two forces, one of 18.4 pounds and the outer 13.1 pounds, act upon the same onject. the angle between these forces is 16.5°. find the magnitude of the resultant force
Fr = 18.4[0o] + 13.1[16.5o].
X = 18.4 + 13.1*Cos16.5 =
Y = 13.1*sin16.5 =
Fr = Sqrt(x^2+Y^2).
To find the magnitude of the resultant force, you can use the concept of vector addition. Here's how you can calculate it step by step:
1. Convert the forces into vector form: Since the given forces are given in pounds, you need to convert them into vectors. A vector has both magnitude and direction. You can represent a vector by its components along x and y directions. Assume the x-axis points horizontally and the y-axis points vertically.
The 18.4-pound force can be represented as a vector F1 with components F1x and F1y. Similarly, the 13.1-pound force can be represented as a vector F2 with components F2x and F2y.
2. Resolve the forces into their components: To find the components of the forces, you can use trigonometry. Since you know the magnitudes of the forces and the angle between them, you can use the cosine and sine functions.
For F1:
F1x = F1 * cos(angle)
F1y = F1 * sin(angle)
For F2:
F2x = F2 * cos(180 - angle) (the angle between F2 and x-axis is 180 - angle)
F2y = F2 * sin(180 - angle)
Plug in the given values to calculate the components.
3. Add the components of the forces: Now that you have the components of F1 and F2, you can add them together to get the resultant force.
Resultant force FR:
FRx = F1x + F2x
FRy = F1y + F2y
4. Calculate the magnitude of the resultant force: To find the magnitude of the resultant force, you can use the Pythagorean theorem:
Magnitude of the resultant force FR:
|FR| = sqrt(FRx^2 + FRy^2)
Plug in the computed values of FRx and FRy to calculate the magnitude.
By following these steps, you will be able to find the magnitude of the resultant force.