Answer:
10.83 m/s
Explanation:
Case 1:
m = mass attached to spring = 2 kg
x = compression of the spring = 40 cm = 0.40 m
k = spring constant
v₀ = maximum speed = 10 m/s
Using conservation of energy
maximum spring potential energy = maximum kinetic energy
(0.5) k x² = (0.5) m v₀²
k (0.40)² = (2) (10)²
k = 1250 N/m
Case 2 :
m = mass attached to spring = 2 kg
A = amplitude = 50 cm = 0.50 m
x = compression of the spring at half amplitude = A/2 = 50/2 = 25 cm = 0.25 m
k = spring constant = 1250 N/m
v = speed = ?
Using conservation of energy
maximum spring potential energy = spring potential energy + kinetic energy
(0.5) k A² = (0.5) k x² + (0.5) m v²
(1250) (0.50)² = (1250) (0.25)² + (2) v²
v = 10.83 m/s
