This lesson explains what happens when multiple forces act on a single object. Understanding the "resultant force" is key to predicting how an object will move.

1. Short Notes: Core Concepts

A. What is a Resultant Force?

• Definition: The resultant force is the single force that has the same effect as all the other individual forces acting on an object combined.

• Key Idea: It's the "net" or "overall" force. If there is a non-zero resultant force, the object will accelerate (change its motion). If the resultant force is zero, the object will be in equilibrium (either at rest or moving at a constant velocity).

B. Collinear Forces (Forces on the same line) This is the most common type of problem you'll see.

1. Forces in the SAME Direction:

   • Rule: You ADD the forces together.

   • Direction: The resultant force acts in the same direction as the individual forces.

   • Example: Two people push a box. Person A pushes with 10 N and Person B pushes with 15 N in the same direction.

     • Resultant Force = 10 N + 15 N = 25 N (in the same direction).

2. Forces in OPPOSITE Directions:

   • Rule: You SUBTRACT the smaller force from the larger force.

   • Direction: The resultant force acts in the direction of the larger force.

   • Example: In a tug-of-war, Team A pulls with 100 N to the left and Team B pulls with 80 N to the right.

     • Resultant Force = 100 N - 80 N = 20 N (to the left, because 100 N was the larger force).

C. Parallel Forces (in the same direction)

• Rule: Same as collinear forces in the same direction. You ADD them together.

• Key Idea: These forces act on different points of the object but are parallel to each other (like two people pushing a car on different parts of the bumper).

• Example: Two parallel forces of 8 N and 16 N act on a trolley.

  • Resultant Force = 8 N + 16 N = 24 N.

D. Inclined Forces (Forces at an angle)

• Rule: You do not need to calculate this, just understand the concept.

• Key Idea: When two forces act at an angle, the resultant force will be somewhere between the two forces. The object will move in the direction of this resultant force.

2. Tips & Tricks for the Exam

• Direction is Everything: Force is a vector. Always state the magnitude (the number) and the direction of the resultant force in your answer.

• Draw a Diagram: For any problem, quickly sketch the object and draw arrows to represent the forces. This makes it much easier to see whether you need to add or subtract. Label the arrows with their values.

• Zero Resultant Force = Equilibrium: If an object is not moving or is moving at a constant speed, the resultant force on it is zero. This means the forces acting on it are balanced (e.g., a 10 N force to the left is balanced by a 10 N force to the right).

3. Important Points & Common Exam Questions

• Simple Calculations: Most questions will be straightforward calculations like the examples above.

  • "A box is pushed to the right with a force of 15 N and to the left with a force of 11 N. Find the magnitude and direction of the resultant force."

  • Answer: Resultant force = 15 N - 11 N = 4 N. Direction is to the right.

• Finding a Missing Force:

  • "An object is pulled to the west with 10 N. What force (X) must be applied to the east for the resultant force to be 5 N to the west?"

  • Answer: The resultant is to the west, so the westward force must be bigger. Resultant = West Force - East Force 5 N = 10 N - X X = 10 N - 5 N = 5 N to the east.