An object is acted upon by two forces of 5N 10N. Calculate the resultant of the two forces if:
i.The forces act perpendicular to each other
ii. The two forces act on angle of 40° to each other
iii. The two forces act on an angle of 45° to each other
To calculate the resultant of two forces, we can use the concept of vector addition. The resultant can be found by adding the two forces together using either graphical or trigonometric methods.
i. Forces act perpendicular to each other:
When the forces act perpendicular to each other, we can use the Pythagorean theorem to find the magnitude of the resultant force. The formula for finding the resultant force is:
Resultant force = √(Force₁² + Force₂²)
Here,
Force₁ = 5N
Force₂ = 10N
Using the formula, we can calculate:
Resultant force = √(5² + 10²) = √(25 + 100) = √125 ≈ 11.18 N
So, the magnitude of the resultant force is approximately 11.18 N.
ii. Forces act at an angle of 40° to each other:
To find the magnitude and direction of the resultant force, we need to use trigonometry. The formula for finding the magnitude of the resultant force is:
Resultant force = √(Force₁² + Force₂² + 2 * Force₁ * Force₂ * cos(θ))
Here,
Force₁ = 5N
Force₂ = 10N
θ = 40°
Using the formula, we can calculate:
Resultant force = √(5² + 10² + 2 * 5 * 10 * cos(40°)) ≈ 11.85N
So, the magnitude of the resultant force is approximately 11.85 N.
iii. Forces act at an angle of 45° to each other:
Again, we can use the trigonometric method to find the magnitude and direction of the resultant force. Using the same formula as in ii., we have:
Resultant force = √(Force₁² + Force₂² + 2 * Force₁ * Force₂ * cos(θ))
Here,
Force₁ = 5N
Force₂ = 10N
θ = 45°
Calculating:
Resultant force = √(5² + 10² + 2 * 5 * 10 * cos(45°)) ≈ 14.14N
So, the magnitude of the resultant force is approximately 14.14 N.