Resultant forces

This section explains resultant forces, how to calculate them, and how to use diagrams to analyze forces acting on objects. Examples and explanations are provided to help you understand and apply these concepts.

Resultant force

When multiple forces act on an object, they can be combined into a single force called the resultant force. The resultant force has the same overall effect as all the original forces combined.

Example:

• If a car is being pushed forward with a force of 500 N and friction opposes this motion with a force of 200 N, the resultant force is: 

500 N − 200 N = 300 N forward

Key Point:

• If the resultant force is zero, the object remains at rest or continues moving at a constant speed.

Interpreting and calculating resultant forces

How to Calculate Resultant Forces

1. Forces in the Same Direction: Add the forces.

   • Example: Two people push a box with forces of 30 N and 20 N in the same direction. The resultant force is: 

30 N + 20 N = 50 N

2. Forces in Opposite Directions: Subtract the smaller force from the larger force.

   • Example: If a car is pushed forward by 100 N and dragged backward by 40 N, the resultant force is: 

100 N − 40 N = 60 N forward

Free body diagrams

A free body diagram shows all the forces acting on an object. Each force is represented by an arrow. The length of the arrow shows the magnitude, and the direction of the arrow shows the direction of the force.

• Example 1: A parachutist falling at constant speed experiences:

  • Weight acting downward due to gravity.

  • Air resistance acting upward, balancing the weight.

• Example 2: A car accelerating experiences:

  • Driving force from the engine.

  • Friction and air resistance acting in the opposite direction.

Resolution of forces

A single force can be split into two components acting at right angles.

Example:

A box is pushed along a ramp with a force of 100 N at an angle.

• The force can be resolved into:

  • A horizontal component that pushes the box along the ramp.

  • A vertical component that pushes it into the ramp.

Steps to Resolve a Force:

1. Use a protractor to measure the angle of the force.

2. Use trigonometry to calculate components:

   • Horizontal component: Fx=Fcos⁡θF_x = F \cos \thetaFx​=Fcosθ.

   • Vertical component: Fy=Fsin⁡θF_y = F \sin \thetaFy​=Fsinθ.

Vector diagrams

Use vector diagrams to calculate the resultant of two forces at an angle to each other.

Example:

A toy car is pulled with:

• A force of 10 N east.

• A force of 5 N north.

Steps:

1. Draw arrows to represent the forces (to scale).

2. Complete the parallelogram.

3. Draw the diagonal of the parallelogram to represent the resultant force.

4. Measure the length of the diagonal to find the magnitude of the resultant force.

5. Measure the angle to find the direction.

Key skills and application