# Problem:  6 kg bucket of water is being pulled straight up by a string at a constant speed. I determined that the tension on the string wasF = maF = (6kg * 9.8 m/s2)F = 58.8 N.(a) At a certain point, the speed of the bucket begins to change. The bucket now has an upward constant acceleration of magnitude 3 m/s2. What is the tension in the rope now?(b) Now assume that the bucket has a downward acceleration, with a constant acceleration of magnitude 3 m/s2. What is the tension in the rope?

###### FREE Expert Solution

Newton's Second Law Equation:

$\overline{){\mathbf{\Sigma F}}{\mathbf{=}}{\mathbf{ma}}}$

(a) Forces acting on the bucket:

$\begin{array}{rcl}\mathbf{T}\mathbf{-}\mathbf{mg}& \mathbf{=}& \mathbf{ma}\\ \mathbf{T}& \mathbf{=}& \mathbf{m}\mathbf{g}\mathbf{+}\mathbf{m}\mathbf{a}\\ & \mathbf{=}& \mathbf{m}\mathbf{\left(}\mathbf{g}\mathbf{+}\mathbf{a}\mathbf{\right)}\end{array}$

• m = 6kg
• g = 9.8 m/s2
• a = 3 m/s2
###### Problem Details

6 kg bucket of water is being pulled straight up by a string at a constant speed. I determined that the tension on the string was

F = ma
F = (6kg * 9.8 m/s2)
F = 58.8 N.

(a) At a certain point, the speed of the bucket begins to change. The bucket now has an upward constant acceleration of magnitude 3 m/s2. What is the tension in the rope now?

(b) Now assume that the bucket has a downward acceleration, with a constant acceleration of magnitude 3 m/s2. What is the tension in the rope?