imported>Patrick: Created page with 'Select the y-axis pointing downward. Then, draw the forces acting on the mass when it has moved a distance $y$ . The gravitational force $F_G$ and the force …'

2011-07-29T17:00:26Z

Created page with 'Select the y-axis pointing downward. Then, draw the forces acting on the mass when it has moved a distance <math>y</math>. The gravitational force <math>F_G</math> and the force …'

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Select the y-axis pointing downward. Then, draw the forces acting on the mass when it has moved a distance <math>y</math>. The gravitational force <math>F_G</math> and the force of the spring <math>F_{sp}</math>. The y-components of these forces are: <math>{F_G}_y = m g</math> and <math>{F_{sp}}_y = -k y</math>. The first graph shows the y-component of the gravitational force <math>{F_G}_y</math> as a function of the position <math>y</math> of the falling mass. The second graph shows the y-component of the force of the spring <math>{F_{sp}}_y</math> as a function of the position <math>y</math> of the falling mass. 
[[image:Helena_Work_Ex_3_SolnA.png|TOP]] 

'''(a)''' Compute the area of the graph from y = 1 cm to y = 5 cm. 
[[image:Helena_Work_Ex_3_SolnB.png|TOP]] 

{| border="1" cellpadding="2"
|-
!
! Displacement
! The area under the <math>F_y - y</math> (measured in <math>N \times m</math>)
! Work
|-
! <math>W_G</math>
| 1 to 5 cm
| <math>10 \times (5 - 1) \times 10^{-2}</math>
| 0.4 J
|-
! <math>W_{sp}</math>
| 1 to 5 m
| <math>(0.5 \times (-10) \times 5 \times 10^{-2}) - (0.5 \times (-2) \times 1 \times 10^{-2})</math>
| -0.24 J
|}
 
'''(b)''' The total work is <math>W_G + W_{sp} = 0.16 J</math>
 
'''(c)''' The total work done is zero when the mass falls from 0 to some point y:

<math>W_G + W_{sp} = 0</math>

<math>m g y - \frac{1}{2} k y^2 = 0</math>

<math>y = {2 m g \over k} = \frac{20}{200} = 0.1 m = 10 cm</math>

Work EX 3 - Revision history

imported>Patrick: Created page with 'Select the y-axis pointing downward. Then, draw the forces acting on the mass when it has moved a distance y. The gravitational force F_G and the force …'

imported>Patrick: Created page with 'Select the y-axis pointing downward. Then, draw the forces acting on the mass when it has moved a distance $y$ . The gravitational force $F_G$ and the force …'