A physics professor uses an air-track cart of mass m to compress a spring of constant k by an amount x from its equilibrium length. The air-track has negligible friction. When she lets go, the spring launches the cart. What cart velocity should she expect after it is launched by the spring
Question
Answer:
v = √k/m x
Explanation:
We can solve this exercise using the energy conservation relationships
starting point. Fully compressed spring
Em₀ = [tex]K_{e}[/tex] = ½ k x²
final point. Cart after leaving the spring
[tex]Em_{f}[/tex] = K = ½ m v²
Em₀ = Em_{f}
½ k x² = ½ m v²
v = √k/m x