Prove the average external force is Zero

In summary, the problem is to prove that the average external force of a system of particles, starting from rest and ending at rest, is zero. This can be shown through the use of Newton's laws, specifically the fact that the effect of an internal force on the motion of the system is zero. Therefore, the sum of the internal forces must be equal to the sum of the external forces, resulting in a net average external force of zero from rest to rest.
  • #1
Manolisjam
49
0
1.Problem statement
Prove the average external force of a system of particles N starting from rest and ending at rest is zero.

Homework Equations


If the system moves periodically prove the av. external force is zero in a period

The Attempt at a Solution


I don't quite understand what i am asked .Since i don't have a definition for a average force of a system of particles. Yet i tried to derive the eq for momentum of a system.So this is the momentum of the system i found. Now i know that going from rest to rest change of momentum must be zero . But i have internal and external forces. So don't know how to proceed
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  • #2
There is someething with internal forces you need to exploit here. has to do with one of the Newton laws...:
what is the effect of an internal force on the motion of the system ?
 
  • #3
BvU said:
There is someething with internal forces you need to exploit here. has to do with one of the Newton laws...:
what is the effect of an internal force on the motion of the system ?
Its zero the rest of the math is ok? SO the double sum is zero.
 
  • #4
Can't read the small writing. What I hinted at is action = - reaction so the internal forces can't influence the center of mass of the system
 

1. What does it mean to prove that the average external force is zero?

Proving that the average external force is zero means showing that the sum of all external forces acting on a system is equal to zero. This indicates that the system is in a state of equilibrium, with no net force acting on it.

2. Why is it important to prove that the average external force is zero?

Proving that the average external force is zero is important because it helps us understand and analyze the behavior of a system. If the average external force is not zero, it means that there is an unbalanced force acting on the system, which can cause it to accelerate or move in a certain direction. By proving that the average external force is zero, we can determine if a system is in equilibrium or not.

3. How is the average external force calculated?

The average external force is calculated by taking the sum of all external forces acting on a system and dividing it by the number of forces. This gives us the average value of the external forces acting on the system. If this value is zero, it means that the average external force is zero.

4. What are some techniques used to prove that the average external force is zero?

Some techniques used to prove that the average external force is zero include drawing a free body diagram, applying Newton's laws of motion, and using vector addition to determine the net force acting on the system. These techniques help us analyze the forces acting on a system and determine if the average external force is zero or not.

5. Can the average external force ever be negative?

Yes, the average external force can be negative if the net force acting on the system is in the opposite direction of the motion. This indicates that there is an unbalanced force acting on the system, causing it to decelerate or move in the opposite direction. However, the average external force can also be zero or positive, depending on the direction and magnitude of the net force acting on the system.

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