Moments of Inertia Homework: Find Max Height H

AI Thread Summary
In the discussion about calculating the maximum height H that a block and a thin hoop reach on a frictionless incline, the key point is that both objects are analyzed using energy conservation principles. For part a, the block's maximum height is derived as H = (1/2)(v0^2/g) based on its initial kinetic energy converting to potential energy. In part b, participants note that the hoop's moment of inertia does not affect the height reached since it slides without rolling, leading to the conclusion that it should yield the same height as the block. The consensus is that the center of mass is the relevant factor for determining height, not the moment of inertia. Thus, both objects achieve the same maximum height on the incline.
hold AP 2010
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Homework Statement


part a) A block of mass m slides up an incline with an initial speed v0. The incline is on an angle,
Code: 
θ
, and block stops sliding at height H.
-If the incline is frictionless, determine the max height H to which the block will rise, in terms of given quantities and appropriate constants.

part b) A thin hoop of mass m and radius R slides up an incline with an initial speed v0. The incline is on an angle,
Code: 
θ
, and block stops sliding at height H.
-If the incline is frictionless, determine the max height H to which the hoop will rise, in terms of H and the given quantities.


Homework Equations



thin hoop I = MR2

The Attempt at a Solution



part a)

mgH = 1/2 mv02
therefore, H = (1/2)(v02/g)

& wouldn't part b be the same answer? or am I missing something mathematically?
 
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hold AP 2010 said:
wouldn't part b be the same answer? or am I missing something mathematically?
I agree, it should be the same. It has nothing to do with the moment of inertia of the hoop if the hoop is sliding. The centre of mass is what you have to measure the height from.

AM
 

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