To find the magnitude and direction of the resultant force when two forces are applied at an angle to each other, we can use vector addition.
Let's call the two forces F1 and F2. F1 has a magnitude of 5N, and F2 has a magnitude of 8N. The angle between them is 45°.
To find the resultant force, we can use the following formula:
Resultant Force = √(F1² + F2² + 2F1F2cosθ)
where θ is the angle between the two forces.
Plugging in the values, we have:
Resultant Force = √(5² + 8² + 2 * 5 * 8 * cos 45°)
Resultant Force = √(25 + 64 + 80 * cos 45°)
Resultant Force = √(89 + 80 * 0.7071)
Resultant Force = √(89 + 56.568)
Resultant Force = √145.568
Resultant Force ≈ 12.07 N (rounded to two decimal places)
The magnitude of the resultant force is approximately 12.07 N.
To find the direction of the resultant force, we can use trigonometry. The angle between the resultant force and the horizontal axis can be found using the formula:
θ = arctan(F2sinθ / (F1 + F2cosθ))
Plugging in the values, we have:
θ = arctan(8 * sin 45° / (5 + 8 * cos 45°))
θ = arctan(8 * 0.7071 / (5 + 8 * 0.7071))
θ = arctan(5.6568 / (5 + 5.6568))
θ = arctan(5.6568 / 10.6568)
θ ≈ 30.96° (rounded to two decimal places)
The direction of the resultant force is approximately 30.96° with respect to the horizontal axis.