# Two carts with masses of 8.0 kg and 1.8 kg, respectively, move on a friction

1. Dec 8, 2007

### lettertwelve

[SOLVED] Two carts with masses of 8.0 kg and 1.8 kg, respectively, move on a friction

1. The problem statement, all variables and given/known data

Two carts with masses of 8.0 kg and 1.8 kg, respectively, move on a frictionless track with velocities of 8.0 m/s and 3.5 m/s. The carts stick together after colliding head-on. Find the final speed.

2. Relevant equations

m1v1+m2v2 = v (m1 + m2)

v_final = (m1*v1 + m2*v2)/(m1+m2)

3. The attempt at a solution

(8*8)+(1.8*3.5)=70.3
so
70.3=(8+1.8)V
which is then 70.3=9.8V
V=7.17

but it says i'm doing it wrong. (webassign problem)
please show me how i did it wrong?? or whats wrong?

2. Dec 8, 2007

### hotcommodity

You're adding the initial momenta, this is your problem. Define a coordinate system and determine which cart is moving in the positive direction, and which cart is moving in the negative direction (that is, which cart has a positive momentum, which cart has a negative momentum?).

3. Dec 8, 2007

### meganw

Everything is perfect...except you forgot one little thing.

Since both Cars are going in opposite directions when they hit each other "head on" (one going left and one is going right), then one of them must be going in the "negative" direction. Let's define "left" as the positive direction:

m1v1-m2v2 = v (m1 + m2)

8(8) - 1.8(3.5) = Vfinal (8+1.8)
57.7=Vfinal (9.8)
Vfinal = 5.89 m/s