Question

1. A 1 kg cart moving with a speed of 3 m/s collides with a 2 kg cart at rest. If the carts stick together after the collision, with what speed will they move after the collision?

Answer 1

The final speed of the two carts stuck together after the collision is 1 m/s

Step-by-step explanation:

This is an example of an inelastic collision where two separate carts each with different momentum collide and become a single object.

The conservation of momentum (p) equation is:
`p_(1i)+p_(2i)=p_f` where
`p_(1i)` is the initial momentum of cart 1:
`p_(1i)=m_1\,*\,v_(1i)=1\,kg\,*\,3\,(m)/(s) = 3 (kg*m)/(s)`

Notice that cart 2 is at rest, therefore its velocity is zero, which makes its initial momentum zero:
`p_(2i)=m_2\,*\,v_(2i)= 2\,kg \,*0\,(m)/(s) =0`

The final momentum (
`p_f`) for which we don't know the velocity (
`v_f`) is the product of the final mass (addition of the two masses) times the final velocity of this new object (two carts stuck together):

`p_f=(m_1+m_2)* v_f = 3\,kg\,*\,v_f`

Now we re-write the conservation of momentum equation to isolate and obtain the unknown final velocity:

`p_(1i)+p_(2i)=p_f\\3\,(m*kg)/(s)+0=3\,kg\,*\,v_f\\3\,(m*kg)/(s)=3\,kg\,*\,v_f\\v_f=(3)/(3)\, (m)/(s) \\v_f=1\,(m)/(s)`