A 4.0kg particle collides with a 6.0 kg particle that is at rest at 10m/s. What is the velocity of the particles after the collision
To find the velocity of the particles after the collision, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a system of particles remains constant before and after a collision, as long as no external forces act on the system. In this case, we can assume that there are no external forces.
The formula for momentum is given by:
Momentum = mass × velocity
Before the collision, the 4.0 kg particle is moving but the 6.0 kg particle is at rest. So the total initial momentum of the system is given by:
Initial momentum = (mass of the 4.0kg particle × velocity of the 4.0kg particle) + (mass of the 6.0kg particle × velocity of the 6.0kg particle)
= (4.0 kg × velocity of the 4.0kg particle) + (0 kg × velocity of the 6.0kg particle)
= 4.0 kg × velocity of the 4.0kg particle
After the collision, the two particles will have velocities. Let's call them v1 and v2, where v1 is the velocity of the 4.0 kg particle and v2 is the velocity of the 6.0 kg particle.
According to the principle of conservation of momentum, the total final momentum of the system is equal to the initial momentum. Therefore,
Total final momentum = 4.0 kg × velocity of the 4.0kg particle
Since only the 4.0 kg particle is moving after the collision, the 6.0 kg particle must be at rest. Therefore, the velocity of the 6.0 kg particle after the collision is 0 m/s.
Now, we can equate the total final momentum with the initial momentum to solve for the velocity of the 4.0 kg particle.
4.0 kg × velocity of the 4.0kg particle = 4.0 kg × velocity of the 4.0kg particle
Hence, the velocity of the 4.0 kg particle after the collision is equal to its initial velocity, which is 10 m/s.