forces of 3N and 4N and 12N act at a point in mutually perpendicular directions. Tha magnitude of the resultant force in newton is
To find the magnitude of the resultant force, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the forces of 3N and 4N as the two sides of a right-angled triangle, and the 12N force as the hypotenuse. Let's label the forces as follows:
Force A: 3N
Force B: 4N
Force C: 12N (resultant force)
Using the Pythagorean theorem:
Force C^2 = Force A^2 + Force B^2
Substituting the values:
Force C^2 = 3^2 + 4^2
= 9 + 16
= 25
Taking the square root of both sides, we find:
Force C = √25
= 5
Therefore, the magnitude of the resultant force is 5 Newtons.
To find the magnitude of the resultant force, we can utilize the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (resultant) is equal to the sum of the squares of the lengths of the other two sides (individual forces).
In this case, we have three forces: 3N, 4N, and 12N, acting at a point in mutually perpendicular directions. Since the forces are acting at right angles to each other, we can treat them as the sides of a right triangle.
Let's label the forces as follows:
- Force A: 3N
- Force B: 4N
- Force C: 12N
To find the magnitude of the resultant force, we need to calculate the length of the hypotenuse in the right triangle formed by the forces.
Using the Pythagorean theorem, we have:
Resultant Force^2 = Force A^2 + Force B^2 + Force C^2
Substituting the given values:
Resultant Force^2 = 3N^2 + 4N^2 + 12N^2
Calculating the squares:
Resultant Force^2 = 9N^2 + 16N^2 + 144N^2
Further simplifying:
Resultant Force^2 = 169N^2
Taking the square root of both sides to find the magnitude of the resultant force:
Resultant Force = √169N^2
Finally, simplifying the square root:
Resultant Force = 13N
Therefore, the magnitude of the resultant force is 13N.
Fr = 3N[0o] + 4N[90o] + 12N[180o] =
3 + 4i -12 = -9 + 4i, Q2.
Fr = Sqrt ((-9)^2 + 4^2)