three forces each of magnitude 50 N, act in eastward, westward, and northwest directions, Find the resultant force.
To find the resultant force, we need to consider the vector sum of the three forces.
First, we will represent the eastward force as a vector in the positive x-direction with a magnitude of 50 N.
Next, we will represent the westward force as a vector in the negative x-direction with a magnitude of 50 N since it acts in the opposite direction.
Lastly, we need to represent the northwest force. To do this, we can break it down into two components: one in the x-direction and one in the y-direction. Let's call the magnitude of the northwest force "F_nw".
Since the northwest direction is between the north and west directions, we can use trigonometry to find the x and y components of this force. We can represent the x-component as F_nw * cos(45°) since 45° is the angle between the x-axis and the northwest force. Similarly, the y-component can be represented as F_nw * sin(45°).
Since the northwest component is in the opposite direction, the x-component will be negative.
Now let's calculate the magnitudes of the x and y components of the northwest force.
x-component: F_nw * cos(45°) = F_nw * cos(45°) = F_nw * sqrt(2) / 2
y-component: F_nw * sin(45°) = F_nw * sin(45°) = F_nw * sqrt(2) / 2
Now we can combine the three forces and find the resultant force. The x-direction forces cancel each other out, leaving only the y-components:
Resultant force in the y-direction = (F_nw * sqrt(2) / 2) + (F_nw * sqrt(2) / 2) = F_nw
So, the resultant force is equal to the magnitude of the northwest force.
In this case, the resultant force is equal to 50 N.