For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional force must be applied and at what angle with positive x-axis so that the net acceleration of body is zero?

Solution

Physics sir · 4 steps

Find the net force the four forces leave behind, then apply its exact opposite to cancel it.

1. Net along x. 5 N acts along +x and 6 N along -x, so the net is 5 - 6 = -1 N, that is, 1 N towards -x.
2. Net along y. 7 N acts along +y and 8 N along -y, so the net is 7 - 8 = -1 N, that is, 1 N towards -y.
3. Cancel the leftover. For zero acceleration the extra force must supply +1 N along x and +1 N along y. Its magnitude is √(1² + 1²) = √2 N, and since both components are equal and positive, it points at tan⁻¹(1/1) = 45° to the +x axis.
4. So. The additional force is √2 N at 45° with the positive x-axis, which is option (a).

The idea to keep. To balance a set of forces, resolve them into x and y nets first. The balancing force has the same size as that resultant and points exactly opposite to it.

Answer from the NTA final answer key. Solution by PrepWiser.