Calculating Chair Stability: Solving the Angle of a Rocking Chair Tipping Over

[jobsism]

I found a pretty interesting question on the net. Can anyone please attempt at answering it? This is NOT a Homework question. I haven't reached this portion in my school, but I'm pretty interested in solving it.

A German childrens' book, "Der Struwwelpeter" show as humor various misbehavior of children. (And of course the bad outcomes of this behavior). This story is about a child who rocked back and forward on his chair while sitting at the table.

Now, assuming the thin legs of the chair are in the form of a square each side of which is 40 cm and the thick padded chair seat is 50 cm from the floor, at what angle form the vertical will the chair fall over backwards?

The mass of the chair is 12 Kg, and the mass of the child is 30 Kilograms. When the child is sitting down, his center of mass is 18 cm from the seat of the chair.

 

[rock.freak667]

If there is a resultant moment, the child will tip, you just need to find the minimum moment needed.

 

[Danger]

The kid weighs 30 kg (more than half of my body weight) and is still rocking about in his chair? Shouldn't he be trying for his driver's license instead?

 

[Sarah Brown]

I found a pretty interesting question on the net. Can anyone please attempt at answering it? This is NOT a Homework question. I haven't reached this portion in my school, but I'm pretty interested in solving it.

A German childrens' book, "Der Struwwelpeter" show as humor various misbehavior of children. (And of course the bad outcomes of this behavior). This story is about a child who rocked back and forward on his chair while sitting at the table.

Now, assuming the thin legs of the chair are in the form of a square each side of which is 40 cm and the thick padded chair seat is 50 cm from the floor, at what angle form the vertical will the chair fall over backwards?

The mass of the chair is 12 Kg, and the mass of the child is 30 Kilograms. When the child is sitting down, his center of mass is 18 cm from the seat of the chair.

Can anyone post steps how to figure this out? I know there are some assumptions to be made like center of mass at the belly button.

Please help if you can!

 

[JDługosz]

Start by drawing a sketch.

Personally I'm more worried about shearing the chair apart than falling over. If I tip back, I think the back and arms will pull out of their joints. (I'm four times the mass of that child.)