Is momentum conserved when 2 carts having the same mass & the same speed collide, stick together and stop? what about the velocity
To determine if momentum is conserved in a collision, we need to consider the total momentum before and after the collision.
Momentum is defined as the product of an object's mass and velocity. It is a vector quantity, which means it has both magnitude and direction. In a collision, the total momentum of the system (consisting of both carts) before the collision is equal to the total momentum of the system after the collision, as long as no external forces are acting on the system.
In this scenario, we have two carts with the same mass and the same speed initially. When they collide, stick together, and come to a stop, we can analyze whether momentum is conserved.
Since both carts have the same mass and speed initially, their momenta (mass × velocity) will be the same and in the same direction before the collision. The direction will be determined by your frame of reference.
When the carts collide and stick together, they form a single object with a combined mass that is the sum of the individual masses. However, the velocity of this combined object will change because it now has a larger mass. Due to conservation of momentum, the total momentum after the collision must be equal to the total momentum before the collision.
Therefore, if the initial momentum was zero (because the carts had opposite but equal momenta), the final momentum must also be zero. This means that the velocity of the combined object after the collision is zero.
In conclusion, momentum is conserved in this scenario because the total momentum before the collision is zero (since the carts have equal but opposite momenta), and the total momentum after the collision is also zero (because the combined object comes to rest). However, the velocity of the combined object is not conserved since it changes from its initial value to zero after the collision.