Final answer:
The magnitude of the net force is determined using the Pythagorean theorem and has a value of approximately 74.48 N for the example given. The direction is found using the inverse tangent function to determine the angle which the net force makes with the coordinate axis.
Step-by-step explanation:
What is the magnitude and direction of the Net Force (Sum of forces)? In physics, when calculating the net force on an object, we employ vector addition since forces are vector quantities. The magnitude of the net force is calculated using the Pythagorean theorem when the forces act perpendicularly to each other.
For example, if we have a northward force of 64 N and a westward force of 38 N, as indicated by a free-body diagram, the magnitude of the net force is found by squaring each force, adding them together, and taking the square root of that sum, resulting in the formula: Fnet = √(64 N)² + (38 N)². The resulting magnitude would then be calculated as Fnet = √(4096 N² + 1444 N²) = √5540 N², which simplifies to approximately 74.48 N.
The direction of the net force can be found using trigonometric functions such as the tangent. The angle θ can be calculated using θ = tan⁻¹(opposite/adjacent), where the opposite side would correspond to the westward force and the adjacent side would correspond to the northward force in this case. This angle helps determine the direction of the net force relative to the coordinate axis.
Therefore, the net force acting on an object is both a magnitude, calculated using the square root of the sum of the squares of the components, and a direction, which is found using the inverse tangent function.