Finding acceleration after cutting a string supporting a ball at angle

[Auburn2017]

Homework Statement

Refer to figure please.

Homework Equations

∑F_y=0 before string is cut

The Attempt at a Solution

I tried summing the two forces in the y direction before the strings were cut which would be the two tensions at a sin40° and minus the weight of the ball(mg). That gave me T in terms of mg. Then I summed the forces when the string was cut and got T minus mgcos40. Then I thought that would be my ratio but my answer didnt match that of the solution. Help Please!

 

[TSny]

Your approach seems good. Are you sure that you should be using cos40^o in the calculation after the string is cut? You left out the details of your calculations and you did not state what you actually got for the tension before and after one of the strings is cut.

 

[Auburn2017]

Your approach seems good. Are you sure that you should be using cos40^o in the calculation after the string is cut? You left out the details of your calculations and you did not state what you actually got for the tension before and after one of the strings is cut.

This is what I ended up doing. Does my work look right or did I just happen to get it right? Oh and there should be a mg on the end of my T=0.643 equation. I don't really know why I used mgsinΘ, I just know it gets you the right answer. An explanation on that would be greatly appreciated.

 

[TSny]

In your first diagram your analysis looks good. Here you are taking the y-axis to be vertically upward.

In your second diagram (one string), what direction are you taking for the y-axis? Also, you should show the gravitational force in this diagram.

 

[Auburn2017]

In your first diagram your analysis looks good. Here you are taking the y-axis to be vertically upward.

In your second diagram (one string), what direction are you taking for the y-axis? Also, you should show the gravitational force in this diagram.

Oh that is what it is. If you take the y-axis to be at an angle of 40 degrees then the y component of the weight becomes mg sin40. Makes sense now.

 

[TSny]

OK. Good work.