Fine the resultant of two force 200N and 10N acting at right angle other ?
To find the resultant of two forces acting at right angles to each other, we can use the Pythagorean theorem. The Pythagorean theorem states that 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.
Let's label the forces:
- Force 1: 200N
- Force 2: 10N
To find the resultant, we need to calculate the magnitude and direction of the resultant force.
Step 1: Calculate the magnitude (the length) of the resultant force using the Pythagorean theorem:
Magnitude of resultant force (F) = √(Force1^2 + Force2^2)
F = √(200^2 + 10^2)
F = √(40000 + 100)
F = √40100
F ≈ 200.25N
Step 2: Calculate the direction of the resultant force:
Since the two forces are at right angles to each other, the direction of the resultant force will be the same as the direction of the diagonal (hypotenuse) of a right triangle.
Using trigonometry, we can calculate the angle (θ) between the resultant force and one of the forces:
cos(θ) = Adjacent side / Hypotenuse
cos(θ) = Force2 / F
cos(θ) = 10 / 200.25
θ = arccos(10 / 200.25)
θ ≈ 88.19°
So, the resultant force is approximately 200.25N and it makes an angle of approximately 88.19° with Force 1.