# Acceleration of a Bucket and Tension Forces

1. Feb 9, 2012

### PeachBanana

1. The problem statement, all variables and given/known data

A 14.0 bucket is lowered vertically by a rope in which there is 169 of tension at a given instant.

What is the acceleration of the bucket?

Is it up or down?

2. Relevant equations

F = ma

3. The attempt at a solution

F / m = a

(169 N) / (14 kg ) = 9.81 m/s^2 - x

12.07 m / s ^2 - 9.81 m/s^2 = - x

2.3 m/s^2 = - x
-2.3 m/s^2 = x

I initially thought the acceleration of the bucket was down because of what I got for "x" but that is incorrect. Is the acceleration of the bucket up because 9.81 - (-2.3 ) = +12.07 ?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 9, 2012

### PhanthomJay

You are correct that the acceleration is up. But you shouldn't be solving the problem by your method. Instead, draw a free body diagram and use Newton's 2nd law, which states that $F_{net} = ma$, where $F_{net}$ is the sum of the tension force up and the weight force mg down. Since the Tension force is greater than the weight, the net force, and acceleration, must be up.
a = __?___?