Sum of work = Work done by net force

In summary, when multiple forces act on an object in a given time interval, their individual scalar values of work can be summed to find the net work done on the object. Forces that are acute to the object's displacement tend to increase the net work, while obtuse forces tend to decrease it. On the other hand, summing the vectorial values of all the forces acting on the object will result in the net force, which can then be treated as a single force to find the work done. The answer obtained through this method will be the same as the net work calculated through summing the scalar values. This is also confirmed in the work-kinetic energy theorem, where the change in kinetic energy of an object is equal to the
  • #1
Bipolarity
776
2
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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  • #2
The answer is yes, you're correct (about everything).
 

1. What is the concept of "sum of work = Work done by net force"?

The concept of "sum of work = Work done by net force" is a fundamental principle in physics that states that the total work done on an object is equal to the work done by the net force acting on the object. This means that all the individual forces acting on an object are added together to determine the total work done.

2. How is the sum of work related to the net force?

The sum of work is directly related to the net force acting on an object. This means that the total work done on an object is determined by the net force, which is the vector sum of all the forces acting on the object.

3. Why is the concept of "sum of work = Work done by net force" important?

The concept of "sum of work = Work done by net force" is important because it allows us to understand the relationship between forces and the resulting work done on an object. It also helps us to calculate the total work done on an object in a given situation, which is essential in many practical applications of physics.

4. Can you give an example of how the concept of "sum of work = Work done by net force" is applied in real life?

One example of how this concept is applied in real life is in calculating the work done by a car's engine to accelerate the car. In this situation, the force of the engine is the net force acting on the car, and the resulting work done is equal to the sum of all the individual forces acting on the car, such as friction and air resistance.

5. How does the concept of "sum of work = Work done by net force" relate to the principle of conservation of energy?

The concept of "sum of work = Work done by net force" is closely related to the principle of conservation of energy. This is because the total work done on an object is equal to the change in its kinetic energy, and according to the principle of conservation of energy, energy cannot be created or destroyed, only transferred or converted. Therefore, the sum of work done by all forces must be equal to the change in kinetic energy, which is a manifestation of the principle of conservation of energy.

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