how do you find the magnitude of the net force if you have 2 forces acting on an object: 8.4 N[S] and 7.5 N[E]
To find the magnitude of the net force, you first need to understand the concept of vector addition. Forces, like the ones mentioned in your question, are vector quantities, which means they have both magnitude (size) and direction.
In this case, you have two forces: 8.4 N[S] (south) and 7.5 N[E] (east). To find the net force, you need to add these forces together. Since they are at right angles to each other, you can use the Pythagorean theorem to calculate the magnitude of the net force.
Here's how you can do that:
1. Draw a diagram or use a coordinate system to visualize the forces. In this case, you can draw an x and y-axis, with the 7.5 N[E] force pointing to the right (positive x-direction) and the 8.4 N[S] force pointing downwards (negative y-direction). This will form a right triangle.
2. Use the Pythagorean theorem, which states that the square of the hypotenuse (net force) is equal to the sum of the squares of the other two sides (individual forces). In this case, the net force (hypotenuse) is represented by "F_net" and can be found using the equation:
F_net^2 = (7.5 N)^2 + (8.4 N)^2
Note that the square of a number is obtained by multiplying the number by itself.
3. Plug in the values and calculate using a calculator or algebraic solving techniques:
F_net^2 = 56.25 N^2 + 70.56 N^2
F_net^2 = 126.81 N^2
Therefore, the square of the net force is equal to 126.81 N^2.
4. To find the magnitude of the net force, take the square root of both sides of the equation:
F_net = √(126.81 N^2)
F_net ≈ 11.27 N
Therefore, the magnitude of the net force is approximately 11.27 N.