A bug starts walking away from the top of a spherical ball of ice and will start to slip when the normal force exerted on it drops to 1/2 of its weight. If the ice ball has a diameter of 35 cm, how far can the bug walk before it begins to slip?

1 answer

the normal force is ... m * g * cos(Θ)

where Θ is the angle between
... the tangent to the sphere (ball), and the horizontal

the central angle at this point is ... 90º - Θ
... you can draw the diagram to see this

cos(Θ) = 1/2 ... Θ = 60º

so the bug can walk 2/3 of the way down the sphere (60º / 90º)

walking distance ... 2/3 * π * 35 cm / 4