Point of application of force

[zorro]

Homework Statement

Three forces are applied to a square plate of side a. The point of application (on side BC) of the resultant force is ?

The Attempt at a Solution

Resultant force acts along AC with magnitude 2F. How to find the point of application that too on a given side?

 

[PhanthomJay]

The resultant force does not act along a line from A to C. The resultant force is the force that is the vector sum of the individual forces, the line of action of which produces the same torque about any point as the sum of the torques of the individual forces about that point. It is often best to first break each force into its component forces.

 

[SammyS]

To make things easier, look at the torque about point A.

You do have the correct direction (to the right) and magnitude for the resultant force, just not the correct location.

 

[zorro]

the line of action of which produces the same torque about any point as the sum of the torques of the individual forces about that point.

I did not know about this. Now the problem is a piece of cake
Thanks!

 

[rwisz]

I would approach this problem by first analyzing the given information and identifying any relevant equations or principles that can be applied. In this case, we are dealing with forces and their resulting effect on an object.

To find the point of application of the resultant force on side BC, we can use the concept of torque. Torque is the measure of the force's ability to rotate an object around a pivot point. In this case, the pivot point can be considered as the intersection of the two sides where the resultant force is acting (point A).

We can use the equation τ = Fd, where τ is the torque, F is the force, and d is the perpendicular distance from the pivot point to the line of action of the force. In this case, we know that the magnitude of the resultant force is 2F and it acts along AC, which is perpendicular to side BC. This means that the distance from the pivot point to the line of action of the force is equal to the length of side a.

Therefore, the point of application of the resultant force can be found by dividing the length of side a into two equal parts, with one part starting from point B and the other from point C. The point where these two parts meet is the point of application of the resultant force on side BC.

In summary, by using the concept of torque and the given information about the resultant force, we can determine the point of application on side BC. This approach can be applied to similar problems involving the point of application of a force on an object.