Determine the resultant of two or more forces acting along the same straight line

1.5.1 Effects of Forces

Objective

Determine the resultant of two or more forces acting along the same straight line.

Key Concepts

• Force – a push or pull that can change the state of motion of an object. Measured in newtons (N).
• Resultant force – the single force that has the same effect as all the individual forces acting together.
• Collinear forces – forces whose lines of action lie on the same straight line.
• Direction – forces are treated as positive when they act in the chosen positive direction and negative when they act opposite.

Method for Finding the Resultant of Collinear Forces

1. Choose a convenient positive direction (e.g., to the right or upwards).
2. Assign a sign to each force:

   • Positive (+) if the force acts in the chosen direction.
   • Negative (–) if the force acts opposite to the chosen direction.

3. Write down the magnitude of each force with its sign.
4. Add the signed values:

   \$F{\text{resultant}} = \sum{i=1}^{n} F_i\$

5. Interpret the sign of the resultant:

   • If \$F_{\text{resultant}} > 0\$, the resultant acts in the chosen positive direction.
   • If \$F_{\text{resultant}} < 0\$, the resultant acts opposite to the chosen direction.
   • If \$F_{\text{resultant}} = 0\$, the forces are balanced (no net motion).

Worked Example

Three forces act on a sled along a horizontal line. Choose “to the right” as positive.

Calculate the resultant:

\$F_{\text{resultant}} = (+30) + (–45) + (+20) = +5\ \text{N}\$

The resultant force is \$5\ \text{N}\$ to the right.

Common Mistakes

• Forgetting to assign a sign to each force.
• Adding magnitudes without considering direction.
• Choosing opposite directions for the same problem, leading to inconsistent signs.

Practice Questions

1. Two forces act on a crate along a straight line: \$FA = 12\ \text{N}\$ to the left and \$FB = 18\ \text{N}\$ to the right. Find the resultant force and its direction.
2. A tugboat pulls a barge with \$F1 = 250\ \text{N}\$ forward. A current pushes the barge backward with \$F2 = 80\ \text{N}\$. Determine the net force on the barge.
3. Four forces act on a sled: \$+15\ \text{N}\$, \$-10\ \text{N}\$, \$+5\ \text{N}\$, and \$-8\ \text{N}\$. What is the resultant?
4. Explain why the resultant is zero when \$F1 = 50\ \text{N}\$ to the right and \$F2 = 50\ \text{N}\$ to the left.

Summary

When forces act along the same straight line, the resultant is found by assigning consistent signs based on a chosen positive direction, adding the signed magnitudes, and interpreting the sign of the sum. This technique is essential for solving many IGCSE physics problems involving linear forces.