Sum of work = Work done by net force

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SUMMARY

The discussion centers on the relationship between net work and net force acting on an object. It establishes that the total work done by multiple forces, when summed as scalars, equals the net work done on the object. Additionally, it confirms that the work calculated from the net force, derived from vector summation of individual forces, is indeed the same as the net work calculated from the scalar summation. The work-kinetic energy theorem is also affirmed, stating that the change in kinetic energy (KE) is equal to the net work done on the system.

PREREQUISITES
  • Understanding of vector and scalar quantities in physics
  • Familiarity with the concept of net force
  • Knowledge of work-energy principles
  • Basic grasp of the work-kinetic energy theorem
NEXT STEPS
  • Study the implications of the work-energy theorem in various physical systems
  • Explore examples of net force calculations in multi-force scenarios
  • Investigate the effects of acute, obtuse, and orthogonal forces on net work
  • Learn about the mathematical representation of work in different coordinate systems
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in understanding the principles of work and energy in physical systems.

Bipolarity
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Suppose you have many forces acting on an object, and the object moves in space in some time interval. Each force has done some work on the object.
Suppose you took all these values for work, added them up, (they are all scalars). You'd obtain a scalar equal to the net work done on the object. Forces that are acute to the object's displacement at some instant tend to increase this net work, whereas forces obtuse tend to decrease this net work. Forces orthogonal to the displacement at an instant do not affect the net work done on the object.

On the other hand, suppose you took each force acting on the object and summed them all up vectorially, obtaining the net force on the object. You then treat this force as a single force, and find the work done by this one force. Would this work be the same as that obtained in the previous answer?

I've been thinking about this, and am pretty sure the answer is yes, but can anyone confirm this with a yes or a no? I don't want any explanations I'll figure those out myself.

Also, in the work-kinetic energy theorem, the change in KE of the object is equal to the net-work done on the system right? The same net work calculated above in two different ways, right?

Just need a confirmation. Thank you all.

BiP
 
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