A 10Kg ball moving with velocity 2m/s collides with a 20Kg mass initially at rest. If both of them stick together, the final; velocity of combined mass is:
Question
A 10Kg ball moving with velocity 2m/s collides with a 20Kg mass initially at rest. If both of them stick together, the final; velocity of combined mass is:
Solution
This problem can be solved using the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
Step 1: Calculate the initial momentum The initial momentum (P_initial) is the sum of the momentum of the 10Kg ball and the 20Kg mass. Since the 20Kg mass is initially at rest, its momentum is 0. The momentum of the 10Kg ball is its mass times its velocity (10Kg * 2m/s = 20Kgm/s). So, P_initial = 20Kgm/s.
Step 2: Calculate the final momentum After the collision, the 10Kg ball and the 20Kg mass stick together and move with the same velocity. Their combined mass is 30Kg. The final momentum (P_final) is the combined mass times the final velocity (30Kg * V_final).
Step 3: Set the initial momentum equal to the final momentum and solve for the final velocity 20Kgm/s = 30Kg * V_final V_final = 20Kgm/s / 30Kg = 0.67 m/s
So, the final velocity of the combined mass is 0.67 m/s.
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