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

[apathetic_operator]

Homework Statement

see image

Relevant Equations

potential energy

"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)?

 

[PeroK]

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?

 

[haruspex]

how about (a)?

Can you construct counterexamples to any of the options?

 

[Mister T]

"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.