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One-dimensional collisions

If two carts collide, how will their speeds change? Compare momentum and kinetic energy.

    P04 · Conservation of momentum0.00 s · Ready
    A scene where two carts collide once and move on a horizontal rail

    Physics/Mechanics/Principles and Exploration

    One-dimensional collisions — principles and investigation

    When two carts collide, although their respective speeds change, there is a quantity that is conserved when looking at the two carts together. Compare the momentum and kinetic energy before and after the collision by changing the mass, initial velocity, and coefficient of restitution. Bouncing collisions and sticking collisions can be interpreted using the same criteria.

    How does it work?

    If there is no external force, total momentum is conserved. Kinetic energy is conserved when e = 1.

    Key relationship

    m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ · v₂ − v₁ = e(u₁ − u₂)

    Try this investigation

    1. Collide the two carts and look at the speed arrow. e = 1 is elastic, e = 0 is completely inelastic.
    2. The orange cart is fixed at 1 kg. In the elastic collision, change the mass of the blue cart to 1 kg, 2 kg, and 3 kg and record it.
    3. Set the two masses to 1 kg and the initial speed to 3 m/s and 0 m/s. Compare e = 1 and e = 0.

    Interpreting your results

    What is conserved in elastic collisions with e = 1?

    Elastic collisions conserve both total momentum and total kinetic energy.

    Assumptions and limitations

    It is a single collision of two one-dimensional objects without external force, friction, or rotation. The coefficient of restitution is limited to 0~1. Skip the transformation process and change the speed at the moment of contact. The screen scales according to the cart.