Answer:
a) x = 5.48 10⁻² m and b) 0.05 m
Explanation:
a) For a system in oscillatory motion the mechanical energy conserves and is described by the equation
Em = ½ k A²
Where k is the spring constant and at the amplitude of the movement
When the spring has the greatest extent, the kinetic energy is zero
Em = U = ½ k x²
Therefore, the amplitude of the movement is the same amplitude of the spring
Let's calculate
A = √ (2Em / k)
A = √ (2 0.12 / 80)
A = 0.0548 m = 5.48 10⁻² m
b) In this case the spring has kinetic energy that becomes elastic potential energy, let's calculate the mechanical energy before and after compressing the spring
Initial
Em = K = ½ m v²
Final
Em = Ke = ½ k x²
½ m v² = ½ k x²
x = √(m/k) v
x = 2 √(0.50 /800.0)
x = 0.05 m
Answer:
a) The greatest extension of the spring is 0.055 m
b) The spring compress 0.05 m
Explanation:
Please look at the solution in the attached Word file