Given are four concurrent forces: 10 N east, 20 N north, 15 N west, 25 N south. What is the direction of the resultant force?
South-west
To find the resultant of concurrent forces we resolve them along two perpendicular axes (East–West and North–South), add algebraically, and then interpret the signs. Let East and North be positive.
Horizontal (East–West) components:
- 10 N East (+10) and 15 N West (−15)
- Sum = +10 − 15 = −5 N, i.e. 5 N directed West.
Vertical (North–South) components:
- 20 N North (+20) and 25 N South (−25)
- Sum = +20 − 25 = −5 N, i.e. 5 N directed South.
The resultant therefore points partly West and partly South, which places it in the South-West quadrant. That is why South-West is correct.
Its magnitude is R = √((−5)² + (−5)²) = √(25 + 25) = √50 = 5√2 ≈ 7.07 N, and because the West and South components are equal, the direction is exactly 45° below the West axis (i.e. midway between South and West).
The other directions are ruled out by the signs: North-east would need both components positive (net East and net North), South-east would need a net East component, and North-west would need a net North component. Here both net components are negative (West and South), so only South-West fits.
Similar Questions
In the parallelogram method of vector addition, two vectors are drawn from the same point as adjacent sides of a parallelogram. What does the diagonal passing through the common point represent?
Two vectors have equal magnitudes. If the magnitude of their resultant is equal to the magnitude of either vector, what is the angle between the two vectors?
A force of 10 N acts along a line OB, which makes an angle of 60° with the horizontal line OA. What is the component of the force along the direction of the acute angle bisector of angle ∠AOB?
The horizontal and vertical components of a 100 N force inclined at 37° with the horizontal are: (consider the approximation of sin 37°=0.6, cos 37°=0.8 and tan 37°=0.75)
A force of 100 N acting on a rigid body is moved to another point along the same line of action. What is the effect on the external equilibrium of the body?
Important Questions from Equilibrium
Bee sting leaves an acid which causes pain and irritation. The acid released is
Which one of the following salts does not possess water of crystallization?
Which one of the following was the first mineral acid discovered?
What is the colour of the precipitate obtained by passing CO 2gas through lime water ?
Which among the following is NOT true with respect to colloidal solution?
