Explanations & Calculations
- Refer to the sketch attached
- Consider a situation when the person is at an arbitrary point on the dome as shown & write equations for his equilibrium.
- The contact force on him at that point from the dome
R=mgcosθ
- The person can safely descend some distance down until the component of his weight becomes equal to the maximum static friction available at that point.
fs.maxμRμ⋅mgcosθtanθθ≥mgsinθ≥mgsinθ≥mgsinθ≤μ≤tan−1(0.6)≤30.960
- As mentioned above he can safely come down up to a maximum angle of 30.96 degrees from the verticle
- Then
θmax=30.960=0.540rad
- The distance he can come down is (distance measured from the top of the dome)
S=rθ=10m×0.540=5.4m
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