AI Tutor
Imagine standing completely still on smooth, frictionless ice. If you throw a heavy backpack forward, you glide backward across the rink without ever pushing off the ground.
An isolated system is a collection of objects that interact with each other without any net external forces (like friction or gravity) acting from the outside.
Linear momentum (pp) measures how difficult it is to stop a moving mass, calculated as mass times velocity (p=mvp = mv). Because velocity has direction, momentum is a vector: motion to the right is positive (++), and motion to the left is negative (βˆ’-). In the 1660s, Dutch scientist Christiaan Huygens studied colliding pendulum balls and proved that inside an isolated system, the total initial momentum always equals the total final momentum: βˆ‘pi=βˆ‘pf\sum p_i = \sum p_f.
What happens when two moving objects smash into each other and lock together into a single moving piece?

Inelastic Collisions

In an inelastic collision, colliding objects deform or stick together, converting some kinetic energy into thermal energy and sound. When they stick together completely, they share a single combined final velocity (vfv_f).
The conservation equation for two sticking objects is: m1v1i+m2v2i=(m1+m2)vfm_1 v_{1i} + m_2 v_{2i} = (m_1 + m_2) v_f
Let's solve a collision: A 2Β kg2\text{ kg} cart moving right at +6Β m/s+6\text{ m/s} collides with a stationary 4Β kg4\text{ kg} cart and locks on.
The initial momentum is (2)(+6)+(4)(0)=12Β kgβ‹…m/s(2)(+6) + (4)(0) = 12\text{ kg}\cdot\text{m/s}. Setting this equal to (2+4)vf=6vf(2 + 4)v_f = 6v_f gives a combined final velocity of vf=+2Β m/sv_f = +2\text{ m/s} to the right.
A common mistake is treating velocities as purely positive numbers: if the second cart were moving left at 3Β m/s3\text{ m/s}, you must enter it as βˆ’3Β m/s-3\text{ m/s}, which would subtract momentum from the initial total.
What happens if a single stationary object suddenly blasts apart into separate pieces?