Find the magnitude of the frictional force acting on the spherical shell. x.i5 s

Question

Find the magnitude of the frictional force acting on the spherical shell.
x.i5 spherical shell with mass 2.20 kg rolls without slipping down a slope that makes an angle of40.0^circ with the horizontal. Find the magnitude of the acceleration a cm of the center of mass of the spherical shell. A cm =3.78 { m/s^{2}} Find the magnitude of the frictional force acting on the spherical shell. Take the free-fall acceleration to be g = 9.80 m/s^2. f =5.54 {N} Find the minimum coefficient of friction mu needed to prevent the spherical shell from slipping as it rolls down the slope. fx.i5[x.i5(x.i5

Explanation / Answer

M g R sin = (2/3 + 1) M R2       a = R = 3 g sin / 5 = 3.78 (taking torque about point of contact) F = M g cos = I / R   where Iis moment of inertia about center of mass M g cos =2/3 M R2 /R  = 2/3 M R = 2/3 M a = 2 a / (3 g cos 40) = .34     Or F = M g sin - M g cos = Ma        acceleration of centerof mass = (g sin - a) / g cos = .34

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