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

Answer:

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

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: $p_{1i}=m_1\,*\,v_{1i}=1\,kg\,*\,3\,\frac{m}{s} = 3 \frac{kg*m}{s}$

Notice that cart 2 is at rest, therefore its velocity is zero, which makes its initial momentum zero: $p_{2i}=m_2\,*\,v_{2i}= 2\,kg \,*0\,\frac{m}{s} =0$

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:

$p_{1i}+p_{2i}=p_f\\3\,\frac{m*kg}{s}+0=3\,kg\,*\,v_f\\3\,\frac{m*kg}{s}=3\,kg\,*\,v_f\\v_f=\frac{3}{3}\, \frac{m}{s} \\v_f=1\,\frac{m}{s}$