The resultant force acting on an object is the single force that represents the combined effect of all the individual forces acting on it. You can find its magnitude by following these steps:
1. Identify All Forces
First, identify all the forces acting on the object. These forces can be:
- Contact forces: Forces that arise from direct contact between objects, like friction, normal force, and applied force.
- Non-contact forces: Forces that act at a distance, like gravity, magnetic force, and electric force.
2. Draw a Free Body Diagram
Next, draw a free body diagram. This is a simple diagram that shows all the forces acting on the object, represented by arrows.
- Direction: The arrow's direction indicates the force's direction.
- Magnitude: The arrow's length represents the force's magnitude.
3. Resolve Forces into Components
If the forces are not acting along the same axis, resolve them into their horizontal and vertical components. This will make it easier to calculate the resultant force.
4. Apply Vector Addition
Now, add the force vectors using the parallelogram law or the triangle law of vector addition.
- Parallelogram law: Draw the two force vectors as adjacent sides of a parallelogram. The diagonal of the parallelogram, starting from the common point of the two vectors, represents the resultant force.
- Triangle law: Draw the first force vector. Then, starting from the tip of the first vector, draw the second force vector. The resultant force is the vector connecting the tail of the first vector to the tip of the second vector.
5. Calculate the Magnitude
Finally, calculate the magnitude of the resultant force using the Pythagorean theorem or trigonometry.
- Pythagorean theorem: If the forces are perpendicular, you can use the Pythagorean theorem: Resultant force² = Force 1² + Force 2².
- Trigonometry: If the forces are not perpendicular, you can use trigonometry to find the magnitude and direction of the resultant force.
Example
Imagine a box being pulled across a horizontal surface by a force of 10 N at an angle of 30° to the horizontal. The box also experiences a frictional force of 5 N opposing its motion.
- Forces: Applied force (10 N), friction (5 N), and normal force (equal to the box's weight).
- Free Body Diagram: Draw the box with arrows representing each force.
- Components: Resolve the applied force into horizontal and vertical components.
- Vector Addition: Add the horizontal components and the vertical components separately.
- Magnitude: Calculate the magnitude of the resultant force using the Pythagorean theorem or trigonometry.
By following these steps, you can determine the resultant force acting on an object and its magnitude.
