Question

Two vehicles (masses m₁ and m₂, velocities v₁ and v₂) crash head-on, see  After a plastic impact the vehicles are entangled and slide with locked wheels a distance s to the right. The coefficient of kinetic friction between the wheels and the road is µ. Calculate v₁ if v₂ and s are known.

Answer 1

The total momentum of the system remains unchanged during the collision. We assume that positive velocities are directed to the right (note the direction of v₂). We then obtain the velocity ¯v of the vehicles after the impact : 

 In order to relate the distance s to the velocity v  we apply the work-energy theoram

T_1-T₀=U.

. We insert the kinetic energies

T₀ = (m₁ + m₂)v^-2/2, T₁=0

 the work of the friction force

U= -RS

and Coulomb's friction law