Question

Two forces 100 N and 200 N are acting in east direction and north-west direction respectively. Calculate the magnitude and direction of resultant force.

Answer 1

LHS=RHS

In opposite directions the force takes on a negative value .

that means that the value of the opposite force is zero .

so

100=-200

as force on one side is greater the object faces external unbalanced force causing it to move in the direction that the 200N wants to move in.

As there is 100N on both direction and a extra 100N on one direction the 2 100N shall cancel and you will be left with 100N which is the resultant force.

Answer 2

The magnitude and direction of the resultant force is 100N and north-west direction, respectively.

Given:

The magnitude of the first force, F₁ = 100 N.

The direction of the first force, F₁ = South-east.

The magnitude of second force, F₂ = 200 N.

The direction of the second force, F₂ = North-west.

To Find:

We have to calculate the magnitude and direction of the resultant force.

Solution:

A resultant force that is smaller than either single force is generated while two unequal forces act in opposing directions.

The magnitude of the resultant force is obtained by deducting the smaller force's magnitude from the larger force's magnitude.

∴, The magnitude of the resultant force, $F_{R}$ = F₂ - F₁.

On substituting the values, the above equation becomes,

$F_{R} = 200 -100 = 100 N.$

Now, we have to find the direction of the resultant force ($F_{R}$).

The direction of the resultant force is identical to the direction of the greater force.

∴, The direction of the resultant force = The direction of F₂ = North-west direction.

Hence, the magnitude of the resultant force is 100N and its direction is north-west direction.

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