## Task 2 - 010922

a) A hemp rope with a diameter of $15 \mathrm{~mm}$ can withstand a load of $175 \mathrm{kp}$ without breaking.

What length of the rope corresponds to this load, i.e., when does the rope break under its own weight, if a rope of $1 \mathrm{~m}$ length weighs $1 \mathrm{p}$ per $\mathrm{mm}^{2}$ cross-sectional area?

b) A Dederon rope of the same cross-sectional area can withstand a much greater load, namely 400 $\mathrm{kp}$.

What length of the rope corresponds to this load, if a rope of $1 \mathrm{~m}$ length weighs $0.8 \mathrm{p}$ per $\mathrm{mm}^{2}$ cross-sectional area?
a) The hemp rope has a cross-sectional area of $A=\frac{\pi}{4} d^{2}=176.7 \mathrm{~mm}^{2}$, so it weighs $176.7 \mathrm{p}$ per meter. Therefore, it can be at most

$$
l_{\max }=\frac{175000 p}{176.7 \frac{p}{m}}=990.3 m
$$

long without tearing under its own weight.

b) For the maximum length of the Dederon rope, on the other hand: $l_{\text {max }}=2829.4 \mathrm{~m}$.