A ball of mass 5kg moving with a velocity of 10 collides with a 15kg ball moving with a velocity of 4.if both balls stick together after collision, calculate their common velocity after impact if they initially move in opposite and the same direction
opposite, 5kg ball moving in the + direction:
5(-10) + 15(4) = (5+15)v
v = 1/2
do again, with both moving in the + direction.
rats -- I did it with 5kg moving in the - direction.
To calculate 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.
First, let's calculate the initial momentum of the system before the collision.
Initial momentum of the 5kg ball (moving in opposite direction):
Momentum = mass x velocity
Momentum = 5kg x -10m/s (negative sign indicates opposite direction)
Momentum = -50kg⋅m/s
Initial momentum of the 15kg ball (moving in the same direction):
Momentum = mass x velocity
Momentum = 15kg x 4m/s
Momentum = 60kg⋅m/s
The total initial momentum of the system is the sum of the momentum of the two balls:
Total initial momentum = -50kg⋅m/s + 60kg⋅m/s
Total initial momentum = 10kg⋅m/s
Now, let's calculate the final momentum of the system after the collision.
Since the balls stick together after the collision, their masses will combine. The total mass of the system after the collision is the sum of the masses of the two balls:
Total mass after collision = 5kg + 15kg
Total mass after collision = 20kg
Let's assume the common velocity of the balls after the collision is v.
Final momentum of the system after the collision = Total mass after collision x Common velocity
Using the law of conservation of momentum, we can equate the initial and final momentum:
Total initial momentum = Total final momentum
10kg⋅m/s = 20kg x v
Solving for v, we get:
v = 10kg⋅m/s ÷ 20kg
v = 0.5m/s
Therefore, the common velocity of the balls after the collision is 0.5 m/s.
To calculate the common 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 should be equal to the total momentum after the collision.
The momentum of an object is obtained by multiplying its mass by its velocity. So, the momentum before the collision is:
For the first ball: Momentum1 = mass1 * velocity1
= 5 kg * 10 m/s
= 50 kg m/s
For the second ball: Momentum2 = mass2 * velocity2
= 15 kg * 4 m/s
= 60 kg m/s
Now, let's examine the different scenarios separately:
1. Opposite direction:
If the balls are moving in opposite directions, we need to consider the sign of the velocities when calculating the total momentum. We assume that the first ball is moving towards the right, and the second ball is moving towards the left before the collision.
Total momentum before collision: Momentum_total_initial = Momentum1 - Momentum2
= 50 kg m/s - (-60 kg m/s)
= 50 kg m/s + 60 kg m/s
= 110 kg m/s
Since the balls stick together after the collision, their masses are combined, so the total mass after the collision is 5 kg + 15 kg = 20 kg.
Therefore, the common velocity after the impact can be calculated using the equation of momentum:
Total momentum after collision: Momentum_total_final = Total mass * Common velocity
Substituting the values:
110 kg m/s = 20 kg * Common velocity
Therefore, the common velocity after impact is:
Common velocity = 110 kg m/s / 20 kg
= 5.5 m/s
2. Same direction:
If the balls are moving in the same direction, we add the momenta together.
Total momentum before collision: Momentum_total_initial = Momentum1 + Momentum2
= 50 kg m/s + 60 kg m/s
= 110 kg m/s
Following the same steps as above, we find that the common velocity after impact is also 5.5 m/s.
So, in both cases, the common velocity of the balls after the impact is 5.5 m/s.