Understanding Cart Collisions: A Physics Puzzle

Explaining the Relationship:

Inertia is the resistance of an object to changes in its state of motion. In the scenario described, the red cart and the green cart are traveling towards each other at the same speed v. The red cart is moving to the right, while the green cart, with three times the inertia of the red cart, is moving to the left.

When the moving carts collide with the black cart that has a spring on one end and putty on the other, they do so at the same instant. The red cart ends up moving to the left at speed v, while the green and black carts move together at a speed of v/5.

The key to understanding the relationship between the inertia of the black cart and the red cart lies in the conservation of momentum principle. This principle states that the total momentum of a closed system remains constant before and after a collision. Using this principle, we can set up an equation to represent the collision:

mRvR + mGvG = (mR + mG)v'

Where mR and mG are the masses of the red and green carts, vR and vG are their velocities, and v' is the final velocity after the collision. Since we know that the final velocity is v/5, we can substitute this value into the equation:

mRvR + 3mR*(-v) = (mR + 3mR)*(v/5)

After solving the equation, we find that the inertia of the black cart, mB, is three times that of the red cart, mR.

This relationship highlights how the masses of objects in a collision scenario can affect the resulting motion and velocities of the system. Understanding these concepts is essential in analyzing and predicting the outcomes of physical interactions like cart collisions.