183_notes:examples:calculating_the_force_due_to_a_stretched_spring

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183_notes:examples:calculating_the_force_due_to_a_stretched_spring [2014/07/22 02:43] – [Solution] caballero183_notes:examples:calculating_the_force_due_to_a_stretched_spring [2014/07/22 04:54] pwirving
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  $ |\vec{s}| = |L - L_0|$  $ |\vec{s}| = |L - L_0|$
  
-{{183_notes:spring_force_jpeg.jpg}}+{{183_notes:spring237.jpg}} 
 + 
 +{{183_notes:spring_235.jpg}}
  
 <WRAP todo>This FBD needs the forces of the Earth and the surface. It should also be abstract. For example, see the early fan cart problems.</WRAP> <WRAP todo>This FBD needs the forces of the Earth and the surface. It should also be abstract. For example, see the early fan cart problems.</WRAP>
 ==== Solution ==== ==== Solution ====
- 
-<WRAP todo>Needs more steps/explanatory words; Remember they are intro students (see below for the right level of detail)</WRAP> 
  
 To determine the spring force, you will need to compute: To determine the spring force, you will need to compute:
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  $$\hat{s} = \hat{L} = \dfrac{\langle 0.38,0,0\rangle}{0.38} = \langle 1,0,0 \rangle$$  $$\hat{s} = \hat{L} = \dfrac{\langle 0.38,0,0\rangle}{0.38} = \langle 1,0,0 \rangle$$
  
-You can then compute the magnitude of the stretch (|\vec{s}|):+You can then compute the magnitude of the stretch $(|\vec{s}|)$:
  $$ |\vec{s}| = |L - L_0| = 0.38m - 0.20m = 0.18m$$  $$ |\vec{s}| = |L - L_0| = 0.38m - 0.20m = 0.18m$$
  
 Finally, you can compute the force: Finally, you can compute the force:
  
-$$\vec{F} = -k_s|\vec{s}|\hat{s} = -(8N/m)(0.18m)(1,0,0= \langle 1.44,0,0 \rangle\,N/m$$ +$$\vec{F} = -k_s|\vec{s}|\hat{s} = -(8N/m)(0.18m)\langle 1,0,0\rangle = \langle -1.44,0,0 \rangle\,N$$
  
 +which points to the left. That is consistent with the diagram above.
  
  
  • 183_notes/examples/calculating_the_force_due_to_a_stretched_spring.txt
  • Last modified: 2014/07/22 04:55
  • by pwirving