- #1

phantomvommand

- 265

- 39

- Homework Statement
- See picture below

- Relevant Equations
- Y = Stress / Strain

A solid ball of radius R, density ρ, and Young’s modulus Y rests on a hard table. Because of its weight, it deforms slightly, so that the area in contact with the table is a circle of radius r. Estimate r, assuming that it is much smaller than R.

I have no issues understanding the estimation of stress, but the estimation of strain greatly confuses me.

1. How did the author know that "at heights greater than r, the pressure will be smaller"? Isn't r a horizontal quantity? What does it have to do with heights?

2. "Since stress is proportional to strain, that means that the part of the ball that is significantly strained has height r." Again, how does this have anything to do with r, given that r is a horizontal quantity and that the strain is vertical (ish).

3. Even if assuming that the previous 2 claims are true, how was the equation ##\frac {\delta} {r} \sim \frac {r} {R}## obtained?

I have no issues understanding the estimation of stress, but the estimation of strain greatly confuses me.

1. How did the author know that "at heights greater than r, the pressure will be smaller"? Isn't r a horizontal quantity? What does it have to do with heights?

2. "Since stress is proportional to strain, that means that the part of the ball that is significantly strained has height r." Again, how does this have anything to do with r, given that r is a horizontal quantity and that the strain is vertical (ish).

3. Even if assuming that the previous 2 claims are true, how was the equation ##\frac {\delta} {r} \sim \frac {r} {R}## obtained?