Two force 5n and 4n to each other at 30 degree find the resultant force by triangular method
To find the resultant force using the triangular method, we need to draw a vector triangle and use trigonometry to find the magnitude and direction of the resultant force.
Here are the steps to find the resultant force using the triangular method:
Step 1: Draw a scale diagram of the given forces.
Draw a horizontal line to represent the vector 5N and label it as Force A. From the end of Force A, draw a line at a 30-degree angle representing the vector 4N and label it as Force B. Complete the triangle by drawing a line from the endpoint of Force B back to the initial point, forming a closed triangle.
Step 2: Measure the lengths of the sides of the triangle.
Measure the lengths of the sides of the triangle using a ruler. In this case, Force A has a magnitude of 5N, and Force B has a magnitude of 4N.
Step 3: Measure the angle between the two forces.
Using a protractor or angle measuring tool, measure the angle between Force A and Force B. In this case, the angle is given as 30 degrees.
Step 4: Calculate the resultant force.
Using the measured lengths and the angle, we can use trigonometry to find the magnitude of the resultant force.
The magnitude of the resultant force (R) can be found using the formula:
R = √(A^2 + B^2 + 2AB * cosθ)
where A and B are the magnitudes of the two forces and θ is the angle between them.
In this case, A = 5N, B = 4N, and θ = 30 degrees. Plugging in these values into the formula, we have:
R = √(5^2 + 4^2 + 2 * 5 * 4 * cos30°)
R = √(25 + 16 + 40 * √(3)/2)
R = √(25 + 16 + 20√(3))
R ≈ √61 + 2√(15)
R ≈ 7.81N
Therefore, the magnitude of the resultant force is approximately 7.81N.
Step 5: Determine the direction of the resultant force.
To determine the direction of the resultant force, we need to find the angle it makes with the positive x-axis.
Using trigonometry, we can find the angle using the formula:
tanθ = (sum of vertical components)/(sum of horizontal components)
tanθ = (B sinθ)/(A + B cosθ)
In this case, B = 4N and θ = 30 degrees. Plugging in these values into the formula, we have:
tanθ = (4 sin30°)/(5 + 4 cos30°)
tanθ = (4 * 0.5)/(5 + 4 * √(3)/2)
tanθ = 2/(5 + 2√(3))
Using a calculator, find the inverse tangent (arctan) of this value to determine the angle.
θ ≈ arctan(2/(5 + 2√(3)))
θ ≈ 26.57 degrees
Therefore, the angle that the resultant force makes with the positive x-axis is approximately 26.57 degrees.
Therefore, the resultant force has a magnitude of approximately 7.81N and makes an angle of approximately 26.57 degrees with the positive x-axis.