Question

2 kg ball of clay moving at 40 m/s collides with a 5 kg ball of clay moving at 10 m/s directly toward the first ball. What is the final velocity if both balls stick together after the collision?

Answer 1

Answer:

vf = 4.3 m/s

Explanation:

• Assuming no external forces acting during the collision, total momentum must be conserved:

        $p_{o} = p_{f} (1)$

        where p₀ = initial momentum, and pf = final momentum.

• The initial momentum is just the sum (vector sum) of the initial momenta of both balls, as follows:

       $p_{o} = m_{1} * v_{1o} + m_{2} * v_{2o} = 2 kg* 40 m/s - 5kg* 10m/s = 30 kg*m/s (2)$

• The final momentum, assuming both balls stick together after the collision, can be expressed as follows:

       $p_{f} = (m_{1} + m_{2} ) * v_{f} = 7 kg * v_{f} (3)$

• From (2) and (3), solving for vf, we get:

        $v_{f} =\frac{30 kg*m/s}{7 kg} = 4.3 m/s (4)$