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A sphere or mass, m and radius r rolls along a horizontal surface with a constant velocity, Vi approaches an incline with (angle theta). ie bottom angle If it rolls without slipping,

a) what is the maximum distance,x it will travel on the incline?

b) If it begins to roll back down, find the time it takes to get to horizontal surface.

c)What will be its final velocity. ie. at time it gets to horizontal surface.

My solution:

I want to write energy equations and use conservation of energy to solve it.

K.E. = 1/2M(Vi^2) + 1/2I(w^2) where I = 2/5 r^2

P.E = mgh(max) - kNx where k is coeficient of friction and N is normal force

using trig, h(max) = xsin(theta) so x = h(max)/sin(theta)

so

P.E = mgh (max) - [kNh(max)] /sin(theta) ; N = mgcos(theta)

P.E = mgh(max) - [kmgcos(theta)h(max)]/ sin(theta)

h(max) is the vertical distance travelled ie. less than h and

x is distance travelled on incline i.e less than d

Are my equations right? and if so,the way to go now is to substitute w= v/r, set K.E = P.E and solve for x?

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# Homework Help: Sphere rolling up an incline then back down

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