Exam question about Conservative Forces

[nebbione]

Homework Statement

(This was a problem in an examination test of physics)

Problem:
point 1) Make an example of conservative force;
point 2) Write the vectorial expression
point 3) Choose a coordinate system and find the expression of the potential energy in a generic point in the space

Homework Equations

I know how to do the first two points but i can't understand what he's asking me in the third point, when he asks me about the "generic point in the space".
How should i Proceed? What is he asking me ?

The Attempt at a Solution

point 1) I made the example of "Costant force"
point 2) U=Fx
point 3) I got no idea what he's asking me. Can you help me please?

 

[Simon Bridge]

For point 1.
I suspect the idea is to come up with an example from nature.

for point 2.
This is not a vector expression as written.

for point 3.
You are supposed to know how to derive potential energy from a force ... but if your example comes from nature you will see what is needed quite quickly.

 

[voko]

The answer to point 3 you gave in point 2. Which means you did not answer point 2, and, depending on the attitude of the examiner, point 3, either.

 

[Simon Bridge]

@voko: assuming that Fx means "force times distance" and not "the x component of force" or "the force is in the x direction". Need more information.

 

[nebbione]

from nature ? for example ? i don't understand why it is not a good choice constant force ?
and what is wrong in point 2 ?

 

[nebbione]

with Fx i intended Force per distance

 

[voko]

Point 2 must be the vector of your force. What you have their is a scalar, and symbol U leaves an impression it is the potential of your force.

 

[nebbione]

Ok i understand so what i have to do ?
Sorry can you be a little bit more clear?Can you write at least what i should do? or a solution to point 2 ? i don't understand.

 

[voko]

Do you know what a vector is? How would you write one?

 

[nebbione]

I would write it like v= x*i+y*j+z*k

where i j and k are unit vector.
Sorry can you write and explain me a solution? because I'm confusing myself and on monday i have an exam.

 

[voko]

Point 2 of the problem requires that you write the force as a vector. You clearly did not. It should be Ai + Bj +Ck, where A, B, C are the components of force along the X, Y, Z axes. Can you do that for your constant force?

 

[Simon Bridge]

from nature ? for example ? i don't understand why it is not a good choice constant force ?
and what is wrong in point 2 ?

The "constant force" is not a good example because it does not have to be conservative.

A block pushed around a closed path (eg. a circle) in a conservative force-field, involves zero total work. If a constant force pushed a block around a circle then the total work is not zero.

To answer the question properly - look for a conservative force-field in nature ... you know what "nature" is surely? You have heard of "mother nature"? I mean, something that exists as a physical reality in the Universe outside our imaginations. The Real World.

There are four basic force fields in the Universe. Pick one.
I'll start you off:
Answer to Q1: Gravity close to the Earth's surface.
Q2. What is the force?
Q3. What is the potential?

 

[voko]

The "constant force" is not a good example because it does not have to be conservative.

I am not sure what you mean by "constant", but to me that means a vector that is constant in time and space. Such a force is conservative.

Answer to Q1: Gravity close to the Earth's surface.

Isn't it "constant"?

 

[Simon Bridge]

OK - It seems I have not been clear enough.

This is an exam question. The object is to anticipate the intent of the examiner and so collect as many of the assigned marks as possible.

Just writing down "a constant force" as the answer to question 1 is unlikely to satisfy the examiner for two reasons:
(a) it will not allow the examiner to make the distinction between the different common students' misunderstandings about force-fields - in this case: it is unclear that the student intends "constant" to refer to direction as well, and it is not clear that the force is intended to be a non-contact force.
(b) even giving the benefit of the doubt from (a) it is not an "example" but a general class of what may constitute a conservative force.

Admittedly the question could be more precisely worded ... however, from years of marking such exams the examiner almost always intends a more specific example here and will have instructed markers to mark-down answers like that given. Note: OP could also have chosen a gravitational field from a spherical mass... i.e. not a constant force. It just makes the math a bit trickier than needed to be sure of collecting all the marks.

Pedagogically - starting from a particular example aught to nicely clear-up OPs misunderstandings.

I had intended the reply to be complimentary to your more mathematical treatment ;)

 

[voko]

Thanks for the explanation - appreciate it.