Chapter 4, Problem 12P

To determine

The magnitude and direction of acceleration of bucket moving in the vertical plane.

Answer to Problem 12P

Solution:

Bucket is moving in an upward direction with acceleration, $a=1.84{\text{ m/s}}^{\text{2}}$

Explanation of Solution

Given:

Mass of the bucket, $m=14\text{ kg}$

Tension in the rope, $T=163\text{ N}$

Formula:

According to Newton’s second law of motion:

  ${\displaystyle \sum F} =ma$

Where, m is the mass and a is the acceleration.

Calculation:

  

Tension T acts in upward direction and weight (mg) acts downwards.

  $\begin{array}{l} {\displaystyle \sum F} =ma\\ T–mg=ma \\ 163-\left(14\right)\left(9.8\right)\text{=}14a\\ a=1.84{\text{ m/s}}^{\text{2}}\end{array}$

Conclusion:

Positive acceleration value of $a=1.84{\text{ m/s}}^{\text{2}}$ shows that bucket is moving upward.