May-6-2015 Lab 14: Collisions in two dimensions

the Purpose of this lab: look at a two-dimensional collision and determine if momentum and energy are conserved.

           -steel ball with steel ball

           -steel ball with aluminum ball

we got the experiment equipment like the picture.

Open the program, go to set up the camera by following those steps:

Camera settings (continued):

Lab setup:

Before we start the lab, we need to level the table first. 

Then gently set the stationary ball on the leveled glass table. 

Aim the rolling ball so that it hits the side of the stationary ball. 

The balls should ideally roll of at some decent angle from one another. 

after we got the video of two ball collision, we need to do something on the video: Grab the point which two ball just collided to rotate the axes, set origin and add point series for the way of ball path. 

First, we do steel ball collide with steel ball. what we got from the experiment is : 

We measured the mass of steel ball m(sb) = 0.07 kg.

after linear fit all of those point, we could have the velocities at x-axis (horizontal with initial velocity) and y-axis(vertical with initial velocity ) before and after two ball collision. 

Here is the calculation:

before two ball collision:

we got the velocity at x-axis V(x) = 0.8474 m/s (which is the slope of green points) and V(y) = 0.0062 m/s (which is the slope of red points) of first steel ball. 

second ball is at rest.

from the data we collected, we calculated the momentum of two balls before collision p(x) = 0.059 kg*m/s and the momentum of two balls after collision p(2x) = 0.056 kg*m/s at x-axis. 

in addition, we calculated the momentum of two balls before collision p(y) = 0.004 kg*m/s and the momentum of two balls after collision p(2y) = -0.003 kg*m/s at y-axis. 

here is the calculation of energy:

conclusions:  p(x) and p(2x) are pretty close, p(y) and p(2y) are also very close, so we could say the momentum is conserved in this two steel balls of two-dimensional collision. 

however, the initial kinetic energy KE(i) is bigger than final kinetic energy KE(f). there were some energy lost from this collision. so we could say the energy is not conserved in this two steel balls of two-dimensional collision.

Right now, we do the steel ball collide with aluminum ball. we measured the mass of aluminum ball m(ab) = 0.02 kg. there is what we got from the experiment:

after linear fit all of those point, we could have the velocities at x-axis (horizontal with initial velocity) and y-axis(vertical with initial velocity ) before and after two balls collision.

Here is the calculation:

before two ball collision:

we got the velocity at x-axis V(x) = 0.6071 m/s (which is the slope of green points) and V(y) = -0.0034 m/s (which is the slope of red points) of the steel ball. 

the aluminum ball is at rest.

from the data we collected, we calculated the momentum of two balls before collision p(x) = 0.0425 kg*m/s and the momentum of two balls after collision p(2x) = 0.0444 kg*m/s at x-axis. 

we calculated the momentum of two balls before collision p(y) = -0.00024 kg*m/s and the momentum of two balls after collision p(2y) = 0.0016 kg*m/s at y-axis. 

here is the calculation of energy: 

conclusions:  p(x) and p(2x) are pretty close, p(y) and p(2y) are also very close, so we could say the momentum is conserved in this two steel balls of two-dimensional collision. 

however, the initial kinetic energy KE(i) is smaller than final kinetic energy KE(f). there were some energy lost from this collision. so we could say the energy is not conserved in this two steel balls of two-dimensional collision.