An 8kg ball traveling to the east at 10m per sec collides, with a 2kg ball traveling to the west with a velocity of 5 meters per sec. After the collision they move together.Determine the final velocity of the balls. Assume that there are no resistive forces.
To determine the final velocity of the balls after the collision, we can use the principle of conservation of momentum.
The momentum of an object is calculated by multiplying its mass by its velocity. Therefore, the momentum before the collision can be calculated as follows:
Momentum of the 8kg ball before collision = (mass of 8kg ball) × (velocity of 8kg ball) = (8kg) × (10m/s) = 80 kg·m/s (to the east)
Momentum of the 2kg ball before collision = (mass of 2kg ball) × (velocity of 2kg ball) = (2kg) × (-5m/s) = -10 kg·m/s (to the west)
The negative sign for the momentum of the 2kg ball indicates that it is moving in the opposite direction.
Using the conservation of momentum, the total momentum before the collision should equal the total momentum after the collision. Therefore:
Total momentum before collision = Total momentum after collision
(80 kg·m/s) + (-10 kg·m/s) = (total mass) × (final velocity)
Now, let's calculate the total mass of the balls:
Total mass = mass of 8kg ball + mass of 2kg ball = 8kg + 2kg = 10kg
Substituting the values into the equation, we have:
70 kg·m/s = (10kg) × (final velocity)
Simplifying the equation, we obtain the final velocity of the balls:
final velocity = 70 kg·m/s ÷ 10kg = 7 m/s (to the east)
Therefore, the final velocity of the balls is 7 m/s to the east
To determine the final velocity of the balls after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. Therefore, the momentum of the 8kg ball before the collision is calculated by multiplying its mass (8kg) by its initial velocity (10m/s), which gives us 80 kg·m/s (kilogram meter per second).
Similarly, the momentum of the 2kg ball before the collision is calculated by multiplying its mass (2kg) by its initial velocity (-5m/s since it is traveling to the west), resulting in -10 kg·m/s.
Since momentum is conserved, the total momentum after the collision is equal to the sum of the individual momenta before the collision. Therefore, the total momentum after the collision can be calculated as 80 kg·m/s + (-10 kg·m/s) = 70 kg·m/s.
Since the balls move together after the collision, we can consider them as a single system with a combined mass. The combined mass is calculated as the sum of the individual masses, which is 8kg + 2kg = 10kg.
Now, we can determine the final velocity of the balls according to the principle of conservation of momentum. The total momentum after the collision is equal to the product of the combined mass and the final velocity. Therefore, we can rearrange the equation to solve for the final velocity:
Total momentum after collision = combined mass * final velocity
70 kg·m/s = 10kg * final velocity
Dividing both sides of the equation by 10kg, we find:
final velocity = 70 kg·m/s ÷ 10kg
Final velocity = 7 m/s
Hence, the final velocity of the balls after the collision is 7 m/s.