Four Tangential Forces on a Circle of Radius 4cm

To determine the resultant force and its location with respect to the center of the circle, we need to follow these steps:

Step 1: Draw the diagram and label the forces
We start by drawing the diagram of the circle and the four tangential forces. We label the forces F1, F2, F3, and F4, and indicate their directions.

Step 2: Resolve the forces into components
Next, we resolve each force into its horizontal and vertical components. We use trigonometry to do this, using the angles between each force and the horizontal axis.

Step 3: Sum the horizontal and vertical components separately
We then sum the horizontal components of all the forces, and separately sum the vertical components of all the forces. This gives us two values, which we can call the horizontal and vertical components of the resultant force.

Step 4: Compute the magnitude and direction of the resultant force
Using the horizontal and vertical components of the resultant force, we can compute its magnitude using the Pythagorean theorem. We can also compute its direction using trigonometry.

Step 5: Determine the location of the resultant force
To determine the location of the resultant force with respect to the center of the circle, we need to find the point where its line of action intersects the circle. This can be done by drawing a line perpendicular to the line of action of the resultant force, and finding its intersection with the circle. The distance between this intersection point and the center of the circle gives us the location of the resultant force.

Result:
In this case, let's assume that the horizontal and vertical components of the four forces are as follows:

F1x = 2N, F1y = 3N
F2x = -4N, F2y = 2N
F3x = -1N, F3y = -4N
F4x = 3N, F4y = -1N

Summing these components separately gives us:

Horizontal component = F1x + F2x + F3x + F4x = 0N
Vertical component = F1y + F2y + F3y + F4y = 0N

Therefore, the resultant force is zero. This means that the four tangential forces are in equilibrium, and there is no net force acting on the circle.

Since the resultant force is zero, its location with respect to the center of the circle is undefined. However, we can still compute the position of the point where the line of action of the resultant force intersects the circle, by finding the intersection point of the lines perpendicular to the four forces. This point is the center of the circle, since the four tangential forces are all perpendicular to the radius of the circle.

Therefore, the location of the point where the line of action of the resultant force intersects the circle is at the center of the circle, which is 4cm from any point on the circumference.