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.

 

[nlightner]

I would suggest using the conservation of momentum principle to solve for the initial velocity of Cart 1 and 2 combined. This principle states that the total momentum before a collision is equal to the total momentum after the collision. In this case, the total momentum before the collision is (4 kg x 5 m/s) + (10 kg x 3 m/s) = 50 kg*m/s. After the collision, the carts stick together and have a total mass of 14 kg, so the final momentum is (14 kg x vf). Setting these two equal to each other, we can solve for vf and get a final velocity of 3.57 m/s.

Once we have the final velocity, we can use the equation provided to solve for the initial velocity of Cart 1 and 2 combined. This will give us an initial velocity of 4.32 m/s. We can then use this value in the original equation to solve for the final velocity of the entire system, which will be the same as the final velocity of the combined carts. This final velocity will be 3.57 m/s, as calculated before.

In conclusion, by using the conservation of momentum principle and the inelastic collision equation, we can determine the final velocity of the three carts after the collision. This approach allows us to accurately analyze and solve for the outcome of an inelastic collision, which is important in understanding the laws of motion and predicting the behavior of objects in real-world scenarios.