TWO FORCES 8N & 10N AT AN ANGLE OF 30' ACTING ON A PARTICLE WHAT IS RESULTANT FORCE AND IT'S DIRECTION.
First, please do not use all capitals. Online it is like SHOUTING. Not only is it rude, but it is harder to understand. Thank you.
To find the resultant force and its direction when two forces are acting at an angle on a particle, we can use vector addition.
Given:
Force 1 (8N) at an angle of 30 degrees.
Force 2 (10N) at an angle of 0 degrees (we assume it is along the x-axis).
To find the components of each force, we can use trigonometry. Let's break down each force into its x and y components:
For Force 1:
Fx1 = 8N * cos(30°)
Fy1 = 8N * sin(30°)
For Force 2:
Fx2 = 10N * cos(0°) = 10N (force is along the x-axis)
Fy2 = 10N * sin(0°) = 0N (force is along the x-axis)
Now, let's add the x-components and y-components separately:
Total Fx = Fx1 + Fx2
Total Fy = Fy1 + Fy2
Total Fx = 8N * cos(30°) + 10N
Total Fy = 8N * sin(30°) + 0N
To find the magnitude (resultant force), use the Pythagorean theorem:
Resultant Force (R) = √(Total Fx² + Total Fy²)
Now, calculate the magnitude:
R = √((8N * cos(30°) + 10N)² + (8N * sin(30°) + 0N)²)
Finally, to find the direction of the resultant force, we can use trigonometry again:
θ = arctan(Total Fy / Total Fx)
θ = arctan((8N * sin(30°) + 0N) / (8N * cos(30°) + 10N))
The resultant force is the magnitude R, and its direction is θ.
Please calculate R and θ using a scientific calculator or online tool with the given values and equations.