I=mv^2/w^2-2mgh/w^2Find Inertia of Wheel for Block & Pulley Homework

[eagles12]

Homework Statement

A block of mass m=2.4kg is attached to a string that is wrapped around the circumference of a wheel of radius r=7.6cm. The wheel rotates freely about it's axis and the string wraps around it's circumfrence without slipping. Initially, the wheel rotates with an angular speed ω, causing the block to rise with a linear speed v=.29m/s.
Find the moment of inertia of the wheel if the block rises to a height of h=7.7cm before momentarily coming to rest.

Homework Equations

Ei=Ef

The Attempt at a Solution

Ei=1/2mv^2+1/2Iw^2+mgy
Ei=1/2mv^2+1/2Iw^2+0
Ef=1/2mv^2+1/2Iw^2+mgy
Ef=0+0+mgh
mgh=1/2mv^2+1/2Iw^2

 

[eagles12]

I had found the equation
h=(v^2/2g)(1+I/mR^2)
and i got I=.2349
I had to use two significant digits in my answer and I used .23 but it is saying that I need to check the rounding or number of significant digits.

 

[gneill]

I had found the equation
h=(v^2/2g)(1+I/mR^2)
and i got I=.2349
I had to use two significant digits in my answer and I used .23 but it is saying that I need to check the rounding or number of significant digits.

What value did you use for g? You should use values for constants that have more digits of accuracy than the result requires.

 

[eagles12]

I used 9.8 would 9.81 be better? or should I go further than that?

 

[eagles12]

got it! thanks!

 

[gneill]

I used 9.8 would 9.81 be better? or should I go further than that?

g = 9.807 m/s² is usually good enough. I usually use g = 9.80665 m/s² in my calculations so I never have to worry about it

Round results, not intermediate values, so you don't lose accuracy through the calculation process.