Thermodynamics- I Law 3?

Question

A m=6 kg weight is dropped from height h =2.0 m onto a cart containing sand , mass M= 22 kg, initially moving at horizontal speed v= 3.1 m/s. How much heat is released in the process ?

Answer 1

First consider the (horizontal) momentum conservation (do you know why we do not consider vertical momentum conservation?) The final horizontal speed of both weight and cart of sand:
(22kg)*(3.1 m/s)/(6kg+22kg) = 2.436 m/s
Now consider the energy conservation:
Ei = mgh + 0.5Mv^2 = 6*9.8*2.0+0.5*22*3.1*3.1 = 223J
Ef = 0.5*28*2.436^2 = 83J
The heat released in the process is Ei - Ef = 1.4x10^2 J (answer)