A body of mass 8kg moving with a velocity of 10m/s collides with another body of mass 6kg moving in the opposite direction with a velocity of 50m/s.determine their common velocity in the direction of A after collision
I guess they stick together.
8*10 - 6*50 = (6+8) v
-220 = 14 v
v = -15.7 m/s
8*10 + 6*50 = (8+6)v
80+300 = 14v
380=14v
v=27.14m/s
To determine the common velocity of the bodies after collision, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that 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. Mathematically, it is expressed as:
Momentum = Mass * Velocity
Let's denote the velocity of the 8kg mass as v1 and the velocity of the 6kg mass as v2. Since the mass moving with a velocity of 10m/s is colliding with the other mass moving with a velocity of 50m/s in the opposite direction, we have:
Initial momentum before collision = Final momentum after collision
(8kg * 10m/s) + (6kg * -50m/s) = (8kg + 6kg) * v
Simplifying the equation:
80kg·m/s - 300kg·m/s = 14kg * v
-220kg·m/s = 14kg * v
Dividing both sides by 14kg:
-220kg·m/s ÷ 14kg = v
Therefore, the common velocity of the masses in the direction of A after the collision is approximately -15.71 m/s. The negative sign indicates that the bodies will move in the opposite direction to the initial motion.
To determine the common velocity of the bodies after the collision, we need to apply the principles of conservation of momentum.
1. First, calculate the momentum of each body before the collision:
Momentum of body A = mass of A * velocity of A
= 8 kg * 10 m/s
= 80 kg m/s (in the positive direction)
Momentum of body B = mass of B * velocity of B
= 6 kg * (-50 m/s) (since B is moving in the opposite direction)
= -300 kg m/s (in the negative direction)
2. Next, calculate the total initial momentum before the collision:
Total initial momentum = momentum of A + momentum of B
= 80 kg m/s - 300 kg m/s
= -220 kg m/s
3. According to the principle of conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision.
4. Let the common velocity after the collision be represented by 'v'.
Momentum of A' = mass of A * velocity of A'
Momentum of B' = mass of B * velocity of B'
Momentum of A' = 8 kg * v
Momentum of B' = 6 kg * v
5. The total momentum after the collision is the sum of the momenta of the two bodies:
Total momentum after the collision = 8 kg * v + 6 kg * v
= 14 kg * v
6. Equate the total initial momentum to the total momentum after the collision:
-220 kg m/s = 14 kg * v
7. Solve for 'v':
v = -220 kg m/s / 14 kg
v ≈ -15.71 m/s (approx.)
Therefore, the common velocity of the bodies in the direction of A after the collision is approximately -15.71 m/s.