Question

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?

Answer 1

`\text{(a)}\\\text{Given that current energy at starting point }h_(1) \text{ is}:\\E_(h1)=mgh+(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))+(1)/(2)mv^2\\=258J=10g+v^2\\=160=v^2\\\therefore v=40m/s \text{ at }h_(2)\\`
`\text{(b)}\\\text{Again, apply conservation of energy: } 258J=mg(h_(3)-h_(2))+(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)`