2.3 Exercises from the Feynman Lectures on Physics

[new90]

Homework Statement

a body is acted upon by n forces and is in static equilibrium.Use the principle of virtual work t prove that
if n = 1 the magnitude of the force must be zero

Relevant Equations

no equation

i don't know what's the answer but I think that the force needs to be gravity because is going down to the floor

 

[DrClaude]

i don't know what's the answer but I think that the force needs to be gravity because is going down to the floor

What if the body is the middle of outer space?

 

[new90]

then there willl be work because there there will be a force pusing in some direction

 

[sysprog]

Please try to understand what Professor Feynman meant by the words 'static equilibrium'.

 

[new90]

i think it means that the body its not moving

 

[sysprog]

i think it means that the body its not moving

It means that any force acting on the body in any direction is counter-balanced by a force acting in an oppositional direction.

 

[kuruman]

Somewhere in your analysis you must use the principle of virtual work as the problem directs you to do. Write an expression in the case of a body at equilibrium when acted upon by $n$ forces and then see what happens when you set $n=1$.

 

[etotheipi]

Also remember that the principle of virtual work says the virtual work must be zero for any infinitesimal displacement. Because you could easily choose $d\vec{r}$ to be orthogonal to the resultant force!

 

[sysprog]

Also remember that the principle of virtual work says the virtual work must be zero for any infinitesimal displacement. Because you could easily choose $d\vec{r}$ to be orthogonal to the resultant force!

Well, equally true is that it must be non-zero for any non-zero force -- if it is infinitesimal it is still infinitesimally non-zero. Let's please not abuse zero while we are petting our pet inconsistencies . . .

 

[Adesh]

Are you able to do it just by condition implied by static equilibrium? I mean do you know that $\Sigma$ notation for statics?

 

[etotheipi]

Well, equally true is that it must be non-zero for any non-zero force -- if it is infinitesimal it is still infinitesimally non-zero. Let's please not abuse zero while we are petting our pet inconsistencies . . .

My apologies, I was being careless. I meant to say "for any virtual displacement".

 

[sysprog]

Are you able to do it just by condition implied by static equilibrium? I mean do you know that $\Sigma$ notation for statics?

In my view, the sigma notation, in this instance, refers to sum, I think that I don't quite fully understand your question . . .

 

[new90]

It means that any force acting on the body in any direction is counter-balanced by a force acting in an oppositional direction.
but there's its says only one force

 

[Adesh]

In my view, the sigma notation, in this instance, refers to sum, I think that I don't quite fully understand your question . . .

Does OP know this $\sum_{i=1}^{n} \vec{F_i} =0$ ?

 

[new90]

whos OP

 

[Adesh]

whos OP

OP : Original Poster.

 

[new90]

OK

 

[new90]

I DINT KNOW THANKS

 

[Adesh]

I DINT KNOW THANKS

Do you know for Static Equilibrium we should have $$ \sum_{i =1}^{n} \vec{F_i} =0 $$ ?

 

[new90]

i don't know what it means the n

 

[Adesh]

i don't know what it means the n

$$\sum_{i=1}^{n} \vec{F_i} = \vec{F_1}+ \vec{F_2} + \vec{F_3} +... + \vec{F_n} =0$$ Are things a little clearer now?

 

[new90]

yes thanks

 

[new90]

but in this case its just
Fi= 0

 

[Adesh]

but in this case its just
Fi= 0

If $n=1$ we have $$ \sum_{i=1}^{1} \vec{F_i} = F_1 = 0$$ How about now?

 

[new90]

yes its clear
thanks

 

[Adesh]

yes its clear
thanks

But you don’t have to do it like this
You have to do it by the Principle of virtual work.

 

[new90]

Principle of virtual work = the force x the virtual
displacement?

 

[new90]

thanks I answered with principle of virtual work

 

[sysprog]

$$\sum_{i=1}^{n} \vec{F_i} = \vec{F_1}+ \vec{F_2} + \vec{F_3} +\dots+ \vec{F_n} =0$$

I 'corrected' your $\LaTeX$ $-$ you had 4 dots instead of 3 $-$ your math was just fine $\dots$

 

[Adesh]

I 'corrected' your $\LaTeX$ $-$ you had 4 dots instead of 3 $-$ your math was just fine $\dots$

It seems that you have adjusted it’s height too!