Answer to Question #3846 in Mechanics | Relativity for mia

Question

A thread holds two carts together on a frictionless surface as in the figure below. A
compressed spring acts on the carts. After the thread is burned, the 1.5 kg cart moves with
a velocity of 27 cm/s to the left. What is the velocity of the 4.5 kg cart?

Answer 1

Let m₁ be the mass of the first cart (m₁ = 1.5 kg), m₂ - the mass of the second cart (m₂ = 4.5 kg).
V₁ - velocity of the first cart, V₂ - velocity of the second cart.
According to the law of conservation of linear momentum:


0 = m₁V₁ - m₂V₂
V₂ = V₁*m₁/m₂
V₂ = 27*1.5/4.5 = 9 cm/s


So, the velocity of the 4.5 kg cart is 9 cm/s.