Ball rolling onto an inclined plane: energy and velocity

[dimitri24]

lets say that:
a ball rolls on flat surface at a constant velocity towards an inclined plane

how would u answer the following, this is very confusing for me. i don't have the exact values =/

a)calculate KEtotal before it gets to the plane
b)calculate linear velocity when it makes it up to the top of the inclined plane
c)find out how far it falls after it leaves the inclined plane
d)and if the inclined plane were frictionless, would the ball's speed at the top of the incline be greater than, equal to, or less than the speed you already calculated

this is the best i can remember off the top of my head. any help is appreciated, thx

 

[dextercioby]

Okay.Rolling without slipping surely makes life easier,metaphorically speaking.

U have a rigid body which undergoes both rotation & translation movement.What's the total KE...?

Daniel.

P.S.The problem doesn't say it explicitely,but u know the initial velocity & and the mass & the radius of the ball.

 

[dimitri24]

(1/2)(Icm)(w^2) + (1/2)(M)(Vcm^2) ?

 

[dextercioby]

Perfect.For point b),u need to apply the total mechanical energy conservation law.

Daniel.

 

[dimitri24]

im not familiar with that, is it easy to explain? thanks

 

[dextercioby]

Well,in the absence of any external forces,the total energy of the system formed by Earth & sphere is conserved (a theorem following from Newton's axioms).

Assuming the Earth to have an $\infty$ mass,this law can be written for the sphere only.

Intially u have KE and 0 PE,atop the ramp u have $\neq 0$ KE & PE.U know that the sum of both is the same,both at the botton of the ramp & atop.

Daniel.

 

[dimitri24]

but how do u account friction into the equation when the ball is going up the incline. how would i attack part b?

 

[dextercioby]

Well,energy is conserved in part b).So solve part b) and then worry about the friction on the incline.

Daniel.

 

[Doc Al]

but how do u account friction into the equation when the ball is going up the incline. how would i attack part b?

Since the ball is assumed to roll up the incline without slipping, no energy is wasted doing work against friction. (It's static friction.) So, as Daniel says, mechanical energy is conserved.

Hint: What's the relationship between $\omega$ and the translational speed v when the ball "rolls without slipping"?