An Inelastic Collision Crash Course

[PrideofPhilly]

1. Homework Statement

Three carts move on a frictionless horizontal track with different masses and speeds.

Cart 1: 4 kg (5 m/s to the right)
Cart 2: 10 kg (3 m/s to the right)
Cart 3: 3 kg (4 m/s to the left)

Cart 1 and 2 are right behind each other on the left side of the track while Cart 3 is by itself on the right side of the track.

The carts stick together after colliding.

Find the final velocity of the three carts. Answer in units of m/s.

2. Homework Equations

Inelastic collision:
Vf = v1(i) (m1/m1 + m2)

3. The Attempt at a Solution

Since we know that the masses stick together after colliding, then we know this system is fully inelastic; therefore, we can use the above equation.

Furthermore, we can say that Cart 1 and Cart 2 are one mass or m1 (4+10 = 14 kg) and Cart 3 is m2 (3 kg).

So:

Vf = v1(i) (14 kg/14 kg + 3 kg)
vf = v1(i) (0.8235294118)

However, I cannot figure out how to find the initial velocity of Cart 1 and 2 together.

 

[rl.bhat]

First of all find the combined velocity of m1 and m2 using the relevant equation. To find the final velocity of all masses, use the equation for combined mass of m1 and m2 with m3.