Question

Four forces $\sf { X_{1}}$ , $\sf { X_{2}}$ , $\sf { X_{3}}$ and $\sf { X_{4}}$ are acting on an object in different direction as shown in the given figure. the magnitude force $\sf { X_{1}}$ is twice of $\sf { X_{3}}$ i.e. $\sf { X_{1}}$ = $\sf { 2X_{3}}$ and the magnitude of the force $\sf { X_{2}}$ is equal to thrice of $\sf { X_{4}}$ i.e. $\sf { X_{2}}$ = $\sf { 3X_{4}}$ . What will be the resultant force acting on the object in Newton . ​

Answer 1

ANSWER -

$\sf { X_{3}}$ + $\sf { 2X_{4}}$newton

STEP BY STEP SOLUTION -

Net Force = ( $\sf { X_{1}}$ + $\sf { X_{2}}$ ) - ( $\sf { X_{3}}$ + $\sf { X_{4}}$ )

Note - Because sum of the forces acting towards the east direction is greater than the sum of the force acting towards the west direction

⟹ ( $\sf { 2X_{3}}$ + $\sf { 3X_{4}}$ ) - ( $\sf { X_{3}}$ + $\sf { X_{4}}$ )

⟹ $\sf { 2X_{3}}$ + $\sf { 3X_{4}}$ - $\sf { X_{3}}$ + $\sf { X_{4}}$

⟹ $\sf { 2X_{3}}$ - $\sf { X_{3}}$ + $\sf { 3X_{4}}$ + $\sf { X_{4}}$

⟹ $\sf { X_{3}}$ + $\sf { 2X_{4}}$newton

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MORE INFORMATION -

RESULTANT FORCE or NET FORCE

★ When two or more forces are applied on an object in the same direction, they add up. The net force on the object is a single force whose magnitude is the sum of the two forces. The net or resultant force acts in the same direction as the two forces.

★ When two or more forces are applied on an object in opposite directions, they oppose each other. The net force on the object is the difference between the two forces. This net force will act in the direction of the larger force. If the two opposing forces are equal, the net or resultant force is zero.