15_5_24 - a φ θ is d F = km σ dS a 2 cos φ = km σ sin...

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24. By symmetry, the force of attraction of the hemisphere shown in the figure on the mass m at the origin is vertical. The vertical component of the force exerted by area element dS = a 2 sin φ d φ d θ at the position with spherical coordinates
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Unformatted text preview: ( a , φ, θ) is d F = km σ dS a 2 cos φ = km σ sin φ cos φ d φ d θ. Thus, the total force on m is F = km σ Z 2 π d θ Z π/ 2 sin φ cos φ d φ = π km σ units. x y z φ d S a a a m Fig. 5-24...
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