Conservation of Momentum

Observing Conservation of Momentum Blog

By: Victor Paiz

For this blog, we were asked to demonstrate and observe the law of conservation of momentum. This law states that in a closed system, linear momentum remains constant throughout time regardless of any possible changes within the system. In other words, the momentum of any two objects before a collision would be the same after the collision.

With this comes two different types of collisions ... Elastic and Inelastic. In an elastic collision both momentum and kinetic energy are conserved, while in an inelastic collision only momentum is conserved and not kinetic energy.

This Conservation of Momentum can be shown through this mathematical formula:

m1*v1 + m2*v2 = m1*v1final + m2*v2final  


To prove the law of conservation of momentum, I came to the conclusion that the collision between two household objects (water bottle full of marbles and a tube of caulk) would be fitting for an experiment.  First, I placed down a tape measure on my desk and measured out 39 inches (or about 1 meter) so that I may track the position of the objects in respect to time elapsed. Secondly, I placed the tube of caulk at the 20 inch (0.5 meter) mark and the water bottle full of marbles at the start of the measuring tape. I then proceeded to roll the water bottle into the tube of caulk in as straight of a line as possible so that the two objects may collide in a straight line.

Then I used Logger Pro to graph the position of both the water bottle and tube of caulk in respect to the time elapsed. After finding my points, I graphed the x positions vs time for the water bottle before the collision (became stationary after the collision) and the tube of caulk after the collision (was stationary before the collision). Lastly, I found the slope of the X Position vs Time graphs which gives us the velocity of the object. 

Velocity of Water Bottle Before the Collision (Initial Velocity)

Vi = 0.8282 m/s

Velocity of Tube of Caulk After the Collision (Final Velocity)

Vf = 0.3102 m/s

From here we use the equations: P(Momentum) = Mass * Velocity and PInitial = PFinal

M1*V1i + M2*V2i = M1*V1f + M2*V2f

Mass are approximated ... Water Bottle = 0.5 kg and Tube of Caulk = 1.2 kg

0.5(0.8282) + 1.2(0) = 0.5(0) + 1.2(0.3102)

0.4141 Kg*m = 0.37 Kg*m

I was roughly 0.0441 Kg*m off from my initial momentum. However, the error in my calculations can be attributed to errors made in video analysis, outside forces not accounted for in my experiment, and inaccurate weight approximations due to not having a scale.  Some of the outside forces not accounted for would be the friction between my desk and both the water bottle and tube of caulk as it accelerates across the surface. This friction causes the objects to slow down quicker than if the surface were to be frictionless and this was not accounted for anywhere in my experiment. Apart from friction, the collision in itself could have been imperfect, meaning the two objects did not collide with one another head on, but rather they collided with each other at a slight angle. Given the possibility of these potential errors, the law of conservation of momentum still holds to be true. 

Kinetic Energy Lost

KE Lost is equal to KE (Initial) - KE (final)

((Bottle) + (Caulk))  - ((Bottle)+ (Caulk))

(0.5*0.5*0.8282^2 + 0.5*1.2*0^2) - (0.5*0.5*0^2 + 0.5*1.2*0.312^2)

So, approximately 0.11 Joules were lost during the course of the collision