What does a force of zero indicate about the total force acting on a particle?

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SUMMARY

The discussion centers on the implications of a zero total force acting on a particle, specifically in relation to potential energy. It is established that if the total force is zero, then the external force must also be zero, leading to the conclusion that the force component, Fx, equals zero. The equation Fx = d(U(x))/dx is critical in understanding this relationship, particularly in determining the outcomes for parts (a) and (b) of the homework statement regarding potential energy.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with potential energy concepts
  • Knowledge of calculus, specifically differentiation
  • Basic grasp of force vectors and their components
NEXT STEPS
  • Study the relationship between force and potential energy using the equation Fx = d(U(x))/dx
  • Explore examples of systems where the total force is zero
  • Investigate the implications of external forces on particle motion
  • Review counterexamples to the assumptions made in force analysis
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators and anyone involved in teaching or learning about forces and potential energy in particle systems.

apathetic_operator
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Homework Statement
see image
Relevant Equations
potential energy
Capture1.PNG

"The force is zero" means the total force act on the particle is zero? Then there must be an external force. If not, then Fx=0 ?
since Fx = d(U(x))/dx, the answer of (b) should be (i), but how about (a)?
 
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apathetic_operator said:
Homework Statement:: see image
Relevant Equations:: potential energy

View attachment 263194
"The force is zero" means the total force act on the particle is zero? Then there must be an external force. If not, then Fx=0 ?
since Fx = d(U(x))/dx, the answer of (b) should be (i), but how about (a)?
Yes for part b). For part a):

If ##U(x) = 0##, what does that tell you?
 
apathetic_operator said:
how about (a)?
Can you construct counterexamples to any of the options?
 
apathetic_operator said:
"The force is zero" means the total force act on the particle is zero?

It means the value of ##F_x## is zero.

since Fx = d(U(x))/dx,

... you should be able to answer the question you asked.
 

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