imported>Patrick at 14:31, 12 August 2011

2011-08-12T14:31:41Z

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The diagram below shows our understanding of the situation. There are two forces acting on a bucket of water: <math>F_G</math> and <math>F_T</math>. The tension in the rope lifts the water up. Therefore, the question in this problem is to find the work done by the tension. We choose the x-axis parallel to the displacement and thus the x-component of the displacement is <math>\Delta x = 12 m</math>. 
[[image:Helena_Work-Energy_Ex_4_Soln.png|TOP]] 

We can determine the net work because we know the acceleration, which is related to the net force:

<math>{F_{net}}_x = m a = (15)(0.7) = 10.5 N</math>
 
Consequently, the net work is

<math>W_{net} = {F_{net}}_x \Delta x = (10.5)(12) = 126 J</math>
 
Since the net work is the sum of the work done by gravity and by the tension (<math>W_{net} = W_{F_T} + W_{F_G}</math>) we can find the work done by tension by first finding the work done by gravity. The x-component of the gravitational force is <math>{F_G}_x = 150 \cos(180^{\circ}) = -150 N</math>:

<math>W_{F_G} = (-150)(12) = -1800 J</math>
 
From the net work and the work done by gravity, we find

<math>W_{F_T} = W_{net} - W_{F_G} = 126 - (-1800) = 1926 J</math>

Work-Energy Theorem EX 4 - Revision history

imported>Patrick at 14:31, 12 August 2011