how do i find the equilibrant force of two forves acting on a point? one is 75N due north and the other is 105N due east.
Add the two forces to get a resultant. THe equivalent is equal to this resultant, but in the opposite direction.
To find the equilibrant force, you need to find the net force acting on the point. The net force is the vector sum of the two given forces. Here's how you can calculate it:
1. Draw a diagram: Start by drawing a scale diagram with a coordinate system. Place the point of interest at the origin. Draw one arrow with a length of 75 units pointing due north and another arrow with a length of 105 units pointing due east. Label these arrows with their respective magnitudes.
2. Resolve the forces into their components: To determine the components of each force, draw lines perpendicular to the axes of your coordinate system. For the 75N force, draw a line downward to represent its north component and label it as F1. For the 105N force, draw a line to the left to represent its east component and label it as F2.
3. Calculate the components: To determine the magnitudes of the components, use trigonometry. For F1, you have a right-angled triangle with the hypotenuse of length 75N and the opposite side (F1) being the north component. You can use the sine function to find F1. For F2, you have a right-angled triangle with the hypotenuse of length 105N and the adjacent side (F2) being the east component. You can use the cosine function to find F2.
4. Calculate the net force: The net force is the vector sum of the two components. Since the north and east components are perpendicular, you can add them using vector addition. The net force can be found by using the Pythagorean theorem on the two components: Net Force^2 = F1^2 + F2^2.
5. Find the equilibrant force: The equilibrant force is equal in magnitude but opposite in direction to the net force. So, the magnitudes of the equilibrant force and the net force are the same, but the direction of the equilibrant force is exactly opposite to the direction of the net force.
By following these steps, you should be able to find the magnitude and direction of the equilibrant force resulting from the two given forces.