Undergrad What's the restoring force, if there's a mass on a string.

[axer]

Hello, I'm finding difficulties understanding the logic behind the multiple choice answers and the exams are near(finals!
What's the restoring force, if there's a mass on a string?

mg
m
m/g
– m
– mg

I know F=-kx and that F=weight and weight=mg. But i don't know which answer is the correct,

 

[scottdave]

The weight is the downward force on the mass (due to gravity). I assume this is a mass hanging vertically on a spring?
Can you identify all of the forces on the mass?
Which ones do not make sense? Think about the dimensions of each answer.
The sign (pos/neg) will depend on the convention chosen.

 

[axer]

The weight is the downward force on the mass. I assume this is a mass hanging vertically on a spring?
Can you identify all of the forces on the mass?
Which ones do not make sense? Think about the dimensions of each answer.
The sign (pos/neg) will depend on the convention chosen.

I would exclude
m
-m
m/g

Wait a second, if the restoring force is in the opposing direction of the weight. so the answer is -mg? ( - )indicates direction.right? :/

 

[scottdave]

I would exclude
m
-m
m/g

Wait a second, if the restoring force is in the opposing direction of the weight. so the answer is -mg? ( - )indicates direction.right? :/

That's the answer I would pick. Since g points down, the spring pulls in the opposite direction. The magnitude is equal to mg, if it is not accelerating.

The net sum of forces = mass x acceleration.

 

[sophiecentaur]

What's the restoring force

I don't think this is a good question. (Not for the first time) But you have to play their game.
The units of force means the required answer has to be + or - mg (dimensions must always be consistent)
The actual net restoring force is due to the displacement and weight and is mg-kx where x is the displacement from equilibrium position. The restoring force at equilibrium will be zero, if we're being picky and if we're aiming in the SHM direction.
If mg is the weight, the force from the spring will need to be -mg so I guess that's what they want.

 

[scottdave]

It always helps to draw a picture and label all of the forces acting on it.

You may enjoy this Insights article: https://www.physicsforums.com/insights/10-math-tips-save-time-avoid-mistakes/

Also, here is an article, which I recently wrote, about using units: https://www.physicsforums.com/insights/make-units-work/

 

[axer]

Thank you both! :)

 

[Dr.D]

The term "restoring force" indicates two things:
1) a force
2) a force that tends to push things back to an undisturbed state.
For a mass hanging on a string (assumed to be inextensible), I would say that there is no restoring force; there is no previous state to be restored and no force tending to do such an action.
For a mass on a spring (assume to be flexible), the restoring force is the force developed in the spring attempting to return to the system to the state where the spring is unstrained.