Chapter 4, Problem 13P

(II) A 14.0-kg bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant. What is the acceleration of the bucket? Is it up or down?

13.Choose up to be the positive direction. Write Newton's second law for the vertical direction, and solve for the acceleration.

$\sum F=F_{\text{T}}-mg=ma$

$a=\frac{F_{\text{T}}-mg}{m}=\frac{163\text{ N}-(14.0\text{ kg})(9.80{\text{m/s}}^{\text{2}}\text{)}}{14.0\text{ kg}}=1.8{\text{m/s}}^{\text{2}}$

Since the acceleration is positive, the bucket has an upward acceleration.