A certain spring is found not to obey Hooke’s law, it exerts a restoring force F(x) = –αx – βx2 if it is stretched or compressed, where α = 48 N/m and β= 24 N/m2. The mass of the spring is negligible. An object with mass 1 kg on a frictionless, horizontal surface is attached to the spring, pulled a distance 1m to the right to stretch the spring and released. The speed of the object when it is 0.5m to the right of the x = 0 equilibrium position is
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
5 
m/s
Sol. dU = –F x dx – F y dy – F z dz
= 
U = 
+ 
U = – 
KE
U i – U f = KEf – KE i
– 
= 
mv2
v2 = 50
v = 5 
m/s
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