# A 12N force & a 5N force both act at the same point. What are the greatest resultant, least resultant & if the two forces act at right....angles to each other, the size and direction of...

A 12N force & a 5N force both act at the same point. What are the greatest resultant, least resultant & if the two forces act at right....

angles to each other, the size and direction of their resultant.

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### 2 Answers

The resultant of two forces acting on the same point is maximum when the forces are acting in the same direction and minimum when they operate in opposite direction.

When the two forces are acting in the same direction the angle between the direction to the two forces is 0. In this case the resultant force is sum of the two forces and its direction is same as the two independent forces.

In the question the magnitude of the two forces are given as 12 N and 5 N.

Therefor their net magnitude will be 12 + 5 = 17 N

When the two forces are acting in the opposite direction the angle between the direction to the two forces is 180 degrees. In this case the resultant force is the difference in the magnitude of two forces acting in the direction of larger of the two forces.

Thus when the forces with the given magnitude are acting in opposite direction their net magnitude will be:

12 - 5 = 7 N

This resultant force will act in the direction of the component force with magnitude of 12 N.

When the two forces are acting at right angles their magnitude is:

(12^2 + 5^2)^1/2 = (144 + 25)^1/2 = 169^1/2 = 13 N

This resultant force acts at an angle A with the greater of the two forces and towards the smaller force such that:

tanA = (Magnitude of smaller force)/Magnitude of greater force

= 5/12 = 0.41666

Measure of angle A corresponding to this value of tanA is 22.6 degrees.

We represent the forces,12N and 5N acting at apoint O, as adjascent sides of a parallelogram. Then the resultant force is represented by the diagonal of the parallelogram from the point of acting of forces both in magnitude and direction.

If a and b are the forces acting at a point , then by the law of parallelogram of forces, the resultant force F is given by:

F = (a^2+b^2+2abcos x)^(1/2) and is in the direction of the diagonal from the point of acting of forces.Here a= 12N, b=5N and let x be the angle between the forces.

Threfore,

F = (12^2+5^2+2*12*5 cos x)^(1/2) N= (169+120cosx)^(1/2) Newtons. The resultant force is maximum when angle x= 0 and F = 12+5 =17 N and minimum when x= 180 and F = 12-5 = 7N.

When x= 90 dgree,

F = (12^2+5^2+120*cos90)^(1/2) = 13N along the diagonal from O which makes an angle of Tangent inverse (5/12) =22.6199 degree with 12N force and Tangent inverse(12/5) = 67.3801 degree with 5N force.