Child jumping onto a cart

Problem

A cart of mass $M = 4{,}0\;\mathrm{kg}$ is at rest on a frictionless horizontal track. A child of mass $m = 20\;\mathrm{kg}$ jumps onto the cart with a horizontal velocity of $v_0 = 0{,}80\;\mathrm{m/s}$. Find the common velocity of the child and cart after the jump.

Solution

The track is frictionless and the horizontal external forces are zero: horizontal momentum is conserved. The child lands on the cart and the two move on together (totally inelastic collision), so they have a common velocity $v$. Before the collision only the child is moving; after the collision they move together: $m\,v_0 = (m + M)\,v$ Solving for the common velocity: $v = \frac{m\,v_0}{m + M} = \frac{20\;\mathrm{kg}\cdot 0{,}80\;\mathrm{m/s}}{20\;\mathrm{kg} + 4{,}0\;\mathrm{kg}} = \frac{16}{24}\;\mathrm{m/s}$ $\ev{v \approx 0{,}67\;\mathrm{m/s}}$

Links

Topics: Quantità di moto e urti Concepts: Conservazione della quantità di moto · Urto anelastico Skills: Conservazione della quantità di moto Objects: Blocco