Principle of conservation of linear momentum
Introduction
When objects collide, whether locomotives, shopping carts, or your foot and the sidewalk, the
results can be complicated. Yet even in the most chaotic of collisions, as long as there are no
external forces acting on the colliding objects, one principle always holds and provides an
excellent tool for understanding the dynamics of the collision. The principle is called the
conservation of momentum. For a two-object collision, momentum conservation is easily
stated mathematically by the equation:
pi = m1v1i + m2v2i = m1v1f + m2v2f = pf ;
where m1 and m2 are the masses of the two objects, v1i and v2i are the initial velocities of the
objects (before the collision), v1f and v2f are the final velocities of the objects, and pi and pf are
the combined momenta of the objects, before and after the collision. In this experiment, you
will verify the principle of conservation of linear momentum in a collision of two air track
gliders.
Procedure:
Part I: To verify the principle of conservation of linear momentum for collision with a
stationary object
1.
Set up the air track, photogates, gliders with smart timer picket fences and smart
timers as shown in figure 1.
figure 1
2.
Level the air track with the leveling spirit. This may be accomplished by
adjusting the screws on the legs on one side, or by elevating the other end with
the manual jack.
3.
Switch on the air blower. Set the airflow to position 3.
4.
Place glider 1 and glider 2 at rest to the right of photogate 1 and photogate 2
respectively as shown in figure 1. The gliders should not be moving to the
sides. If they do, level the air track again this time with the gliders.
5.
Adjust the height of the photogates so that their sensors are blocked by the
markings of the 1 cm flag on the Smart Timer Picket Fence.
6.
Switch on the Smart Timer. Press the Select Measurement key until the display
indicates Speed mode.
7.
Press Select key to display Collision mode.
8.
Press the Start/Stop to display * to get ready for measurement.
9.
Give glider 2 a slight push to collide with glider 1.
10.
After glider 1 passes photogate 1, stop it with your hand.
11.
Press the Start/Stop key to stop measurement.
12.
The two values displayed correspond to two velocities of gliders passing
through photogate 1.
13.
Press the Select key to read the velocities of gliders passing through photogate
2.
14.
To repeat the experiment, perform steps 4, 7, 8, 9, 10, 11, 12 &13.
15.
Take at least 5 sets of measurements.
15.
Repeat the whole experiment by adding weights of 100 g on glider 1.
Part II: To verify the principle of conservation of momentum for collision of 2 moving
objects
1. Set up the air track, photogates, gliders and smart timers as shown in figure 2.
figure 2
2. Give both gliders a push simultaneously to collide with each other.
3. Read off the initial and final velocities of the gliders from the smart timer as before.
4. Repeat the experiment to get at least 5 different initial speeds.
5. Repeat the above procedure by
i) Adding 50g to each side of glider 1 with no additional weight on glider 2.
ii) Adding 100 g to each side of glider 2 with no additional weight on glider 1.
Do your results in Parts I and II support the principle of conservation of linear momentum?
Explain your conclusion.
Part III: To determine the unknown mass of a given sample.
For the last part of this experiment, you will use the Principle of Conservation of Linear
Momentum to determine the unknown mass of a given sample. Briefly explain the
configuration used and the results you have obtained. Each set of mass is coded. Indicate this
code clearly in your report.