Question

Two equal mass carts approach each other with velocities equal in magnitude but opposite in direction. Friction can be neglected. If the carts collide completely inelastically, what will be the final velocity of the combined system?To the left with half the initial velocityNot enough information!0To the right with half the intial velocity

Answer 1

Answer:

The combined velocity is 0 units per unit time.

Explanation:

Let 'v' be the magnitude of the velocities of both the carts. Let the combined velocity of both the carts after collision be 'V'.

Let their masses be 'm'

Now, as per question, velocity of one cart is opposite to that of the other.

If velocity of one cart is $v$, then the velocity of the other car is $-v$

Since, the collision is completely inelastic, both the carts will stick together and move with same velocity after the collision.

If friction is neglected then the linear momentum is conserved as there is no external force acting on both the carts along their motion.

Therefore, initial momentum is equal to final momentum.

Initial momentum before collision is given as:

$p_i=mv+m(-v)\\p_i=mv-mv=0$

Therefore, initial momentum is 0. So, final momentum should also be 0. This gives,

$p_f=0\\(m+m)V=0\\2mV=0\\\textrm{ As the mass can't be 0 }, \\\therefore V=0$

Therefore, the final combined velocity after collision is 0.