Question

a resultant force of 10. newtons is made up of two component forces acting at right angles to each other. if the magnitude of one of the components is 6.0 newtons, the magnitude of the other component must be

Answer 1

The magnitude of the other component force, when two forces act at right angles to give a resultant of 10.0 Newtons and one component is 6.0 Newtons, is found to be 8.0 Newtons using the Pythagorean theorem.

Step-by-step explanation:

The question revolves around component forces acting at right angles and involves the calculation of the magnitude of one component force when the resultant force and the magnitude of the other component force are known. This can be resolved using the Pythagorean theorem as applied in physics to vector components.

To find the magnitude of the unknown component force, we consider the resultant force and the known component force as the hypotenuse and one of the legs of a right-angled triangle, respectively. According to the Pythagorean theorem, the square of the hypotenuse (resultant force) is equal to the sum of the squares of the two legs (component forces).

Here are the calculations:

1. Resultant force (Fresultant) = 10.0 N (given)
2. Component force 1 (F1) = 6.0 N (given)
3. Component force 2 (F2) = unknown
4. According to the Pythagorean theorem: Fresultant^2 = F1^2 + F2^2
5. Substitute the known values: 10.0^2 = 6.0^2 + F2^2
6. Simplify and solve for F2: 100 = 36 + F2^2
7. F2^2 = 100 - 36
8. F2^2 = 64
9. Component force 2 (F2) = √64
10. Component force 2 (F2) = 8.0 N

Therefore, the magnitude of the other component must be 8.0 Newtons.