22 April 2015. Collisions in two dimensions.

Purpose
to look at the theory of conservation of momentum and conservation of energy.

Apparatus:

1. A glass table. This will be the base of the collision since it generates less friction that any other type of material that we have.
2. Steel balls and aluminium balls. As the object of collision.
3. Video web-cam, logger pro, and laptop. To capture and analysis the data.

Procedure

1. We set up the glass-table and web cam as the picture shown.

2. We record the weight of each ball used (aluminium and steel).

First and second steel ball in first experiment

steel ball in second experiment

aluminium ball in second experiment

3. Then we record the collision using the laptop and the webcam.
4. Do steel ball vs steel ball first, then steel ball vs aluminum ball.
5. Analysis the data and calculate whether momentum or the kinetic energy is conserved.

Data Analysis:

Steel vs steel

• After we capture the movement of the collision, we analyze it by creating points series in every movement of the two ball, set up the x axis and the y axis, and measuring any necessary apparatus that is going to be used as comparison in the video.

• For example, we also measure the length of the glass table used in this experiment for comparison.

65 meters length

• Then, the dots that we give will give us velocity and position data in x and y direction among other things. For example, below is the position of the ball in x and y direction.

The (0) is the second steel ball that is at rest while waiting for the first ball (5) to collide with it

• To see whether the momentum is conserved, we evaluate it in x and y axis.
• We make new calculated momentum in x-axis and y-axis column for both the first and the second ball using the weight that we already recorded. If the total momentum in x axis (the momentum X first ball plus the momentum x second ball) is constant then momentum in x direction is conserved, so as if the total momentum in y axis is constant then the momentum in that direction is also conserved.
• Here is some the examples of calculated momentum column that we made.

Momentum of the first steel ball in the x-axis

Momentum of the second steel ball in the y-axis

Total momentum of the first and second ball in x direction

• Then, this is the graph of the total momentum of the first and second ball in both x and y directions.

• As you can see, the values are more or less almost constant. That means the momentum is conserved in both x and y direction; momentum is conserved in this collision.
• Next, we need to check whether the kinetic energy is also conserved. Therefore, we created new calculated column of kinetic energy of the first ball and the second ball. Then the TOTAL kinetic energy of both balls.

Kinetic Energy of the first steel ball

Kinetic energy of the second steel ball

Total Kinetic Energy

• This is the graph of the TOTAL kinetic energy with the first and the second KE.

the value of the TOTAL KE is almost constant.

• As we can see, the KE is not as constant as the total momentum. This is because this collision is not really elastic. In non-elastic collision, kinetic energy is not conserved because the energy is also transformed to sound energy and heat. That is why the Kinetic energy after collision is a little bit lower than before collision.

Steel vs aluminium

• We did the same exact procedure as we did in the first experiment. The aluminium ball is the ball waiting for the collision from the steel ball.
• When we do the new calculated column, we need to change the mass of the ball. Here is some example of the new calculated column in the second experiment.

Momentum of the steel ball in y direction

Momentum of the aluminium ball in x direction

Total momentum of both balls in y direction

• Then, this is the graph of the total momentum of the first steel ball and second aluminium ball in both x and y directions.

• As you can see, the values are more or less almost constant. That means the momentum is conserved in both x and y direction; momentum is conserved in this collision.
• Next, we also need to check whether the kinetic energy is also conserved. Therefore, we created new calculated column of kinetic energy of the first ball and the second ball. Then the TOTAL kinetic energy of both balls.

Kinetic Energy of the first ball

Kinetic Energy of the second ball

TOTAL kinetic Energy

• This is the graph of the TOTAL kinetic energy with the first and the second KE.

• As we can see, the KE is not as constant as the total momentum. This is because this collision is not really elastic. In non-elastic collision, kinetic energy is not conserved because the energy is also transformed to sound energy and heat. That is why the Kinetic energy after collision is a little bit lower than before collision.

Conclusions

• Momentum is always conserved in collisions whether the mass is lighter or heavier, the speed is slower or faster as long as there is no external forces acting, such as friction. In this case, friction is there in a very small amount, that is why the momentum is not really conserved (not really constant).
• Kinetic energy is also conserved if only the collision is elastic. In these experiments, collision are only nearly elastic. The kinetic energy is also transformed into heat and sound.
• The errors in this experiment comes from;
• The webcam is a fish-eye like lens; meaning that it is more concave in the middle to capture wider angle. This will messed up the 65 m length of glass table that we use as comparison in the video.
• When we add point series, we did not really click it in the center point of mass. This will alter the velocity and the position of each ball.
• Friction from the glass table, but we ignore that.