Snow Day Blog: Conservation of Momentum

In this blog, I tried to demonstrate the conservation of momentum. Momentum is mass times velocity (p=mv), and the conservation of momentum states that in a system, the sum of momentum of the objects does not change. In formula, this can be written as:

m₁v₁+m₂v₂=m₁v_1f+m₂v_2f

One way to demonstrate this is through observing the momentum change during a collision of two objects and see if the momentum before and after the collision are the same. I decided that I would set up a camera and record two objects colliding. However, since using objects that slide on ground will cause too much friction which makes result inaccurate, I decided use two round pencils, both of which can roll on the ground. In this way, both objects are rolling when they collide so the friction is minimum. To make the procedure easier, I chose two identical pencils of same mass and experimented with them to see what is the best way to make them collide. I found through several trial that if the two pencils move towards each other when they collide, the resulting velocity of both pencils are likely to be zero, which means that both pencils stop moving after collision. Thus, I decided to apply initial force to both objects in the same direction, but more force to the first pencil than to the second pencil. In this way, both pencils keep moving throughout the course and it is easier to observe.

The course of the two objects during the observation is like this: first, I place two pencils in front of the camera. Then I apply a greater force onto the pencil on the left and a lesser force onto the pencil on the right; both force are towards right. Then, as they move, the pencil on the left collides into the pencil on the right.

After that, the two pencils keep moving

And they roll towards the right side of the camera.

I then put the result into logger pro and trace the points

Finally, I export the data collected into Excel to calculate the total momentum. To do that, I first need the velocity of the two pencils, which are given in Logger Pro. I also need the mass of the two pencils, which I assume is 3g, or 0.003kg. I then calculated the total momentum (p total), which is according to the formula

P_total=p₁+p₂=mv₁+mv₂

With Excel I calculated the result, and made a total momentum vs. time graph

The graph is like this:

Clearly, the trend of this total momentum vs. time graph is that the total momentum does not change significantly as time changes. In other words, the total momentum of the system of the two pencils remain constant. This is consistent with the conservation of momentum, which is what I have to demonstrate in this blog.

In this collision, the two pencils go in the same direction after they collide, so it is an inelastic collision. The kinetic energy in inelastic collision is not conserved, and I calculated the total kinetic energy of the system of the two pencils using the formula

KE_total=(1/2)mv₁²+(1/2)mv₂²

Then, I find the difference between the initial total kinetic energy and the final total kinetic energy, which is

1.1262*10^-5J-2.30439*10^-5J=-1.17819*10^-5J

The amount of kinetic energy lost during the collision is -1.17819*10^-5J.