- For the solid sphere of raduis R and mass M in the figure calculate the tranla

Question

- For the solid sphere of raduis R and mass M in the figure calculate the tranlational speed of the center of mass and the magnitude of the translational acceleration of the center of mass at the bottom of the incline of height h = 1.8m and angle = 31 degree. The sphererolls without slipping, and has moment of interia I = (2/5)*M*R^2

a) Using conservation of the total energry evaluate the speed Vcm of the center of mass of the sphere

b) How is the vertical displacement of the sphere h rlated to the distance x the sphere moves along the incline? use this expression in the answer of part (a) to get V(X)^2cm

Thank you all

Explanation / Answer

from mgh =0.5mn^2+0.5Iw^2
mgh =0.5mv^2 +0.5(2/5)*mr^2*w^2
gh =0.5(v^2+(2/5)v^2)
10gh = 7v^2
v =sqrt(10gh/7)=5.01 m/s
b)
sin31 =h/x
x =h/sin31 =3.5 m
from the relATION
v^2-u^2=2as
a = v^2/2x = 3.6 m/s^2

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