A ball mass of 200g,travelling with velocity of 100m/s,collide with another ball of mass 800g,moving at 50ml in the same direction. If they stick together, what will be their common velocity??
To find the common velocity of the balls after the collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated as the product of its mass and velocity. Therefore, the total momentum before the collision can be calculated as:
Total momentum before collision = (mass of ball 1 x velocity of ball 1) + (mass of ball 2 x velocity of ball 2)
In this case, ball 1 has a mass of 200g and a velocity of 100m/s, and ball 2 has a mass of 800g and a velocity of 50m/s.
Converting the masses to kilograms:
Mass of ball 1 = 200g = 0.2kg
Mass of ball 2 = 800g = 0.8kg
Using the formula, the total momentum before the collision is:
Total momentum before collision = (0.2kg x 100m/s) + (0.8kg x 50m/s)
= 20kg⋅m/s + 40kg⋅m/s
= 60kg⋅m/s
Since the balls stick together after the collision, we can consider them as a single object with a combined mass of 0.2kg + 0.8kg = 1kg.
Now, we can use the same formula to calculate the common velocity of the balls after the collision:
Total momentum after collision = (combined mass of the balls x common velocity)
Using the formula, the total momentum after the collision is:
Total momentum after collision = (1kg x common velocity)
Since the total momentum before the collision is equal to the total momentum after the collision, we can set the two equations equal to each other:
Total momentum before collision = Total momentum after collision
60kg⋅m/s = 1kg x common velocity
Now, we can solve for the common velocity:
common velocity = 60kg⋅m/s ÷ 1kg
= 60m/s
Therefore, the common velocity of the balls after the collision is 60m/s.