Conservation of momentum mine car problem

[genevievelily]

Homework Statement

A mine car of mass 440kg rolls at a speed of 0.50m/s on a frictionless horizontal track. A chunk of coal of mass 150kg has a speed of 0.80m/s as it leaves a chute above the car. The angle of the chute is 25 degrees from the horizontal. After the coal has come to a rest in the car, what is the velocity of the car and coal system.

Homework Equations

mv1 + mv1 = v(m1+m2)

The Attempt at a Solution

Originally I thought all momentum was conserved but then that wouldn't make sense because if it did the cart would not continue rolling straight forward. I got the correct answer if only taking x component into account. I just don't understand why you do this and how come the y component is not included in calculating momentum.

The solution says:

Momentum is conserved in the horizontal direction during the "collision." Let the coal be object 1 and the car be object 2.

So my question in other words is how come its only conserved in horizontal direction?

Thanks.

 

[Panphobia]

There is an x and y component to the coal's momentum, but when the coal collides with the mine car the only velocity you want is the horizontal. So all you need is the the x component of the coal momentum in the chute. So momentum is always conserved, but the y momentum doesn't matter to the x momentum, but you are looking for the x component.

 

[PeroK]

So my question in other words is how come its only conserved in horizontal direction?

Thanks.

It is conserved in the y-direction (downwards) but the momentum in this direction is transmitted through the car to the Earth. So, technically, the Earth is perturbed ever so slightly. In practice, though, this moment is lost to the system you are observing.

Another example is a bouncing ball. Each time the ball bounces the momentum of the ball changes direction. So, by conservation of momentum, the Earth must also be "bouncing" by a tiny amount.

 

[genevievelily]

got it thanks!

 

[HalfLostAndSearching]

The conservation of momentum principle states that the total momentum of a system remains constant in the absence of external forces. In this problem, the horizontal direction is the only direction in which there are no external forces acting on the system. The vertical direction, on the other hand, is affected by gravity, which is an external force. Therefore, the total momentum in the vertical direction is not conserved.

In this problem, the coal and the car are considered as two separate objects, and their individual momenta are conserved in the horizontal direction. However, in the vertical direction, the momentum of the coal is transferred to the car, causing it to move upward. This is why the y-component of momentum is not conserved in this problem.

I hope this explanation helps clarify why the conservation of momentum is only considered in the horizontal direction in this problem. Additionally, it is important to note that while momentum is conserved in the horizontal direction, kinetic energy is not conserved due to the presence of the external force of gravity.