Find magnitude and direction of resultant force if 50 N force is acting due North and 30 N force is acting due East
sqrt (50^2 + 30^2)
tangent of angle above east ( x ) axis = (5/3)
i need all problem solved details
To find the magnitude and direction of the resultant force from the given forces, we can use the Pythagorean theorem and trigonometric functions.
1. Start by drawing a diagram to represent the forces. Let's label the 50 N force as "F1" acting due North and the 30 N force as "F2" acting due East.
---> F2 (30 N)
|
|
F1 (50 N)
2. To find the magnitude of the resultant force, we need to find the length of the hypotenuse of the right triangle formed by the two forces.
- Use the Pythagorean theorem:
a^2 + b^2 = c^2, where a and b are the magnitudes of the forces F1 and F2, and c is the magnitude of the resultant force.
Substitute the values:
(50 N)^2 + (30 N)^2 = c^2
2500 N^2 + 900 N^2 = c^2
3400 N^2 = c^2
Take the square root of both sides to find the magnitude of the resultant force:
c = √(3400 N^2)
c ≈ 58.31 N (rounded to two decimal places)
Therefore, the magnitude of the resultant force is approximately 58.31 N.
3. To find the direction of the resultant force, we need to find the angle it makes with the positive x-axis.
- Use the tangent function:
tan(θ) = opposite/adjacent = F1/F2
Substitute the values:
tan(θ) = 50 N/30 N
Solve for θ:
θ ≈ 59.04° (rounded to two decimal places)
Therefore, the direction of the resultant force is approximately 59.04° measured counterclockwise from the positive x-axis.
In summary, the magnitude of the resultant force is approximately 58.31 N, and its direction is approximately 59.04° counterclockwise from the positive x-axis.