Lab#15: Collisions in two dimension

Collision in two Dimension

Samuel
Ellis
Mia
10-19-2016

Purpose:

  Look at a two-dimensional collision and determine if momentum and energy is conserved.

Theory:

  Assume there's no friction and outside force acting on the objects. When two object collides, their momentum and energy are conserved. According to conservation of momentum, m1*v1i+m2*v2i = m1*v1f + m2*v2f, if its elastic. Which mean no matter how fast or slow the object is, it will have an effect on its final velocity. Moreover, during the collision, all the energy will transfer from before collision to after collision. We are able to use this theorem to calculate how much energy during collision. 

Procedure:

1. Record masses for metal ball and marble.

2. Gently set the stationary ball on the leveled glass table.

3. Set camera on the stick, make sure its able to record the movement for both balls.

4. Aim the rolling ball so that it hits the side of the stationary ball. (The ball should ideally roll off at some decent angle from one another.

5. Log in into loggerpro

6. Go to Options, then Movie Options..., then choose Override frame rate to 60 or 120 fps.

7. Advance the movie 2 or 4 frame(s) after adding a new point. 

8. Start adding point to every position of ball. 

9. Repeat same procedure for rest of ball.

Date:

Collision between white ball with colored ball

White ball(x): 0(initial) - 0.2941(final)

White ball(y): 0(initial) - 0.1910(final)

Colored ball(x): 0.6901(initial) - 0.3269(final)

Colored ball(y): 0.0357(initial)  - -0.2727(final)

Collision between Metal ball with White ball

Metal(x): 0.5308(initial)  ~ 0.5308(final)

Metal(y): -0.3529(initial)  ~ -0.2317(final)

White(x): 0(initial)  ~  0.1589(final)

White(y): 0(initial)  ~  -0.5489(final)

Graph:

(This is the center of mass graph for marble)

(This is the velocity of marble collide with white ball in x and y direction with before and after collision)

(This is the velocity graph of metal ball collide with white ball in x and y direction with before and after collision)

(This is the graph of position vs time for metal ball collide with white ball in x and y direction)

(Momentum for marbles)

(Momentum for metal ball)

(This is the graph of position vs time for marble collide with white ball in x and y direction)

(velocity of center of mass(marble) meter per second)

(Velocity of center of mass for metal ball)

(Energy over time graph for ball)

(Energy of metal ball)

(Graph of center of mass for metal ball)

Calculation:

We are able to calculate momentum and kinetic energy based on the given date(mass and velocity).

Momentum: m1_1 *v1_i +m2_i*v2_i = m1*v1_f + m2* v2_f
Based on conservation of momentum, the momentum will remain the same during before and after the collision if there's no additional force acting on it.

Marble:
final velocity: x= 0.2941, y= 0.1910
Vf = square root of (0.2941^2 + 0.1910^2)
     = sqrt((0.2941^2) + (0.1910^2))
    sqrt(0.12297)

     = 0.3507 meter per second

Metal:
final velocity: x = 0.1589, y = -0.5489
vf = square root of (0.1589^2+0.5489^2)
     = sqrt(0.3265)
     = 0.5714 meter per second

Conclusion:

Based on the law of conservation of momentum, the momentum is conserve during elastic or inelastic collision. In other word, the product of mass and velocity will become the same. According to this law, we are able to use LoggerPro to enter some given data about object(mass, weight..) and then use video camera to record distance traveled in certain amount of time, which give us velocity. We are able to use mass and velocity to find its momentum. With the given data, on the other hand, we can manually calculate the momentum to see if it match with LoggerPro data. However, our data DID NOT match exactly. The error may due to static or kinetic friction on the surface of balls or glass. Also, it might due to the dots we plotted, it might be a little off. But overall, the data is similar to what it should be.