Ball on a string with initial velocity

[joe_coolish]

Homework Statement

A ball with mass m = 1.72 kg is attached to a peg at the origin using a length of massless string of L = 1.54 m. It is released from the top of a vertical circle with speed v0 = 4.81 m/s. What is the ball’s speed (m/s) when the string makes an angle θ = 21.7° above the positive X axis?

Homework Equations

Kf+Uf = Ki+Ui
K=0.5mv^2
U=mgy

The Attempt at a Solution

I started by using Kf+Uf = Ki+Ui => .5mVi^2 + lmg = .5mVf^2 + lsinθmg
and then I solved for Vf:

Vf=SQRT(Vi^2 + lg - lsinθg)

that came out to be 5.71, but the correct answer is 6.49. Any help would be wonderful!

 

[I like Serena]

I started by using Kf+Uf = Ki+Ui => .5mVi^2 + lmg = .5mVf^2 + lcosθmg

Hi joe_coolish, welcome to PF!

You've used the cosine, while you should have used the sine.

 

[joe_coolish]

Thank you for your reply and for the welcome!

I changed the formula to Vf=SQRT(Vi^2 + lg(1 - sinθ))
which gave me this: SQRT(4.81^2+(1.54*9.8)*(1-SIN(RADIANS(21.7)))) = 5.713832509

(I like to use EXCEL for these things)

Which was my original answer. Sorry, I must have copied it down wrong :) I'll edit my original post.

But still, that is the wrong answer... Am I missing something?

 

[I like Serena]

Thank you for your reply and for the welcome!

I changed the formula to Vf=SQRT(Vi^2 + lg(1 - sinθ))
which gave me this: SQRT(4.81^2+(1.54*9.8)*(1-SIN(RADIANS(21.7)))) = 5.713832509

(I like to use EXCEL for these things)

Which was my original answer. Sorry, I must have copied it down wrong :) I'll edit my original post.

But still, that is the wrong answer... Am I missing something?

In your original equation you have a factor 0.5.
In your final equation there should be a corresponding factor 2 somewhere...

(And yes, Excel is the perfect tool for things like this. )

 

[joe_coolish]

In your original equation you have a factor 0.5.
In your final equation there should be a corresponding factor 2 somewhere...

Ah! I need to lay off the late nighters...

Thank you!

SQRT(4.81^2+(2*1.54*9.8)*(1-(SIN(RADIANS(21.7))))) = 6.493047349


It's always that dang 2!

 

[I like Serena]

Ah! I need to lay off the late nighters...

Thank you!

SQRT(4.81^2+(2*1.54*9.8)*(1-(SIN(RADIANS(21.7))))) = 6.493047349

Yep!

It's always that dang 2!

Uhh, sometimes it's a dang minus sign! :)