question

Given four forces:
F1 = 3i –j + 9k, F2 = 2i - 2j + 16k, F3 = 9i + j +18 k and F4 = i + 2j – 18k.
If all these forces act on a particle at rest at the origin of a coordinate system, then identify the plane in which the particle would begin to move?

Answer 1

Given info : F₁ = 3i –j + 9k, F₂ = 2i - 2j + 16k, F₃ = 9i + j +18 k and F₄ = i + 2j – 18k.  if all these forces act on a particle at rest at the origin of a coordinate system.

To find : identify the plane in which the particle would begin to move.

solution : these all forces are acting on a particle at rest.

so we have to find the net force acting on the particle.

∴ F = F₁ + F₂ + F₃ + F₄

      = (3i –j + 9k) + (2i - 2j + 16k) + (9i + j +18 k) + (i + 2j – 18k)

       = (3 + 2 + 9 + 1)i + (-1  - 2+ 1 + 2)j + (9 + 16 + 18 - 18)k

       = 15i + 0j + 25k = 15i + 25k

here you see the net force acting along xz plane ( it is considered as i lies in x , j lies in y and k lies in z axes). according to Newton's 2nd law of motion, particle moves along the net force acting on it.

therefore the particle would begin to move along xz plane.