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An ideal spring hangs from the ceiling. A 1.95 kg mass is hung from the spring, stretching the spring a distance d=0.0865 m from its origina
Question
An ideal spring hangs from the ceiling. A 1.95 kg mass is hung from the spring, stretching the spring a distance d=0.0865 m from its original length when it reaches equilibrium. The mass is then lifted up a distance L=0.0325 m from the equilibrium position and released. What is the kinetic energy of the mass at the instant it passes back through the equilibrium position?
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Physics
6 months
2021-08-04T12:06:47+00:00
2021-08-04T12:06:47+00:00 1 Answers
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Answer:
kinetic energy = 0.1168 J
Explanation:
From Hooke’s law, we know that ;
F = kx
k = F/x
We are given ;
Mass; m = 1.95 kg
Spring stretch; d = x = 0.0865
So, Force = mg = 1.95 × 9.81
k = 1.95 × 9.81/0.0865 = 221.15 N/m
Now, initial energy is;
E1 = mgL + ½k(x – L)²
Also, final energy; E2 = ½kx² + ½mv²
From conservation of energy, E1 = E2
Thus;
mgL + ½k(x – L)² = ½kx² + ½mv²
Making the kinetic energy ½mv² the subject, we have;
½mv² = mgL + ½k(x – L)² – ½kx²
We are given L=0.0325 m
Plugging other relevant values, we have ;
½mv² = (1.95 × 9.81 × 0.0325) + (½ × 221.15(0.0865 – 0.0325)² – ½(221.15 × 0.0865²)
½mv² = 0.62170875 + 0.3224367 – 0.82734979375
½mv² = 0.1168 J