How Fast Will the Mass Be Just Before It Hits the Ground?

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AI Thread Summary
The discussion revolves around calculating the speed of a 4.0 kg mass just before it hits the ground, connected to an 8.0 kg wheel via a massless string over a frictionless pulley. The problem involves applying the conservation of mechanical energy principle, considering the mass is released from a height of 2.0 m. The user expresses frustration in arriving at the correct answer and requests assistance from others in the forum. Despite the request for help, the user cannot provide their calculations due to their materials being inaccessible. The conversation highlights the challenges of applying theoretical concepts to practical problems in physics.
benp
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Here is the problem, I've been trying for a day but can't seem to come up with the right answer.

A 4.0 kg mass is connected by a massless string over a massless and frictionless pulley to the center of an 8.0 kg wheel. Assume that the wheel has a radius of .5 m and a moment of inertia of 2.0 kg*m^2. The mass is released from rest at a height of 2.0 m above the ground. What will its speed be just before it strikes the ground? (Hint: Apply conservation of mechanical energy.)

Well, any help would be appreciated. I've tried cons. of mech. energy, but I come up with a wrong answer.
 
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Hi benp,

Can you please post what you've done so far, so we can find where the mistake is?

Welcome to the forums.
 
I'd love to but the stuff's in my car (which my sister's using right now). Ugh...if you only knew how long I've been working on this. It's getting late here now (almost 2am) but if you could help any I would apprecaite it very much.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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