Nonuniform circular motion problem

[doctorjuice]

Homework Statement

0.5kg ball swings in a vertical circle at the end of a 1.5m long string. When the ball is at the bottom of the circle the tension in the string is 15 N. What is the speed of the ball at that point?

Homework Equations

a_c=T/m
a_c=v^2/r

The Attempt at a Solution

Using the equations above, I solved for centripetal acceleration by taking the Tension (which =15N) and dividing it by the mass (0.5kg). This gave me 30 m/s^2. I next took the other equation stated above, plugged in all the numbers and solved for v, which = 6.71m/s. The answer in the back of the book was around 5.5m/s, I think. Anyway, I got the problem wrong and I can't see what I did wrong.

Any help would be greatly appreciated, I'm doing this in preparation for a test and really need to understand these problems.

 

[haruspex]

you're forgetting gravity.

 

[doctorjuice]

you're forgetting gravity.

Gravity would affect tension, right? If they say the tension is 15N at the bottom, aren't they including gravity?

 

[haruspex]

Gravity would affect tension, right? If they say the tension is 15N at the bottom, aren't they including gravity?

Yes, they are but you aren't. Draw the free body diagram. What are the forces and what is the resultant (to drive the required acceleration)?