How Do You Solve Equilibrium Problems Using Moments?

[TheePhysicsStudent]

Homework Statement

Hi, I have been doing some questions from the textbook and I got the 2 right answers, however for different forces

Relevant Equations

M = FD

Question:

My answer:

The books answer:

 

[Chestermiller]

(1.2)(0.4)=(SF2)(0.7)

 

[TheePhysicsStudent]

Wow, thanks sir! I realised I was highly overcomplicating things (as per usual)

 

[Herman Trivilino]

Wow, thanks sir! I realised I was highly overcomplicating things (as per usual)

No you weren't. You still need another equation to find $SF_1$. Your solution was actually very close. Your mistake was in the way you wrote your ratios. The ratio of the support distances is not proportional to those two lengths. It's inversely proportional. Think about two kids playing on a seesaw. The heavier kid needs to be closer to the pivot, not further away, to get the seesaw to balance.

Equivalently, you can balance the moments about the center of the metre rule.

 

[kuruman]

Wow, thanks sir! I realised I was highly overcomplicating things (as per usual)

Here are some thoughts so that you do not overcomplicate things next time you see something like this.

First, when you have an equilibrium situation, the sum of moments about any point will be zero. That's because the system doesn't know (and doesn't care) what point you choose as reference for the moments. It will not acquire angular acceleration about that point simply because you chose it.

Second, you have two unknowns, namely the two support forces $SF_1$ and $SF_2.$ This means that you need two equations to find them, i.e. you need to solve a system of two equations and two unknowns. The first equation is the sum of forces equal to zero and the second the sum of moments equal to zero. The procedure for tackling this is to solve one equation, say the force equation, for one unknown in terms of the other, e.g. $SF_2=1.2~(\text{N})-SF_1$, substitute that in the moments equation and solve for $SF_1$.

However, you can take a shortcut and choose as reference point for the moments the point at which one of the forces is applied. This gives you an equation with only one unknown moment which you can solve for the unknown force. That's exactly what @Chestermiller did in post #2 by choosing as reference the point where $SF_1$ is applied. Of course, the remaining force can be found by substituting in the sum of forces is zero equation.

To summarize, in static equilibrium problems the moment balance is simplified by choosing a reference point for moments where one (or more) forces act.

 

[TheePhysicsStudent]

No you weren't. You still need another equation to find $SF_1$. Your solution was actually very close. Your mistake was in the way you wrote your ratios. The ratio of the support distances is not proportional to those two lengths. It's inversely proportional. Think about two kids playing on a seesaw. The heavier kid needs to be closer to the pivot, not further away, to get the seesaw to balance.

Equivalently, you can balance the moments about the center of the metre rule.

Thanks Mister T, the see saw analogy really helped make it more clear for me where I went wrong, as it does ake more sense now

 

[TheePhysicsStudent]

Here are some thoughts so that you do not overcomplicate things next time you see something like this.

First, when you have an equilibrium situation, the sum of moments about any point will be zero. That's because the system doesn't know (and doesn't care) what point you choose as reference for the moments. It will not acquire angular acceleration about that point simply because you chose it.

Second, you have two unknowns, namely the two support forces $SF_1$ and $SF_2.$ This means that you need two equations to find them, i.e. you need to solve a system of two equations and two unknowns. The first equation is the sum of forces equal to zero and the second the sum of moments equal to zero. The procedure for tackling this is to solve one equation, say the force equation, for one unknown in terms of the other, e.g. $SF_2=1.2~(\text{N})-SF_1$, substitute that in the moments equation and solve for $SF_1$.

However, you can take a shortcut and choose as reference point for the moments the point at which one of the forces is applied. This gives you an equation with only one unknown moment which you can solve for the unknown force. That's exactly what @Chestermiller did in post #2 by choosing as reference the point where $SF_1$ is applied. Of course, the remaining force can be found by substituting in the sum of forces is zero equation.

To summarize, in static equilibrium problems the moment balance is simplified by choosing a reference point for moments where one (or more) forces act.

Thank Kuruman, for the shortcut method which explained it more than the other user (though i did sort of grasp it), I am gonna practise more questions with all of this in Mind, Thanks once again