Question

fill out the table below for the carts for before and after the collision. set the simulation to elastic collision. be careful of the sign of the velocities and momentums. the red cart will have a mass of 3 kg and a velocity of 5 m/s. see diagram to the right. the blue cart will have a mass of 1 kg and a velocity of -5 m/s.
cart
mass (kg)
velocity (m/s)
momentum (kg*m/s)
before collision
red cart
3.0
5.0

blue cart
1.0
-5.0

total

after collision
mass (kg)
velocity (m/s)
momentum (kg*m/s)
red cart

blue cart

total

hint?

Explanation:

Step1: Calculate pre-collision momentum (Red)

Momentum = mass × velocity: $p_{red,before} = 3.0\ \text{kg} \times 5.0\ \text{m/s} = 15.0\ \text{kg·m/s}$

Step2: Calculate pre-collision momentum (Blue)

Momentum = mass × velocity: $p_{blue,before} = 1.0\ \text{kg} \times (-5.0)\ \text{m/s} = -5.0\ \text{kg·m/s}$

Step3: Calculate total pre-collision momentum

Sum individual momenta: $p_{total,before} = 15.0 + (-5.0) = 10.0\ \text{kg·m/s}$

Step4: Set post-collision masses

Mass is conserved: $m_{red,after}=3.0\ \text{kg}$, $m_{blue,after}=1.0\ \text{kg}$

Step5: Find post-collision velocities (elastic)

Use elastic collision formulas:
For red cart:
$$v_{red,after} = \frac{(m_{red}-m_{blue})v_{red,before} + 2m_{blue}v_{blue,before}}{m_{red}+m_{blue}}$$
$$v_{red,after} = \frac{(3.0-1.0)5.0 + 2(1.0)(-5.0)}{3.0+1.0} = \frac{10 -10}{4} = 0\ \text{m/s}$$
For blue cart:
$$v_{blue,after} = \frac{(m_{blue}-m_{red})v_{blue,before} + 2m_{red}v_{red,before}}{m_{red}+m_{blue}}$$
$$v_{blue,after} = \frac{(1.0-3.0)(-5.0) + 2(3.0)5.0}{3.0+1.0} = \frac{10 +30}{4} = 10.0\ \text{m/s}$$

Step6: Calculate post-collision momentum (Red)

Momentum = mass × velocity: $p_{red,after} = 3.0\ \text{kg} \times 0\ \text{m/s} = 0\ \text{kg·m/s}$

Step7: Calculate post-collision momentum (Blue)

Momentum = mass × velocity: $p_{blue,after} = 1.0\ \text{kg} \times 10.0\ \text{m/s} = 10.0\ \text{kg·m/s}$

Step8: Calculate total post-collision momentum

Sum individual momenta: $p_{total,after} = 0 + 10.0 = 10.0\ \text{kg·m/s}$

Answer:

Category	Red Cart	Blue Cart	Total
Mass (kg)	3.0	1.0	-
Velocity (m/s)	5.0	-5.0	-
Momentum (kg·m/s)	15.0	-5.0	10.0
After Collision
Mass (kg)	3.0	1.0	-
Velocity (m/s)	0.0	10.0	-
Momentum (kg·m/s)	0.0	10.0	10.0