Collision between sledges

Problem

Summary: collision between sledges. Two sledges on ice: $m_1 = 50\;\text{kg}$ at $5\;\text{m/s}$ and $m_2 = 70\;\text{kg}$ at rest. They collide and stick together. Calculate: (a) common velocity, (b) initial kinetic energy, (c) final kinetic energy, (d) energy dissipated and where it physically ends up.

Solution

(a) Common velocity (conservation of momentum, total mass $120\;\text{kg}$): $v_f = \frac{m_1 v_1}{m_1 + m_2} = \frac{50\cdot 5}{120} = \frac{250}{120} \approx 2{,}08\;\text{m/s}$

(b) Initial kinetic energy: $E_i = \tfrac{1}{2}\cdot 50\cdot 5^2 = 625\;\text{J}$

(c) Final kinetic energy: $E_f = \tfrac{1}{2}\cdot 120\cdot 2{,}08^2 \approx 260\;\text{J}$

(d) Energy dissipated: $\ev{\Delta E \approx 365\;\text{J} \;(\approx 58\%)}$ The missing $365\;\text{J}$ are converted into heat, deformation of the sledges and the sound of the impact. Momentum, on the other hand, is conserved exactly.

Links

Topics: Momentum and collisions Concepts: Inelastic collision · Conservation of momentum · Kinetic energy