Another conservation of energy problem(I think)

[qball1982]

So I have another problem that I'm having some issues with.

Homework Statement

A ball attached to a massless rope is allowed to swing around a circle of radius r=0.8m. When the ball reaches point B, the horizontal rope hits the peg P causing the ball to swing around a smaller circle.

A.)If the ball is started at A with a speed of 6m/s, at what position x should the peg P be placed to allow the ball to just make it past the point C. Hint: Rope tension at C will be zero, the rope remains straight at point C, and ignore air resistance.

B.) If there were air resistance, how much work would be required for it to stop the ball at point B? Assume m=2.2kg.

Homework Equations

A. 1/2mv₁²+mgy₁=1/2mv₂²+mgy₂
a_rad=v²/r
v_min²=rg or r=v_min²/g
B.W_total= K₂-K₁

The Attempt at a Solution

So I calculated the value of v at point B by using:
1/2mv₁²+mgy₁=1/2mv₂
v=4.508m/s

But I don't know how to get from point B to C.

B.) I used W_total=K₂-K₁
W_total=-39.6
air resistance=-39.6-(-9.8*0.8)=-31.76 J
Is that a correct way to work part B?

 

[Nugatory]

You gave yourself a big hint when you picked a title for this thread. Without air restance, the energy (kinetic plus potential) will be the same at points A, B, and C. Think about what the kinetic and potential energy is at each of three points.

But you might also think about conservation of angular momentum here...

 

[qball1982]

I guess I'm having issues with trying to calculate the potential energy at point c since I won't have the value of y or v. The only thing I can think of is using the conservation of momentum which then I can say that the mass going from point b to c would yield v₁=v₂. Is it correct to assume that?