What is the direction of the velocity/ elastic collisions.

In summary: It means that the total momentum vector must be the same before and after the collision. Two vectors are the same if and only if they have the same magnitude and point in the same direction. In (1) you say that the total momentum before the collision points to the left (negative) and up (positive). In (2) you say that the total momentum after the collision points to the right (positive) and down (negative). These two do not point in the same direction, therefore they are not the same before and after the collision, therefore your answers in (1) and (2) are inconsistent with momentum conservation.
  • #1
YMMMA
156
10

Homework Statement


in the attached file

Homework Equations


Momemtum = mass - velocity

The Attempt at a Solution


I solved it E. Since object 2 has the larger mass, the effect is less and will move backwards a little bit.
 

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  • #2
YMMMA said:

Homework Statement


in the attached file

Homework Equations


Momemtum = mass - velocity

The Attempt at a Solution


I solved it E. Since object 2 has the larger mass, the effect is less and will move backwards a little bit.
This is a 2d collision that conserves momentum. Make this the basis of your explanation. Is E consistent with momentum conservation?
 
  • #3
kuruman said:
This is a 2d collision that conserves momentum. Make this the basis of your explanation. Is E consistent with momentum conservation?
I am not sure. But no It should have y and x components , I guess.
 
  • #4
YMMMA said:
I am not sure. But no It should have y and x components , I guess.
You guess correctly. The total initial momentum has x and y components, therefore the total final momentum must have x and y components. You need to reconsider your answer.
 
  • #5
I think it is C. Object 2 is having a y component and is pushed horizontally to the first quadrant. Object 1 is having an x component and is pushed vertically to the fourth quadrant. I am a little bit unsure since I don’t know how to right the momentum in the y.
 

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  • #6
The total momentum is the vector sum of the momenta of the two balls. You don't have to write equations, but you need to be systematic. Not only you have to find the right answer, but also you have to exclude the others as incorrect. Fill in the blanks.

1. The total initial momentum is ____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.

2. Therefore the total final momentum must be
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.

3. The choice that is consistent with (2) is _________ .

4a. Choice _____ is inconsistent because the total final momentum is supposedly
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.
4b. Choice _____ is inconsistent because the total final momentum is supposedly
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.
4c. Choice _____ is inconsistent because the total final momentum is supposedly
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.
4d. Choice _____ is inconsistent because the total final momentum is supposedly
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.
 
  • #7
kuruman said:
The total momentum is the vector sum of the momenta of the two balls. You don't have to write equations, but you need to be systematic. Not only you have to find the right answer, but also you have to exclude the others as incorrect. Fill in the blanks.

1. The total initial momentum is ____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.

2. Therefore the total final momentum must be
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.

3. The choice that is consistent with (2) is ____C_____ .

4a. Choice _____ is inconsistent because the total final momentum is supposedly
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.
4b. Choice _____ is inconsistent because the total final momentum is supposedly
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.
4c. Choice _____ is inconsistent because the total final momentum is supposedly
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.
4d. Choice _____ is inconsistent because the total final momentum is supposedly
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.

That was hard, but helpful. Although I am still not sure. Can’t proceed before making sure I am correct, because basically they are all the same and the rest of the choices..
 
  • #8
You are making progress. This exercise should be an eye-opener for you because it seems you have not grasped what momentum conservation means. It means that the total momentum vector must be the same before and after the collision. Two vectors are the same if and only if they have the same magnitude and point in the same direction. In (1) you say that the total momentum before the collision points to the left (negative) and up (positive). In (2) you say that the total momentum after the collision points to the right (positive) and down (negative). These two do not point in the same direction, therefore they are not the same before and after the collision, therefore your answers in (1) and (2) are inconsistent with momentum conservation. You need to reconsider. Hint: One of the answers, (1) or (2), is correct but the other is not. Which one?
 
  • #9
kuruman said:
You are making progress. This exercise should be an eye-opener for you because it seems you have not grasped what momentum conservation means. It means that the total momentum vector must be the same before and after the collision. Two vectors are the same if and only if they have the same magnitude and point in the same direction. In (1) you say that the total momentum before the collision points to the left (negative) and up (positive). In (2) you say that the total momentum after the collision points to the right (positive) and down (negative). These two do not point in the same direction, therefore they are not the same before and after the collision, therefore your answers in (1) and (2) are inconsistent with momentum conservation. You need to reconsider. Hint: One of the answers, (1) or (2), is correct but the other is not. Which one?
I think it is 2. Is it like vector addition?
 
  • #10
YMMMA said:
I think it is 2. Is it like vector addition?
(2) is what? Correct or incorrect? Yes, it is exactly like vector addition. As I indicated in post #6,
kuruman said:
The total momentum is the vector sum of the momenta of the two balls.
 
  • #11
kuruman said:
(2) is what? Correct or incorrect? Yes, it is exactly like vector addition. As I indicated in post #6,
2 is the right one. Yes, sorry did not concentrate.
 
  • #12
kuruman said:
The total momentum is the vector sum of the momenta of the two balls. You don't have to write equations, but you need to be systematic. Not only you have to find the right answer, but also you have to exclude the others as incorrect. Fill in the blanks.

1. The total initial momentum is ____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.

2. Therefore the total final momentum must be
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.

3. The choice that is consistent with (2) is ____C_____ .

4a. Choice _____ is inconsistent because the total final momentum is supposedly
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.
4b. Choice _____ is inconsistent because the total final momentum is supposedly
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.
4c. Choice _____ is inconsistent because the total final momentum is supposedly
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.
4d. Choice _____ is inconsistent because the total final momentum is supposedly
____________ (positive/negative/zero) in the x-direction and ____________ (positive/negative/zero) in the y-direction.
All blanks are the same as 2. Choices ABDE except C
 
  • #13
OK. I think you got it.
 
  • Like
Likes YMMMA
  • #14
kuruman said:
OK. I think you got it.
Thank you for your help and time!:smile:
 

Related to What is the direction of the velocity/ elastic collisions.

1. What is the direction of velocity in an elastic collision?

In an elastic collision, the direction of velocity remains the same for both objects before and after the collision. This means that if one object is moving to the right before the collision, it will continue to move to the right after the collision. Similarly, if one object is moving to the left before the collision, it will continue to move to the left after the collision.

2. Does the direction of velocity change in an elastic collision?

No, the direction of velocity does not change in an elastic collision. The law of conservation of momentum states that the total momentum of a closed system remains constant before and after a collision. This means that the direction and magnitude of velocity for each object must remain the same in order to conserve momentum.

3. How does the direction of velocity affect the outcome of an elastic collision?

The direction of velocity plays a crucial role in the outcome of an elastic collision. If the directions of velocity for both objects are the same, they will simply bounce off each other with no change in speed. However, if the directions of velocity are opposite, the objects will exchange velocities and continue moving in opposite directions after the collision.

4. Can the direction of velocity be negative in an elastic collision?

Yes, the direction of velocity can be negative in an elastic collision. This simply means that the object is moving in the opposite direction from a chosen reference point. For example, if an object is moving to the left, its velocity would be considered negative if the chosen reference point is to the right.

5. How is the direction of velocity calculated in an elastic collision?

The direction of velocity in an elastic collision can be calculated using vector addition. This involves taking into account the initial velocities and their directions for both objects, as well as the masses of the objects. By applying the law of conservation of momentum and energy, the final velocities and their directions can be determined.

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