19. Resolving Vectors & Scale Drawing | Resultant Forces

1. Using Scale Drawings to Find Resultant Forces

Scale drawings allow you to find the overall (resultant) force when two or more forces act on an object at different angles.

Step-by-Step Method:

• Choose a Scale: For example, 1 cm = 1 Newton.

• Draw the Vectors: Use the scale to draw arrows representing each force.

• Tip-to-Tail Method: Place the "tail" of the second vector at the "tip" of the first vector.

• Draw the Resultant: Draw a straight line from the very beginning (tail of the first) to the very end (tip of the last).

• Measure: Use a ruler to measure the length of this resultant line and convert it back to Newtons using your scale.

• Find Direction: Use a protractor to measure the angle (bearing) of the resultant force.

2. Equilibrium in Scale Drawings

• Definition: An object is at equilibrium if the resultant force is zero.

• Visual Cue: When you arrange all the force vectors "tip-to-tail," they will form a closed shape (like a perfect triangle or square) that ends exactly where it started.

• Rule: If the arrows join up perfectly, there is no overall force acting on the object.

3. Resolving a Vector

Resolving a vector is the opposite of finding a resultant force; it means splitting a single diagonal force into two separate components: horizontal and vertical.

How to Resolve a Vector:

1. Draw the Vector: Draw the original force to scale at the correct angle (e.g., a 50 N force pushed up a ramp).

2. Create a Right-Angled Triangle: From the start and end points of your vector, draw a perfectly horizontal line and a perfectly vertical line until they meet.

3. Add Arrows: Ensure the horizontal and vertical arrows follow the direction of the original force.

4. Measure and Convert: Measure the lengths of these new horizontal and vertical lines with a ruler and use your scale to find the force in Newtons for each.

4. Summary Table