A ball of mass 2.0kg moves with a speed of 15.0ms-1 and collides with another stationary ball of mass 1.5kg .
If the two ball's stick together after collision , calculate their common speed .
The total momentum before the collision is:
p1 = m1v1 = (2.0 kg)(15.0 m/s) = 30.0 kg m/s
The total momentum after the collision is:
p2 = (m1 + m2)v2
where m2 is the mass of the second ball (1.5 kg) and v2 is the common speed of the two balls after the collision.
Since the two balls stick together, we can use the conservation of momentum:
p1 = p2
30.0 kg m/s = (2.0 kg + 1.5 kg) v2
v2 = 30.0 kg m/s / 3.5 kg
v2 = 8.57 m/s
Therefore, the common speed of the two balls after the collision is 8.57 m/s.
To solve this problem, 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.
1. Calculate the momentum of the first ball before the collision:
Momentum = mass * velocity
Momentum1 = 2.0 kg * 15.0 m/s
= 30.0 kg m/s
2. Since the second ball is stationary, its initial momentum is zero:
Momentum2 = 0 kg m/s
3. After the collision, the two balls stick together, so they have a common final momentum:
Total momentum after = Momentum1 + Momentum2
Since the balls stick together, their masses add up:
Total mass = 2.0 kg + 1.5 kg
= 3.5 kg
Therefore, their final momentum is:
Total momentum after = 30.0 kg m/s + 0 kg m/s
= 30.0 kg m/s
4. Calculate their common final speed:
Final momentum = Total mass * final velocity
30.0 kg m/s = 3.5 kg * final velocity
Rearrange the equation to solve for final velocity:
final velocity = 30.0 kg m/s / 3.5 kg
≈ 8.57 m/s
So, the common final speed of the two balls after the collision is approximately 8.57 m/s.