An object in equilibrium has three forces exerted on it. A 25 N force acts at 90 from the x-axis and a 48 N force acts at 60. What are the magnitude and direction of the third force
assuming your given forces are in first quadrant
Fx + 48 cos 60 = 0
Fy + 25 + 48 sin 60 = 0
|F| = sqrt (Fx^2 + Fy^2)
tan theta = Fy/Fx
To find the magnitude and direction of the third force, we need to use the concept of vector addition. The three forces acting on the object can be added together as vectors to determine the resultant force.
1. Convert the given forces into vector form:
- The 25 N force at 90° from the x-axis can be represented as a vector (25 N, 90°).
- The 48 N force at 60° from the x-axis can be represented as a vector (48 N, 60°).
2. Use trigonometry to determine the x and y components of each force:
- For the 25 N force, the x-component is given by 25 N * cos(90°) = 0 N, while the y-component is given by 25 N * sin(90°) = 25 N.
- For the 48 N force, the x-component is given by 48 N * cos(60°) = 24 N, while the y-component is given by 48 N * sin(60°) = 41.569 N.
3. Add the x and y components of the two forces together:
- The x-component of the resultant force is 0 N + 24 N = 24 N.
- The y-component of the resultant force is 25 N + 41.569 N = 66.569 N.
4. Find the magnitude and direction of the resultant force:
- The magnitude of the resultant force can be calculated using the Pythagorean theorem: magnitude = sqrt((x-component)^2 + (y-component)^2) = sqrt((24 N)^2 + (66.569 N)^2) = 70.99 N (rounded to two decimal places).
- The direction of the resultant force can be determined using trigonometry: direction = atan(y-component / x-component) = atan(66.569 N / 24 N) = 71.09° (rounded to two decimal places).
Therefore, the magnitude of the third force is approximately 70.99 N, and its direction is approximately 71.09°.