Physics Torque Equilbrium Question

[singh101]

Homework Statement

I can't seem to figure out this question. I would greatly appreciate any help. I have attached a photo of the question. Thank you!

Relevant Equations

Torque=Ia
Torque= radius x Force

 

[Delta2]

Carefully write the "sum of torques equals zero equation " for this problem. Don't forget to include the torque from the normal reaction from the part of ground that supports the plank and the two torques from the weight of the plank of its two different parts (one will be positive and the other negative).

Which Torque becomes zero (except from the total torque) when the plank is about to start tip over?

 

[singh101]

sorry I am a little confused is their anyway you can show this on a piece of paper?

 

[Delta2]

I am not going to solve the problem for you, you got to show some effort. You got to write a post with some equations that you think are the solution to the problem and then we can talk further.

 

[singh101]

the problem is I don't know what to write for the R for the torque acting on the left side of the beam. I know the Force will be MxG which is 40 x 10= 400 so that lead me to write 400(r)-500(r)=0 The answer we are trying to find is the r which relates to the 50. But I am confused on what the r should be for the 40.

 

[Delta2]

Ok that's a start.

The -500r term is correct and is the torque from the weight of the kid.
The 400r term is not correct for multiple reasons.
Don't you think that first we should "break" the torque from the weight of the plank into two terms one positive and one negative?

 

[singh101]

Attached below is the answer key. I understand how to set up the equation and solve the question. But the part which confused me is the 1.5 which is right next to Mg. My question is why is the 1.5 length used rather than the entire length of 4.5 on the left side. I seem to get stuck on that portion of the question.

 

[Delta2]

OK I see the answer key solves it in a slightly different way than what I had in mind but it is correct.

What is the center of mass (or center of gravity) of the plank?

 

[singh101]

I am think its the orange spot on beam right next the child.

 

[Delta2]

The picture doesnt show so clearly here, so i cant see any orange spot.

But for a moment lets say you have a plank of homogeneous mass density of length 6m. At which distance along the plank is located the center of mass?

 

[singh101]

3 m?

 

[Delta2]

Correct. Now you should know that the torque of weight acts like the weight is totally concentrated on the center of mass of the plank . I mean its like the plank is weightless and you have another kid with weight 40kg sitting at the center of mass of the plank.

That is a theorem in classical mechanics about the torque of the weight of a continuous mass distribution under constant gravitational acceleration.