Acceleration of a Bucket and Tension Forces

[PeachBanana]

Homework Statement

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?

Homework Equations

F = ma

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 ?

 

[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 = __?___?