GCSE Physics Tutorial - Resolving a Force into Components
In physics, when a single force acts on an object at an angle to a given direction, it can be resolved into two perpendicular components. These components are called "resolved forces." This process of breaking a single force into two components allows us to analyse the force's effect in different directions.
Resolving a Force into Components: Consider a force F acting on an object at an angle θ to a reference axis, usually the horizontal axis. To resolve this force into two components, we use trigonometric functions (sine and cosine) as follows:
Horizontal Component ($F_x$): The horizontal component of the force ($F_x$) is the part of the force that acts parallel to the reference axis (usually the x-axis). It can be calculated using the equation:
$$F_x = F \times cos(θ)$$
Vertical Component ($F_y$): The vertical component of the force ($F_y$) is the part of the force that acts perpendicular to the reference axis (usually the y-axis). It can be calculated using the equation:
$$F_y = F \times sin(θ)$$
The magnitude of the original force F can be expressed using the Pythagorean theorem as:
$$F = \sqrt{F_x^2 + F_y^2}$$
Example: Let's consider a force F of magnitude 100 N acting at an angle of 30 degrees to the horizontal axis.
Step 1: Calculate $F_x$, $F_x = 100 N \times cos(30°) ≈ 86.60 N$
Step 2: Calculate $F_y$, $F_y = 100 N \times sin(30°) = 50 N$
Step 3: Verify $F$, $F = \sqrt{(86.60^2 + 50^2)} ≈ √(7500) ≈ 86.60 N$
Resolving a single force into two components allows us to analyse its effect in different directions. The horizontal and vertical components have the same combined effect as the original force. This concept is crucial in physics and engineering, especially when dealing with forces acting at angles to the reference axis. It enables us to perform accurate calculations and predictions in various scenarios, contributing to the understanding of forces and motion.
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