A spring is compressed between two toy carts of masses m1 and m2. When the toy carts are released, the spring exerts on each toy cart equal and opposite forces for the same small time t. If the coefficients of friction μ between the ground and the toy carts are equal, then the magnitude of displacements of the toy carts are in the ratio

Minimum stopping distance = s Work done against the friction =W=μmgsInitial momentum gained by both toy carts will be same because same force acts for same time. Initial kinetic energy of the toy cart =p22mTherefore, μmgs=p22m or s=p22μgm2For the two toy carts, momentum is numerically the same. Further μ and g are the same for the toy carts. So s1s2=m2m12