Solving Beginner Momentum Homework: Collision of 2 Carts

In summary: I think it has to do with the principle of energy conservation. If you use momentum, you are breaking the law of conservation of momentum. If you use kinetic energy, you are still conserving momentum, but you are also conserving energy.
  • #1
Oscar Wilde
49
0

Homework Statement


A dynamics cart with a mass of 2.2kg is moving at 33 cm/s to the right when it has a head-on collision with a second cart with a mass of 1.2kg moving in the opposite direction also at 33 cm/s. After the nearly elastic collision the first cart continues forward at 13 cm/s. What is the new velocity of the second cart?


Homework Equations



conservation of momentum mv initial=mv final

The Attempt at a Solution



(mv of cart 1- mv of cart 2- mv final of cart 1)/(m of cart 2)= 3.6 cm/s to the right

However that's not right, the answer should be 5.3 cm/s to the left, which honestly makes no sense. The teacher hinted that the solution would be counter-intuitive. However, when using the correct values I do not get the desired answer.

It would really help if someone could either confirm my findings or prove me wrong. Also, I know that in elastic collisions kinetic energy is conserved, and the in inelastic collisions, KE is not conserved. I wanted to confirm that in elastic collisions the two masses do not become one, as opposed to inelastic collisions in which they do become one single mass.
 
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  • #2
5.3 is the answer I get.

.5*m1*v1^2 + .5*m2*v2^2 = .5*m1f*v1f^2 + .5*m2f*v2f^2

All of the .5's cancel out.
Be sure to convert cm to m.

Note that m1f = m1 and m2f = m2 in this case, because the problem says nothing about mass being lost.
 
Last edited:
  • #3
carrotcake10 said:
5.3 is the answer I get.

.5*m1*v1 + .5*m2*v2 = .5*m1f*v1f + .5*m2f*v2f

All of the .5's cancel out.
Be sure to convert cm to m.

Note that m1f = m1 and m2f = m2 in this case, because the problem says nothing about mass being lost.


Hmm, interesting. Why didn't you represent the value of m2v2 as negative? Shouldn't it have the opposite value of m1v1 since it is traveling in the opposite direction?
 
  • #4
You do when you plug it in, but the square should make it positive anyway.

And I made an error in that equation, I am sorry, the velocities are supposed to be squared.

MY MISTAKE!
 
  • #5
alright thanks a ton! so you chose to use conservation of kinetic energy rather than conservation of momentum? if you wouldn't mind expanding on your answer, what made you choose conservation of energy rather than momentum?
 
  • #6
After an elastic collision, no kinetic energy is lost. So basically this is a system in which the energy will be constant (not realistic). Also I just looked at what they gave you. Knowing the given data kind of throws that switch about which equation to use, at least for me.
 
  • #7
wow, thanks! your help is much appreciated :)
 

1. What is momentum and why is it important in physics?

Momentum is a physical quantity that describes the amount of motion an object has. It is calculated by multiplying an object's mass by its velocity. In physics, momentum is important because it is conserved in a closed system, meaning it remains constant before and after a collision or interaction between objects. This principle helps us understand and predict the motion of objects.

2. How do you calculate momentum in a collision between two carts?

To calculate the momentum of a cart in a collision, you will need to know the mass and velocity of the cart before and after the collision. The momentum of the cart before the collision is equal to the momentum of the cart after the collision. You can use the formula p = mv, where p is momentum, m is mass, and v is velocity, to calculate the momentum of each cart. Then, you can compare the values to determine if momentum is conserved in the collision.

3. What is an elastic collision and how does it differ from an inelastic collision?

An elastic collision is a type of collision where the total kinetic energy of the system is conserved. In this type of collision, the objects involved bounce off each other without any loss of energy. On the other hand, an inelastic collision is a type of collision where the total kinetic energy of the system is not conserved. In this type of collision, some of the kinetic energy is converted into other forms of energy, such as heat or sound.

4. Can you use the law of conservation of momentum to solve for the velocity of an object in a collision?

Yes, you can use the law of conservation of momentum to solve for the velocity of an object in a collision. As mentioned before, the momentum of an object before and after a collision is equal. So, if you know the momentum of one object and the mass of both objects, you can solve for the velocity of the second object using the formula v = p/m.

5. How does the angle of collision between two carts affect the momentum of each cart?

The angle of collision between two carts can affect the momentum of each cart in different ways, depending on the situation. If the carts collide head-on, the momentum of each cart will be equal but in opposite directions. However, if the carts collide at an angle, the momentum of each cart will be split into two components, one parallel to the angle of collision and one perpendicular to it. This means that the carts may end up with different final velocities and momentum values after the collision.

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