Question

suppose that we attach velcro® to the non-magnetic ends of the two carts in the video and remove the mass bars, so that both carts have the same mass. we repeat the experiment shown in the video, and the carts stick together after they collide. if the launch cart travels at a speed v0, then how fast will the combined two-cart system travel after the collision?

Answer 1

The momentum conservation allows to find the final speed of the cars together are:

• If the second car is stopped, the final speed is:     v = vo / 2

• If the second car moves towards the first, the final speed is:   v = 0

The momentum is defined by the product of the mass and the speed of the body.

        p = m v

Where the bold letters indicate vector, p is the moment, m is the mass and v the velocity.

If we define the system as formed by the two bodies, the forces during the collision are internal and the momentum is preserved, let's find the moment in two instants.

Initial instant. Before crash.

       p₀ = m v₀₀₀+ m v₀₂

Final moment. After the crash.

      $p_f = 2m \ v$

The moment is preserved.

      $p_o =p_f \\m v_o + m v_o_2 = 2m \ v$  

     $v = \frac{m v_o + v_o_2}{2m}\\ v = \frac{1}{2} \ ( v_o + v_o_2)$

We have two cases:

• That the second car is initially stopped, therefore the speed is zero

       v = v₀ / 2

• That the second car move towards the first with velocity v₀₂ = - vo

       v = 0

In conclusion using the momentum conservation we can find the final velocity of the cars together are:

• If the second car is stopped, The final speed is:   v = vo / 2

• If the second car moves towards the first, the final speed is:  v = 0

Learn more here: brainly.com/question/3920210