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
