A hollow, spherical shell with mass 2.00 kg rolls without slipping down a 38.0o slope.?

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A hollow, spherical shell with mass 2.00 kg rolls without slipping down a 38.0o slope. a) Find the acceleration, the friction force, andthe minimum coefficient of friction needed to prevent slipping. b) howwould your answers to part (a) change if the mass were doubled to4.00

Hermina Ferry · Accepted Answer

a)ma = (force due to gravity along slope) – (force due to friction)ma = mgsinθ – Ff [1]torque = (moment of inertia of sphere)(angular acceleration) = (force due to friction)(radius of sphere)Iα = (Ff)(r) [2]Since the sphere doesn’t slip, for [2]:(2mr^2/3)(a/r) = (Ff)(r)Ff = 2ma/3 [3]Substituting Ff into [1]:ma = mgsinθ – 2ma/3a = 3gsinθ / 5 [4]a = 3(9.81 m/s^2)(sin38°)/5 = 3.62 m/s^2Ff = 2(2.00 kg)(3.62 m/s^2)/3 = 4.83 NFf = μmgcosθ [5]4.83 N = μ(2.00 kg)(9.81 m/s^2)cos38°μ = 0.313b)From [4], acceleration doesn’t change when doubling the mass.From [3] and [4], the friction force doubles.From [5], [3], and [4]:2a/3 = μgcosθ2sinθ / 5 = μcosθμ = 2tanθ / 5 (doesn’t change since it’s independent of mass)

Hermina Ferry · Answer

Sphere Shell

Hermina Ferry · Answer

a(cm) ability acceleration on the middle of mass. to discover the Frictional tension, mg sin(forty) – Friction = ma Friction = mg sin(forty) – ma to discover the minimal coefficient of friction united kingdom, Friction = united kingdom * commonplace tension united kingdom = Friction / commonplace tension united kingdom = friction / mg cos (forty)

Hermina Ferry · Answer

Thanks!

Jakob Littel

A hollow, spherical shell with mass 2.00 kg rolls without slipping down a 38.0o slope.?

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