Block and hoop sliding up a frictionless incline

[hold AP 2010]

Homework Statement

part a) A block of mass m slides up an incline with an initial speed v₀. The incline is on an angle,

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,

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?

 

[Andrew Mason]

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