# Answer to Question #21248 in Mechanics | Relativity for Mohamed

Question #21248

how long does it take for the hoop to roll down without sliding from the inclined plane of length 2 m and height 10 cm ?

Expert's answer

L= 2 m - length and h=0.1 m - height.

Angle betweendirection of acceleration of gravitation -g and direction of motion of hoop is

alpha.

Find projection of g - a=g*cos(alpha), cos(alpha) equal h/L.cos meanscosine.

L=a*t^2/2, t- time of motion.

Find t. t=sqrt((2*L)/a)=sqrt((2*L)/(g*h/L)=sqrt((2*L^2)/(g*h))=2.857seconds.g=9.8 m/s^2

Angle betweendirection of acceleration of gravitation -g and direction of motion of hoop is

alpha.

Find projection of g - a=g*cos(alpha), cos(alpha) equal h/L.cos meanscosine.

L=a*t^2/2, t- time of motion.

Find t. t=sqrt((2*L)/a)=sqrt((2*L)/(g*h/L)=sqrt((2*L^2)/(g*h))=2.857seconds.g=9.8 m/s^2

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