Point of application of resultant force from bound vector forces

Click For Summary
SUMMARY

The discussion focuses on the calculation of the point of application of the resultant force from bound vector forces. It highlights the distinction between free vectors, which can be represented anywhere with the same magnitude and direction, and bound vectors, where the point of application is critical. The formula provided by user fog37 for calculating the resultant force's location is Rx = ∑Fixi, indicating that the resultant's position is determined by the sum of the forces multiplied by their respective positions. This emphasizes the importance of understanding the application points of forces in physics.

PREREQUISITES
  • Understanding of vector forces and their properties
  • Familiarity with the head-tail rule for vector addition
  • Knowledge of the concept of resultant vectors
  • Basic principles of mechanics related to force application
NEXT STEPS
  • Study the concept of bound vectors in mechanics
  • Learn about the head-tail rule for vector addition in detail
  • Explore the implications of force application points on rigid bodies
  • Investigate advanced topics in vector calculus related to force systems
USEFUL FOR

This discussion is beneficial for physics students, mechanical engineers, and anyone involved in analyzing forces and their applications in physical systems.

fog37
Messages
1,566
Reaction score
108
Hello Forum,

in the case of two or multiple free vectors, it is easy to determine graphically (head-tail rule) the resultant vector (magnitude and direction). The resultant vector is also a free vector.
A free vector is actually an infinite number of vectors with the same magnitude and direction but different points of application (equivalence class)

In the case of bound vectors, the point of application matters. For example, if an object has two different forces applied at different points on the extended object. How do we calculate the point of application or the line of action of the resultant force which is the sum of the two applied forces?

Is it possible?
thanks,
fog37
 
Physics news on Phys.org
You calculate the location of the resultant R relative to some fixed point x such that:

Rx = ∑Fixi

I don't really understand your definitions of free and bound vectors as I have never heard those terms before.
 

Similar threads

Undergrad Is force a a bound vector or a free vector?
  • · Replies 15 ·
Replies
15
Views
4K
Undergrad Rail gun - point of application of force?
  • · Replies 21 ·
Replies
21
Views
2K
Undergrad Calculate the Resultant Force Between 4 Points
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Distributed Forces and force density....
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Correct understanding of the tension force
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Spring balance analysis from a system point of view
  • · Replies 24 ·
Replies
24
Views
2K
Undergrad What is the zero point for Potential Energy and how to find it from integral limits?
  • · Replies 6 ·
Replies
6
Views
2K
High School Moment of a force about a point
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad Reaction force of and its relation to normal force and friction
  • · Replies 20 ·
Replies
20
Views
5K
Graduate Conceptual questions about Angular Momentum Conservation and torque
  • · Replies 2 ·
Replies
2
Views
3K