Will the Sphere Reach Point C on Its Path?

[Questions999]

The sphere with the mass 1 kg is released from point A without initial speed and moves without friction just like in the figure.
a) Find the mechanic energy in point A
Solution : E=mgh because v=0
b) Find the kinetic energy in B
Using the law of the conservation of mechanic energy, mghA=mghB+Ekb
C) WILL THE SPHERE REACH THE POINT C?

To reach the C point, Emb=Emc
so mghB+ Ekb=mghC+ Ekc
here i find the V of C.BY proving that the ball has a speed in C ,do I prove it reaches the point?

http://s1171.photobucket.com/albums/r549/Elaia06/?action=view&current=untitled.jpg

 

[Doc Al]

a) Find the mechanic energy in point A
Solution : E=mgh because v=0
b) Find the kinetic energy in B
Using the law of the conservation of mechanic energy, mghA=mghB+Ekb

OK.

C) WILL THE SPHERE REACH THE POINT C?

To reach the C point, Emb=Emc
so mghB+ Ekb=mghC+ Ekc
here i find the V of C.BY proving that the ball has a speed in C ,do I prove it reaches the point?

Try it and see. Even easier is to compare the energy at A with the energy at C.

 

[Questions999]

is it correct the c question?

 

[Doc Al]

is it correct the c question?

The basic approach is correct. Compare the energy at A with the energy at C. What would the velocity of the sphere be at that point? Is it possible?

 

[Questions999]

The energy at A is 25 J.The energy at C is 35.Velocity at a is zero.Velocity at C is sqrt10.Seems possible.

 

[Doc Al]

The energy at A is 25 J.The energy at C is 35.

Better check those numbers, especially the second. I presume you mean that to be the gravitational PE at C.

Velocity at a is zero.Velocity at C is sqrt10.Seems possible.

Really? Even though you found that just the PE alone is greater at C than the entire energy at A? How did you solve for the velocity at C. Show the equation.

 

[Questions999]

The law of the conservation of the mechanical energy For points B and C

mghB+ Ekb=mghC+ Ekc
1*10*1.5+10=1*10*3+1*V^2/2
so here V=sqrt10
what does the energy at A have to do with the energy at C? I mean, I found that it has a speed at C,isnt that enough?

 

[Doc Al]

The law of the conservation of the mechanical energy For points B and C

mghB+ Ekb=mghC+ Ekc
1*10*1.5+10=1*10*3+1*V^2/2

Let's do the math:
15 + 10 = 30 + KE
25 = 30 + KE
so... KE = -5 Oops! Can KE be negative?

so here V=sqrt10
what does the energy at A have to do with the energy at C?

Energy is conserved, so it's the same at A, B, and C.

 

[Questions999]

Sorry, u are right :) So there is no kinetic energy at point C,which means that there is no velocity,so the ball can't reach that point.right now?
What if the velocity would be let's say 5 m/s,would the ball reach the C then?

 

[Doc Al]

Right. The sphere cannot roll to a point higher than where it started.