Max Height of Rolling Hoop w/Radius 0.13m and Mass 8.1kg

AI Thread Summary
The discussion focuses on determining the maximum height reached by a thin hoop with a radius of 0.13 m and mass of 8.1 kg as it rolls up an incline at an angle of 33 degrees. The problem utilizes the principle of conservation of energy, equating the total kinetic energy (both rotational and linear) to the potential energy at the height reached on the incline. The moment of inertia for the hoop is considered as 1/2mr² when calculating the rotational kinetic energy. By simplifying the equations, the mass cancels out, allowing for a straightforward calculation of the height. The approach emphasizes the importance of energy conservation in solving rolling motion problems.
melissa_y
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thin hoop of radius r = 0.13 m and mass M = 8.1 kg rolls without slipping across a horizontal floor with a velocity v = 4.0 m/s. It then rolls up an incline with an angle of inclination theta = 33o. What is the maximum height h reached by the hoop before rolling back down the incline
 
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melissa_y said:
thin hoop of radius r = 0.13 m and mass M = 8.1 kg rolls without slipping across a horizontal floor with a velocity v = 4.0 m/s. It then rolls up an incline with an angle of inclination theta = 33o. What is the maximum height h reached by the hoop before rolling back down the incline

do it using conservation of energy...

rotational K.E + linear K.E= P.E( at the hight reached on the inclined plane)
take moment of inertia of a ring=1/2mr sqr abt the central axis while calculating rotational K.E.
u will straightaway get the ans by cancelling out M
 
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