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5. The picture shows a mass that is attached to a spring with constant, K = 500 N/m(20 points)
The mass is of 2 kg and the values of the heights are:h1= 5 meters,h2= 10 meters andh3= 2 meters.•The spring is compressed a length of 80 cm.
What is the speed of the mass when it reaches a height of h2?
•What is the speed of the mass when it reaches a heighth3?

5 The picture shows a mass that is attached to a spring with constant K 500 Nm20 points The mass is of 2 kg and the values of the heights areh1 5 metersh2 10 me class=

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kdai253

Answer:

[tex]\text{(a)}\\\text{Given that current energy at starting point }h_{1} \text{ is}:\\E_{h1}=mgh+\frac{1}{2}kx^2\\\text{Plug in height and mass: }E_{h1}=10g+250(0.8)^2=10g+160=258J\\\text{Using Conservation of Energy: }E_{h1}=E_{h2} \\\therefore 258J=mg(h_{2}-h_{1})+\frac{1}{2}mv^2\\=258J=10g+v^2\\=160=v^2\\\therefore v=40m/s \text{ at }h_{2}\\[/tex][tex]\text{(b)}\\\text{Again, apply conservation of energy: } 258J=mg(h_{3}-h_{2})+\frac{1}{2}mv^2\\\text{Plugging in: }258J=16g+v^2 \\\text{ Simplify: }101.2=v^2\\\therefore v=10.05m/s \text{ at } h_{3}[/tex]

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