Question

fill out the table below for the carts for before and after the collision. be careful of the sign of the velocities and momentums. set the simulation to explosion. the red cart will have a mass of 2 kg and the blue cart will have a mass 1 kg. see diagram to the right.

cart
red cart
blue cart
total
hint?
before collision
mass (kg)
2.0
1.0

velocity (m/s)
1.0
1.0

momentum (kg*m/s)
2.0
1.0
3.0
after collision
mass (kg)
2.0
1.0

velocity (m/s)
1.0
1.0

momentum (kg*m/s)
2.0
1.0
3.0
picture
initial velocity
1 m/s
initial velocity
1 m/s
mass: 2 kg
mass: 1 kg
elastic collision
inelastic collision
explosion

Explanation:

Step1: Recall momentum conservation law

Total momentum before = Total momentum after: $p_{total,before} = p_{total,after}$

Step2: Calculate pre-collision total momentum

$p_{total,before} = m_{red}v_{red,before} + m_{blue}v_{blue,before} = (2.0\times1.0) + (1.0\times1.0) = 3.0\ \text{kg*m/s}$

Step3: Analyze explosion direction sign

Red cart moves left (negative velocity): $v_{red,after} = -1.0\ \text{m/s}$

Step4: Calculate red's post-collision momentum

$p_{red,after} = m_{red}v_{red,after} = 2.0\times(-1.0) = -2.0\ \text{kg*m/s}$

Step5: Solve for blue's post-collision velocity

Use $p_{total,after}=p_{total,before}$:
$p_{blue,after} = p_{total,before} - p_{red,after} = 3.0 - (-2.0) = 5.0\ \text{kg*m/s}$
$v_{blue,after} = \frac{p_{blue,after}}{m_{blue}} = \frac{5.0}{1.0} = 5.0\ \text{m/s}$

Step6: Recalculate total post-collision momentum

$p_{total,after} = p_{red,after} + p_{blue,after} = -2.0 + 5.0 = 3.0\ \text{kg*m/s}$

Answer:

Cart	Before Collision	Before Collision	Before Collision	After Collision	After Collision	After Collision
Red Cart	2.0	1.0	2.0	2.0	-1.0	-2.0
Blue Cart	1.0	1.0	1.0	1.0	5.0	5.0
Total	-	-	3.0	-	-	3.0