# Centripetal Acceleration Question

1. Feb 8, 2014

An object weighing 4 newtons swings on the end of a string as a simple pendulum. At the bottom the swing, the tension in the string is 6 newtons. What is the magnitude of the centripetal acceleration of the object at the bottom of the swing.

Centripetal Acc. = v^2/r Sum of forces = T+Ac=mg???

Attempt

-T-mg=Ac?
-6-4 = Ac
I don't know where to go from here.

2. Feb 8, 2014

### vela

Staff Emeritus
Newton's second law says
$$\sum \vec{F}_i = m\vec{a}.$$ The centripetal acceleration is not a force. It's an acceleration. It goes into the righthand side of F=ma. The tension and the weight go into the lefthand side. Try again and pay attention to the sign of T and mg when summing the forces.

3. Feb 8, 2014

So I set it up as Sum of forces = T-mg=Ac
6-4=Ac
2?

4. Feb 8, 2014

### vela

Staff Emeritus
Closer. The lefthand side is correct, but the righthand side isn't. You can't add up a bunch of forces and then set the result to something that isn't a force. $a_c$ is the centripetal acceleration; it's not a force. It's the $a$ in $ma$ on the righthand side.

5. Feb 8, 2014

so is it 2=mAc
so its 2 g ? the answer choices only come in a number times g

6. Feb 8, 2014

### vela

Staff Emeritus
Not quite. You need to figure out what the mass of the object is from its weight.