Final answer:
Using the Pythagorean theorem, the magnitude of the other component force, when two forces act at right angles to form a resultant force of 10 Newtons and one component is 6.0 Newtons, is found to be 8 Newtons.
Step-by-step explanation:
If we have a resultant force of 10 Newtons made up of two component forces acting at right angles to each other, and one of the component forces has a magnitude of 6.0 Newtons, we can determine the magnitude of the other component force using the Pythagorean theorem. This is because the forces are acting at right angles, arithmetically similar to the sides of a right-angled triangle.
In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This relationship is expressed by the Pythagorean theorem (c² = a² + b²), where c is the hypotenuse and a and b are the other two sides. In this scenario, our 'c' is the resultant force (10 N), and 'a' is the known component force (6.0 N).
Let's calculate the unknown component (b):
c² = a² + b²
10² = 6.0² + b²
100 = 36 + b²
b² = 64
b = √64
b = 8 N
Therefore, the magnitude of the other component must be 8 Newtons.