Net force, also known as resultant force, is the overall force acting on an object when multiple forces are applied. Understanding net force is crucial in physics and engineering to predict the motion of objects under various forces.
The formula for calculating net force involves vector addition of all individual forces:
\[ \vec{F}_{net} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 + ... + \vec{F}_n \]
For two-dimensional problems, we can break this down into x and y components:
\[ F_{net_x} = F_{1x} + F_{2x} + F_{3x} + ... + F_{nx} \]
\[ F_{net_y} = F_{1y} + F_{2y} + F_{3y} + ... + F_{ny} \]
Where:
\(F_x = F \cos(\theta)\)
\(F_y = F \sin(\theta)\)
Where \(F\) is the magnitude of the force and \(\theta\) is the angle relative to the positive x-axis.\(|F_{net}| = \sqrt{F_{net_x}^2 + F_{net_y}^2}\)
\(\theta_{net} = \tan^{-1}(\frac{F_{net_y}}{F_{net_x}})\)
Let's calculate the net force for two forces:
Given:
Step 1: Calculate x and y components
Force 1: \(F_{1x} = 10 \cos(0°) = 10\text{ N}, F_{1y} = 10 \sin(0°) = 0\text{ N}\)
Force 2: \(F_{2x} = 15 \cos(45°) \approx 10.61\text{ N}, F_{2y} = 15 \sin(45°) \approx 10.61\text{ N}\)
Step 2: Sum x and y components
\(F_{net_x} = 10 + 10.61 = 20.61\text{ N}\)
\(F_{net_y} = 0 + 10.61 = 10.61\text{ N}\)
Step 3: Calculate magnitude of net force
\(|F_{net}| = \sqrt{20.61^2 + 10.61^2} \approx 23.17\text{ N}\)
Step 4: Calculate direction of net force
\(\theta_{net} = \tan^{-1}(\frac{10.61}{20.61}) \approx 27.24°\)
Therefore, the net force is approximately 23.17 N at an angle of 27.24° relative to the positive x-axis.
The following diagram illustrates the concept of net force:
This diagram shows two forces (blue arrows) and their resultant net force (red arrow). The x and y axes are shown for reference. The length of each arrow represents the magnitude of the force, and its direction represents the angle of the force.