How Does Ore Loading Affect Kinetic Energy and Momentum of a Car?

[Fusilli_Jerry89]

An empty ore car coasts at a constant horizontal speed under an ore chute. Ore falls vertically into the car. What effect does the addition of the ore have on
(a) The kinetic energy of the loaded car? The book says the answer is the same as the unloaded car.

(b) The momentum of the loaded car? The book says: The ratio of the velocities is equal to the sqare root of the inverse ratio of the masses.

So there is more momentum but not more kinetic energy?

 

[marlon]

What is and "ore" ?

HINT : check out the directions of the vectors in your question.

For example for (a) : the kinetic energy depends on mass and velocity. Mass stays the same and your velocity vector is horizontal because the car moves horizontally. So, given the fact that the velocity vector remains horizontal, how would it change even if some object falls on the car along the vertical direction ?

marlon

 

[m2003]

I would like to clarify and provide further explanation on the concept of kinetic energy and momentum in this scenario.

First, let's define kinetic energy as the energy an object possesses due to its motion. In this case, the empty ore car is moving at a constant horizontal speed, meaning it already has a certain amount of kinetic energy. When ore falls into the car, the kinetic energy of the car does not change because the speed of the car remains the same. Therefore, the addition of the ore does not have any effect on the kinetic energy of the loaded car. This is why the answer provided in the book is the same as the unloaded car.

Now, let's discuss momentum, which is defined as the product of an object's mass and velocity. In this scenario, the loaded car will have a greater mass due to the added weight of the ore. However, the velocity of the car remains the same. This means that the momentum of the loaded car will be greater than the unloaded car, as stated in the book.

To further understand the relationship between velocity, mass, and momentum, we can use the equation p=mv, where p is momentum, m is mass, and v is velocity. From this equation, we can see that the ratio of velocities is equal to the square root of the inverse ratio of masses. This means that as the mass increases, the velocity decreases, and vice versa. Therefore, the momentum of the loaded car will be greater than the unloaded car, but the ratio of their velocities will remain the same.

In conclusion, the addition of ore into the empty ore car does not have an effect on the kinetic energy, but it does increase the momentum of the loaded car. This is because the velocity remains constant, but the mass increases. This is a fundamental concept in physics and is important to understand in various real-life situations.