A sphere of mass 20 kg is suspended by a metal wir

Question

A sphere of mass 20 kg is suspended by a metal wire of unstretched length 4 m and diameter 1 mm. When in equilibrium, there is a clear gap of 2 mm between the sphere and the floor. The sphere is gently pushed aside so that the wire makes an angle θ with the vertical and is released. Find the maximum value of θ so that the sphere does not rub the floor. Young modulus of the metal of the wire is 2.0 × 1011 N m-2. Make appropriate approximations.

Aditi Chauhan · Accepted Answer

Sol. . At equilibrium ⇒ T = mgWhen it moves to an angle θ, and released, the tension the T’ at lowest point is⇒ T’ = mg + mv2/rThe change in tension is due to centrifugal force∆T = mv2/r ….(1)⇒ Again, by work energy principle,⇒ 1/2mv2 – 0 = mgr(1 - cosθ)⇒ v2 = 2gr (1- cosθ)So, ∆T = m[2gr(1 – cos θ)]/r = 2mg(1 – cos θ)⇒ F = ∆T⇒ F = YA ∆L/L = 2mg – 2mg cos θ ⇒ 2mg cos θ = 2mg - YA ∆L/L=cos θ = 1 - YA ∆L/L(2mg)

Mechanics> A sphere of mass 20 kg is suspended by a ...

Shane Macguire , 10 Years ago

Aditi Chauhan

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Mechanics> A sphere of mass 20 kg is suspended by a ...

Shane Macguire , 10 Years ago

Aditi Chauhan

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