Recent content by ymnoklan

Thank you for your help!

That was very helpful - thank you!

Okay, I think I get it now. Thank you so much for all of your help. I have a similar problem: A rod with mass MMM is supported by two supports, one at each end of the rod. Each support exerts a force of Mg/2 on the rod, keeping it at rest. Now, we introduce a third support somewhere between the...

I'm confused. Doesn't the sum of forces HAVE to be zero if the box is at rest? Good point. Thank you for pointing this out. The solid is rigid compared to the liquid? While water flows and is easily deformed (because the molecules are not held in fixed positions), the solid is made up of...

Newton’s first law says that the sum of the forces must be zero (as it is at rest). Newton’s second law says that the acceleration must be zero (as it is not accelerating) and Newton’s third law says that the opposite reaction to the block’s weight (the normal force from the floor to the block)...

I don’t think I get what you mean. Could you give me a hint? I mean if the sum of the forces weren’t zero, the system would accelerate, which is NOT what we want here

Because it balances the weight - the sum of forces is zero?

Okay, if I solve for N then? This gives me N = (d_2 - d_1)/d_2 which must be greater than zero (because the normal force cannot be negative/downward). This gives the condition d_2>d_1.

I thought showing that the sum of forces and the sum of rotational momentum both equal zero would indicate that the system is stable. Is this wrong? What else is required?

Do you mean by perturbation analysis?

Thank you for the figure! This is what actually got me to get an intuition of the situation, but yes, I would prefer to solve it mathematically

Thank you! Those figures were incredibly helpful. What do you think if this solution then? (I know it is probably possible to simplify the mathematical condition further, however I am not sure how?)

Hm, I thought had chosen the bottom cylinder as my pivot point in configuration C already. In D, I did chose the top cylinder as pivot point indeed, but when I try to switch it, the math doesn’t look any simpler. Instead I get a situation where I can’t tell whether d1 or d2 is larger (or equal...

Here is my attempt at the math

Thank you for the hint! Well, D is obviously a more likely candidate to work as the top cylinder changes the center of mass of the system towards the left. I really struggle with the math though.