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Spring constant help needed?
a 0.60-kg metal sphere oscillates at the end of a vertical spring. As the spring stretches from 0.12 to 0.23 m (relative to its unstrained length), the speed of the sphere decreases from 5.70 to 4.80 m/s. What is the spring constant of the spring?
1 Answer
- kuiperbelt2003Lv 71 decade agoFavorite Answer
use conservation of energy, knowing that the total energy at each point is the same
call x1, v1 the values at x=0.12m and x2, v2 the values at x=0.23m, energy conservation tells us
1/2k(x1)^2+1/2m(v1)^2=
1/2 k(x2^2) + 1/2 m(v)^2
dividing through by 1/2 and substituting values, we get
k(0.12)^2+(0.6)(5.7)^2=
k(0.23)^2+(0.6)(4.8)^2
collecting terms:
k[(0.23)^2-(0.12)^2]=
0.6[(5.7)^2-(4.8)^2]
and now just solve for k