Question

A red car with a mass of 1400 kg is traveling at 20 m/s when it strikes a parked blue car (at rest)

with a mass of 1200 kg. The two cars crumple and stick together during the collision.
Complete the table below (including units). You can ignore external forces like friction:
Momentum After
Collision
Change in Momentum
Red Car
Blue Car
System
Momentum Before
Collision

Answer 1

The final velocity is 10.77 m/s. The values are calculated and given in the table below.

let's calculate the values:

1. Initial Momentum:

- Red Car:
`\(1400 \ \mathrm{kg} \cdot 20 \ \mathrm{m/s} = 28000 \ \mathrm{kg \cdot m/s}\)`

- Blue Car:
`\(1200 \ \mathrm{kg} \cdot 0 \ \mathrm{m/s} = 0 \ \mathrm{kg \cdot m/s}\)`

- System:
`\(28000 \ \mathrm{kg \cdot m/s} + 0 \ \mathrm{kg \cdot m/s} = 28000 \ \mathrm{kg \cdot m/s}\)`

2. Change in Momentum:

- Red Car:
`\(m_1 \cdot \Delta v_1 = 1400 \ \mathrm{kg} \cdot (\text{final velocity} - 20 \ \mathrm{m/s})\)`

- Blue Car:
`\(m_2 \cdot \Delta v_2 = 1200 \ \mathrm{kg} \cdot (\text{final velocity} - 0 \ \mathrm{m/s})\)`

- System:
`\(1400 \ \mathrm{kg} \cdot (\text{final velocity} - 20 \ \mathrm{m/s}) + 1200 \ \mathrm{kg} \cdot (\text{final velocity} - 0 \ \mathrm{m/s})\)`

3. Final Velocity:

Since the two cars stick together, their masses combine, and the final mass is
`\(m_1 + m_2 = 1400 \ \mathrm{kg} + 1200 \ \mathrm{kg} = 2600 \ \mathrm{kg}\)`. The conservation of momentum gives us:

`\[m_1 \cdot v_1 + m_2 \cdot v_2 = (m_1 + m_2) \cdot v_{\text{final}}\]`

`\[28000 \ \mathrm{kg \cdot m/s} = 2600 \ \mathrm{kg} \cdot v_{\text{final}}\]`

`v_f= (28000)/(2600)`

`v_f=10.77 m/s`

So, to complete the table,

Momentum After Collision:

Red Car=
`m_1 * (v_f)`= 1400* 10.77= 15,078 kg.m/s

Blue Car=
`m_2 * v_f` = 1200 *10.77= 12,924 kg.m/s

System= (1400+1200) x 10.77= 26000 kg.m/s

Change in Momentum:

Red Car= 1400(
`v_f`-20)=1400(10.77-20)= -12922 kg.m/s

Blue Car: 1200(
`v_f-20)`= 1200(10.77)= 12924 kg.m/s

System= 0 kg.m/s