Question

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

Answer 1

v = √k/m x

Step-by-step explanation:

We can solve this exercise using the energy conservation relationships

starting point. Fully compressed spring

Em₀ =
`K_(e)` = ½ k x²

final point. Cart after leaving the spring

`Em_(f)` = K = ½ m v²

Em₀ = Em_{f}

½ k x² = ½ m v²

v = √k/m x