Could you please validate my answer?

[qwerty11]

Homework Statement

A uniform plank of length 6.00m and mass 30.0 kg rests horizontally across two horizontal bars of a scaffold. the bars are 4.50 m apart, and 1.50m of the plank hangs over one side of the scaffold. How far can a painter of mass 70.0kg walk on the overhanging part of the plank before it tips?

Homework Equations

w1*d-w2*d=0

The Attempt at a Solution

70g*d*Na*0-30g+((6.2)-1.5)+Nb*4.5=0
70g*d-30g+((6/2)-1.5)=0
d=(30g*(6/2)-1.5)=0
d=0.6428m

Is my answer correct and is meters the right unit d should be in?

 

[Andrew Mason]

Your explanation is incomprehensible to me. What are you attempting to do here?

AM

 

[qwerty11]

That is the distance the painter can walk on the overhang park of the plank before it tips.

 

[Andrew Mason]

That is the distance the painter can walk on the overhang park of the plank before it tips.

I understand what the question is asking. I am having difficulty understanding your work. Can you explain the steps you are taking and your reasoning? You have to find the moments about the support nearest the overhang. I don't understand how you get this:

70g*d*Na*0-30g+((6.2)-1.5)+Nb*4.5=0

For example, why do you multiply by 0 in the first term? Why are there 4 terms here and only two in your formula? Why do you subtract 30g? What is Na and Nb? What does 6.2 represent?

AM

 

[qwerty11]

70g should be 70kg which is the mass of the painter. Na is the weight of the plank (again should be kg instead). 6.2 should be 6/2 which is the length of the board on each side of the pivot. -1.5 is subtracting the non-overhang part out. 4.5 is the distance the bars are apart from each other.

 

[qwerty11]

Bump.

 

[qwerty11]

Bump.

 

[Redbelly98]

70g*d*Na*0-30g+((6.2)-1.5)+Nb*4.5=0

It is still difficult to make sense of this.

The torque due to the painter is (70 kg)*g*d that appears at the beginning of your expression. It makes no sense to multiply that by the weight Na of the plank or by zero, and you have done both.

(30 kg)*g is the weight of the plank. You are adding that to the moment arm of the plank's center-of-mass, "6/2 - 1.5", but you need to multiply them in order to get the torque due to the plank's weight.

Why does the plank's weight appear twice in the equation, as Na and as 30*g?

You never explained what Nb is.