100A QUIZ 7

1. A ball of mass m₁ = 5.0kg with a speed of 4.0m/s hits another ball of mass m₂ = 3.0kg originally at rest. What are the velocities of the two balls right after the collision? Assume the perfect elastic collision.

   Solution.

   From the conservation of momentum we have

               m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂';

              (5.0kg)(4.0m/s) + (3.0kg)(0) = (5.0kg)v₁' + (3.0kg)v₂'

   Because the collision is perfect elastic we have v₁ - v₂ = -(v₁' - v₂') or 4.0m/s - 0 = v₂'- v₁'.

   Combining the two equations we get

              v₁' = 1.0m/s. and v₂' =5.0m/s. (in the same direction.)

2. A 1500-kg car traveling with a speed of 45km/h collides with a 2000-kg car stopping for the traffic light. After the collision two cars are joined. What is the speed of the cars right after the collision?

          Solution.

          From the conservation of momentum we have

                        m₁v₁ + m₂v₂ =( m₁ + m₂)V;

                       (1500kg)(45km/h)/(3.6ks/h)  + 0 = (1500kg +2000kg)V,

          which gives V = 5.3m/s = 19km/h.