Conservation of momentum continous mass flow freight cart.

In summary, the conversation discusses the use of initial time in two worked examples, one on page 3 and the other on page 4. In the first example, the initial time is set at t=0, while in the second example, an arbitrary time t is used. This is because the second example involves the use of differential equations, while the first example can be solved using conservation of momentum.
  • #1
BareFootKing
30
0

Homework Statement


I am having difficulty understanding why in 2.1 Worked Example Coal Car on page 3 One can use the initial time as time = 0, but 2.2 Worked example on page 4 they start the initial time at an arbitrary time t.


Homework Equations





The Attempt at a Solution

 
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  • #2
because in the second example if you start with the initial time =0 then the initial momentum is zero because it is initially at rest and this simplifies the second example to a solutions similar to the first. But that is wrong.
 
  • #3
your two links point to the same page, and I can't see anything there that matches either description.
 
  • #4
Thank you I put up the wrong link. Here is the correct link:
 
  • #5
In each case they start at t=0. In 2.2 they also consider some arbitrary later time t and an interval δt from there. That is normal when deriving differential equations. In 2.1 they did not need to do that; they could solve the problem just by considering t=0 and t=tf and applying conservation of momentum. Whether such an approach was available in 2.2 I've not tried to analyse.
 

What is the conservation of momentum?

The conservation of momentum is a fundamental principle in physics that states that in a closed system, the total momentum of all objects before and after a collision remains constant. This means that the total momentum of the objects involved in the collision cannot change, only their individual momenta can change.

How does the conservation of momentum apply to a continuous mass flow freight cart?

The conservation of momentum applies to a continuous mass flow freight cart in the same way it applies to any other system. The total momentum of the cart and its cargo will remain constant, as long as there are no external forces acting on the system. This means that the speed and direction of the cart may change, but the total momentum will remain the same.

What factors can affect the conservation of momentum in a continuous mass flow freight cart?

The conservation of momentum can be affected by several factors in a continuous mass flow freight cart. These include the mass and velocity of the cart and its cargo, as well as any external forces acting on the system such as friction or air resistance. The elasticity of the materials involved in the collision can also impact the conservation of momentum.

How is the conservation of momentum useful in understanding the behavior of a continuous mass flow freight cart?

The conservation of momentum is useful in understanding the behavior of a continuous mass flow freight cart because it allows us to predict the outcome of collisions and understand how the movement of the cart and its cargo will change. By applying this principle, we can also design more efficient and safer freight cart systems.

Are there any limitations to the conservation of momentum in a continuous mass flow freight cart?

The conservation of momentum is a fundamental principle in physics and is applicable to most systems, including continuous mass flow freight carts. However, it does have some limitations, such as not taking into account external forces like air resistance or friction, which can affect the overall momentum of the system. In real-world scenarios, these factors must be considered when applying the conservation of momentum to a continuous mass flow freight cart.

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