Final answer:
To find the net force acting on an object with forces of 20 N north, 30 N south, and 20 N west, subtract the north and south forces to get a 10 N southward component. Then use the Pythagorean theorem with the 20 N west force to calculate a net force magnitude of 22.36 N.
Step-by-step explanation:
Calculating the Net Force Acting on an Object
The question involves determining the net force acting on a body when given the magnitudes and directions of multiple forces. The forces in question are 20 N north (f1), 30 N south (f2), and 20 N west (f3). First, we need to realize that forces in opposite directions will cancel each other out to some extent. Here, the north and south forces partially cancel each other, while the west force acts perpendicular to them.
Since f1 and f2 are directly opposite, we subtract the smaller force (f1) from the larger force (f2). Therefore, the remaining force along the north-south axis is 10 N (30 N - 20 N) pointing south. The force f3 remains the same, as there is no eastward force to oppose it. We can now apply the Pythagorean theorem to these two forces (10 N south and 20 N west) to find the magnitude of the resultant force.
Net force magnitude = √((10 N)² + (20 N)²) = √(100 + 400) = √(500) = 22.36 N approximately. The direction of this force can be found using trigonometry, but the question only requires the magnitude.
In general, when forces are not aligned and are instead exerted in different directions, vector addition must be used, which involves breaking down each force into its x-component and y-component, and summing these components separately to find the overall net force acting on the object.