Softball in vertical circle, find release velocity

[AHinkle]

Homework Statement

A softball pitcher rotates a 0.236 kg ball
around a vertical circular path of radius
0.633 m before releasing it. The pitcher exerts
a 30 N force directed parallel to the motion
of the ball around the complete circular path.
The speed of the ball at the top of the circle
is 12.8 m/s.
The acceleration of gravity is 9.8 m/s2 .
If the ball is released at the bottom of the
circle, what is its speed upon release?
Answer in units of m/s.

Homework Equations

K = 1/2mv²
K_i+U_i=K_f+U_f ?Maybe

The Attempt at a Solution

I believe this is flawed but here's what I tried to do...

r = 0.633meters

K_f = (1/2)mv_f²
K_i = (1/2)mv_i²
U_f = mgh where h=0 (I set the reference point at the bottom of the circle i.e.
h_bottom=0) I believe this is okay because it's only the change in potential energy we're after
U_i=mg(2r) (i used to 2r because if the bottom is 0 then the diameter (2r) is the height above 0)

(1/2)mv_f²=(1/2)mv_i²+2mgr
(I did not include U_f because h is 0 at the bottom so the whole quantity goes to zero)

mv_f² = 2((1/2)mv_i² + 2mgr)
mv_f² = mv_i²+4mgr
m(v_f²) = m(v_i²+4gr)
(the masses cancel)

v_f² = v_i²+4gr

v_f=(v_i²+4gr)^1/2

v_f=((12.8)²+4(9.8)(0.633))^1/2

v_f=13.7351 m/s

This was needless to say, not the correct answer.
Reasons why I think I failed:
1) They gave a force in the question. The model I used was for an isolated system (i.e. no influence from outside agents) is the 30N force from an outside agent? or is the pitcher's hand part of the system?
2) Maybe the work-kinetic energy theorem doesn't work in a circle? I am good with things in a straight line. Circles throw me.

Please help, thanks

 

[Redbelly98]

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.
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Homework Equations

K = 1/2mv²
K_i+U_i=K_f+U_f ?Maybe
.
.
.
v_f=13.7351 m/s

This was needless to say, not the correct answer.
Reasons why I think I failed:
1) They gave a force in the question. The model I used was for an isolated system (i.e. no influence from outside agents) is the 30N force from an outside agent? or is the pitcher's hand part of the system?
2) Maybe the work-kinetic energy theorem doesn't work in a circle? I am good with things in a straight line. Circles throw me.

Please help, thanks

Your intuition is correct about why the approach you used didn't work out. The 30N force comes into play here.

The 30 N force is doing work on the ball, so that will add to the ball's energy. So instead of the ball's energy being conserved, we have

E_f = E_i + [work done on ball by 30 N force]​

If you can figure out the "work done..." part of the equation, it should work out. E is K+U, of course.