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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 dr...Asked by Sara
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?
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Answered by
R_scott
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
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
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