Truck brake failure with sandbags · Physics Brawl 2014 #FoL.5
Physics · mechanics
Problem
A truck experiences brake failure and needs to make an emergency stop. Luckily enough, it's just driving through a flood zone with lots of sand-filled bags. Assume that the mass of the truck is t and that one bag filled with sand weighs kg. How many sandbags will the truck need to collide with until it slows down to 75% of its initial speed km·h? Assume that the collisions are perfectly inelastic and that after colliding with the truck, the bags are pushed in front of it without friction.Intuitive explanation
This is a momentum conservation problem where each collision removes kinetic energy from the system. The key insight is that in each perfectly inelastic collision, the truck and bag stick together momentarily, then the bag slides away—so you need to apply conservation of momentum to each collision separately, tracking how the truck's speed decreases after each impact. Since the bags don't stick permanently, the truck's mass stays constant, but its velocity drops with each collision until it reaches 75% of .
Intuitive explanation
This is a momentum conservation problem where each collision removes kinetic energy from the system. The key insight is that in each perfectly inelastic collision, the truck and bag stick together momentarily, then the bag slides away—so you need to apply conservation of momentum to each collision separately, tracking how the truck's speed decreases after each impact. Since the bags don't stick permanently, the truck's mass stays constant, but its velocity drops with each collision until it reaches 75% of .