# Homework Help: Ellastic collision problem.

1. Mar 4, 2012

### ScienceGeek24

1. The problem statement, all variables and given/known data

Mass m1=7kg with speed of 3 m/s collides at the origin with a mass m2= 8 kg that has a speed of 5 m/s, (at an angle of 33 degree in the 2nd qwuadrant). After the collision , mass 2 remains at rest at the origin. Find the final velocity of mass 1 (magnitude and direction).

2. Relevant equations
vf=m1+m2/m1-m1 time vx

vf=2m/m1+m2 vy

3. The attempt at a solution
I tried using this equation to get the right answer which is 3.59m/s by doind this (2(8kg)cos(33)/7kg+8kg time 5 m/s and i get 4.47 m/s. What i'm I doing wrong here?

2. Mar 4, 2012

### SammyS

Staff Emeritus
Be more specific about the direction of each object before the collision.

3. Mar 4, 2012

### ScienceGeek24

Object 1 is at the orign of a coordinate system and object to is coming from the left to the right at an angle of 33 degree above the x axis.

4. Mar 4, 2012

### Staff: Mentor

The setup is something like this?

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5. Mar 4, 2012

### ScienceGeek24

yes but object 1 goes straight along the x axis.

6. Mar 4, 2012

### ScienceGeek24

as a matter of fact m1 comes from the left side to the right at a speed of 3m/s. after the collision mass 2 remains at rest at the origin . Find the final velocity of mass 1 (magnitude and direction)

7. Mar 4, 2012

### Staff: Mentor

I think you should make your own drawing and post it, because your descriptions all seem to be self-contradictory to my (perhaps limited) understanding!

8. Mar 4, 2012

### ScienceGeek24

ok this is the picture

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9. Mar 4, 2012

### ScienceGeek24

Mass m1=7 kg with a speed oof 3 m/s collides at the origin with a mass m2= 8 kg that has a speed of 5m/s, as shown. After the collision, mass 2 remains at rest at the origin. Find the final velocity of mass 1 (magnitude and direction).

10. Mar 4, 2012

### Staff: Mentor

Momentum must be conserved in the collision. Which body has nonzero momentum after the collision occurs? What are its component values?

11. Mar 4, 2012

### ScienceGeek24

Object m1 one has non zero momentum after the collision. I would say the components are m1v1 I tried doign this. vf= 2(7kg)/ 7kg+8kg times 3m/s if is that what are you telling... it did not give me the answer.

12. Mar 4, 2012

### Staff: Mentor

Momentum is a vector. It has components. What is the momentum vector of the system before the collision?

13. Mar 4, 2012

### ScienceGeek24

I know that momentum is a product of mass times velocity and that velocity has direction. And the product of a scalar quantity and a vector quantity is a vector quantity. for m2 it would be M2cos(33)(5m/s) southwest, and m1 is m1cos(147)(3m/s) east. is that right?

14. Mar 4, 2012

### Staff: Mentor

The components of a vector should be parallel to the axes. That is, they'll be either positive or negative on the x-axis or y-axis.

Your drawing shows m1 initially traveling in the negative direction on the x-axis. So its only contribution will be along the x-axis:-m1*v1, where v1 is its speed (3m/s). Mass m2 is initially traveling more or less "southeast", and we'd expect it to have a positive contribution along the x-axis and a negative contribution along the y-axis. Use trig and the given angle to calculate its two components.

15. Mar 4, 2012

### ScienceGeek24

ok so -(8kg)sin(33) + (8kg) cos(33) = 2.35 is that right??

16. Mar 4, 2012

### Staff: Mentor

The x and y components of the momentum must be kept separate. Also include the velocity;
Px = m*v*cos(θ), Py = m*v*sin(θ).

For these types of problem it is often best to start out by finding the x and y components of the velocities of the objects first. Then the momentum components can be obtained by multiplying each by their masses. Sum the like components of the momentum for each of the objects to find the total momentum components.

17. Mar 4, 2012

### ScienceGeek24

Ok so you are saying that I have to sum Px = m2*v2*cos(θ) -m1*v1 then Py = m*v*sin(θ)-m1*v1?? sorry man i having trouble grasping what you are saying.

18. Mar 4, 2012

### ScienceGeek24

i give up dude. I have no idea what you are saying. I don't see exactly what you mean. This one is too difficult.

19. Mar 4, 2012

### Staff: Mentor

You want to find the total momentum vector for the system. It will be a conserved quantity in any system.

Each individual body has its own momentum vector. You want to find those vectors and add them all together. To do this you first need the momentum vectors in component form (components in the x and y directions). Hence m*v*cos(θ) and m*v*sin(θ) for each one, using the appropriate values of m, v, and θ for each body.

Sum up all the x components. Sum up all the y components. That's your total momentum in its component form.

20. Mar 4, 2012

### ScienceGeek24

I need to know if I'm doing anything right. I think that there is only one y component to sum up and that is just Py = m*v*sin(θ) and there is no other y component to sum up in the y direction other than that one, with that so there is only Py = m*v*sin(θ) for the y components. In the case of the x components i think i have to sum up Px = m2*v2*cos(θ)+-m1*v1 because they are both in the x direction. If i'm correct sum all up it would be m2*v2*cos(θ)-m1*v1+ m*v*sin(θ). If is THAT what you are telling me... I need to know if that is right. Or if i am doing anything right to what you are indicating me to look for...

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