# Really need help with lab derivation -- Rolling objects down an incline

1. Nov 11, 2015

### Dusty912

1. The problem statement, all variables and given/known data
So I attached the page from the lab with the directions for the derivation. It may be easier to view that document. The lab was set up was taking two objects and rolling them down an incline. The time was measured using photo gates. Basically, I need to use conservation of energy and the equation of average velocity with constant acceleration to derive t(theoretical)=sqrt((2(1+c)d)/(gsin(theta)))
I= moment of inertia
w=omega
k=kinetic energy
U=potential energy
m=mass
g=acceleration due to gravity
d=x=distance
v=velocity
i=initial
f=final
t=translation
r=rotation
2. Relevant equations
conservation of energy: (delta)k(translation)+(delta)k(rotational)+(delta)U(gravitational)=0
average velocity=((delta)x)/((delta)t)=(V(initial)+V(final))/2
moment of inertia(sphere)=CMR^2

3. The attempt at a solution
So Heres my attempt for the sphere, pretty lost for the hollow cylinder, I'm guessing I just replace the moment of inertia in the work energy theory?

and sorry ahead of time could not find the subscript symbol so the (i) (t) (g) (f) and (r) should be sub scripted

(delta)k(translation)+(delta)k(rotational)+(delta)U(gravitational)=0
k(i)(r)+k(i)(t) +U(g)(i)=k(f)(r) + k(f)(t) +U(g)(f)
0 +0 +m*g*y=(1/2)*m*v^2(f) + (1/2)I*w^2 +0
sin(theta)D*g=(v^2(f))/2 + (1/2)*c*m*R^2(f)*(v(f)/R)^2

sqrt((2sin(theta)*D*g)/(1+c))=v(f)

then I know I'm supposed to plug this into the average velocity equation but it just yields nonsense. So would appreciate any help. This is my first post on here so let me know if I formatted anything wrong. And also what should I do for the hollow cylinder? do I just replace the the moment of inertia in the conservation of energy with the hollow cylinder's one? and wouldn't that yield a different t(theoretical). Thanks to anyone willing to help.

#### Attached Files:

• ###### Moment_of_Inertia_KMC-page-002.jpg
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2. Nov 11, 2015