A particle of m kilograms mass is acted on by two forces, F[1] and F[2], with magnitudes 3*sqrt(5) Newtons and sqrt(5) Newtons and directions parallel to the vectors i + 2j and i - 2j, respectively. The particle is initially at a position given by the vector 2i + j
I was told to calculate the Cartesian components of F[1] and F[2] and hence calculate the total force F[1] + F[2], acting on the particle in component form
MY SOLUTION
The vector i + 2j has length sqrt{1^2+ 2^2} = sqrt{5}. A vector in that direction, with length is just 3 times that: 3i + 6j. That's the first force vector. Similarly, the vector i - 2j also has length sqrt5 so that is the second force vector. The total force, then, is F1 + F2 = (3i + 6j) + (i - 2j) = 4i + 4j
From there, I need to show the couple of the total force about the point with position vector i is zero.....so the total force is 4i + 4j .
I would appreaciate a explanation to how to tackle this question, so I can do it myself, but I'm assuming that it is a single force and a couple cannot be put in equilibrium by a single force so it must be zero? is that correct?
I was told to calculate the Cartesian components of F[1] and F[2] and hence calculate the total force F[1] + F[2], acting on the particle in component form
MY SOLUTION
The vector i + 2j has length sqrt{1^2+ 2^2} = sqrt{5}. A vector in that direction, with length is just 3 times that: 3i + 6j. That's the first force vector. Similarly, the vector i - 2j also has length sqrt5 so that is the second force vector. The total force, then, is F1 + F2 = (3i + 6j) + (i - 2j) = 4i + 4j
From there, I need to show the couple of the total force about the point with position vector i is zero.....so the total force is 4i + 4j .
I would appreaciate a explanation to how to tackle this question, so I can do it myself, but I'm assuming that it is a single force and a couple cannot be put in equilibrium by a single force so it must be zero? is that correct?