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)?

 

[Nickie]

It looks like you have correctly solved for the centripetal acceleration, but there may have been a mistake in your calculation for the speed. To find the speed of the ball, we can use the equation v=sqrt(ac*r), where ac is the centripetal acceleration and r is the radius of the circle (in this case, 1.5m). Plugging in the values, we get v=sqrt(30*1.5)=6.12m/s. This may be slightly different from the answer in the back of the book due to rounding or significant figures, but it is close enough to show that your method was correct. Keep in mind that it is always a good idea to double check your calculations and make sure you are using the correct units. Good luck on your test!