Answer:
5.831 m/s
Explanation:
According to the work-energy law,
Work done between two points = Change in kinetic energy between the two points.
Since the plastic ball is initially at rest, its initial kinetic energy is 0 since the initial velocity = 0
Work done by the spring = ∫ F.dx
The spring is compressed by 10 cm, so, we integrate from -0.1 m to 0 m
Fₓ(x) = (-30.0 N/m)x+ (60.0 N/m²)x²
F = -30x + 60x²
W = ∫ F.dx = ∫ (-30x + 60x²) dx
W = [- 15x² + 20x³]⁰₋₀.₁ = 0 - [- 15(0.01) + 20(-0.001)] = 0.17 J
W = ΔKE
ΔKE = (mv²/2) - 0
mv²/2 = 0.17
m = 10 g = 0.01 kg
0.01 v² = 0.34
v² = 34
v = 5.831 m/s
