Ball falls in a truck loaded with sand

[10bunny10]

Homework Statement

a ball falls in a truck loaded with sand with velocity v having horizontal and vertical component. The angle under which it enters the truck is α, the mass of the ball is m of the track loaded with sand is M. What happens with the momentum after the collision?

The Attempt at a Solution

This should be considered as completely inelastic collision. In vertical direction the momentum before the collision is the momentum of the ball mcosv. After the collision the track is not moving in horizontal direction, but the momentum should be conserved. The ball sinks in the sand, so is this the explanation? In horizontal direction the momentum before the collision is msinv. What is the momentum after? There is friction during the collision. It should be (m+M)v', but what about the friction?

 

[BruceW]

hi bunny! welcome to physicsforums :)

I'm having some trouble understanding the question. Is it a truck (as in a vehicle, without the brakes on)? Because you said track a couple of times. And the truck is meant to be not moving before the collision? And when you said mcosv is the vertical momentum of the ball before collision, did you mean mvcosα? And so the angle is measured from the vertical, right? (Since the vertical momentum is mv when the angle is zero).

Also, you said: "After the collision the track is not moving in horizontal direction, but the momentum should be conserved. The ball sinks in the sand, so is this the explanation?" I'm guessing you meant to say vertical direction? In this case, why do you think vertical momentum is conserved? Even if you take away the complication of the truck, is the vertical momentum of a falling ball conserved?

You are right that the final momentum in the horizontal direction will be (m+M)v'. And what about the friction? Does the question mention that there is some dissipative friction?