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THE CONSERVATION OF LINEAR MOMENTUM
Introduction In this experiment you will test the validity of the Law of Conservation of Linear Momentum in one dimension utilizing elastic and inelastic collisions on an air track.
Apparatus
Computer with Logger Pro software
Air Track Accessory kit - bumpers for the elastic collision
Right angle clamps (2) or integral photogate clamps
Vernier Lab Pro box Air Track Gliders (2) Laboratory Balance
Pasco Air Track Vernier Photogate (2)
Air supply Ring Stands (2)
Figure 0: Elastic Near Collision
Theory If two objects collide, and are subject to no net external forces, then it can be shown by application of Newton's 2nd and 3rd Laws that the total linear momentum of the system of masses will not be altered by the collision. The linear momentum of an object of mass m 1 and velocity v 1 is given by p 1 = m 1 v 1. In a system consisting of two objects of momentum p 1 and p 2 , the total linear momentum is the vector sum of their individual momenta:
p 1 + p 2 = m 1 v 1 + m 2 v 2
The total linear momentum before collision is m 1 v 1 + m 2 v 2
Figure 1 (Before the collision)
If the two masses collide, in general, their velocities will be altered to v 1 ' and v 2 ', respectively.
The total linear momentum after collision is m 1 v’ 1 + m 2 v’ 2
Figure 2 (After the collision)
According to the conservation of linear momentum principle, the total linear momentum will not be altered by the collision, or
p 1 + p 2 = p 1 '^ + p 2 '^ (1)
that is: m 1 v 1 + m 2 v 2 = m 1 v’ 1 + m 2 v’ 2 (2)
Procedure Conventions: Glider #2 is always the glider that is launched. Glider #1 is always the glider that starts out at rest between the two photogates. Ensure that the photogate that Glider #2 initially passes through is labeled Photogate #2 and that it is plugged into Digital Input #2 in the Vernier Lab Pro box. Ensure that the photogate that Glider #1 passes through is labeled Photogate # and that it is plugged into Digital Input #1 in the Vernier Lab Pro box.
- Start the computer.
- Turn on the air supply and increase the flow volume until the gliders are floating on a cushion of air. Level the air track by placing a glider in the center of the track and adjusting the leveling screws until the glider will remain at rest.
- Clearly label the Gliders as #1 and #2 using a small piece of masking tape.
- Plug the photogate timers into the Digital Inputs # 1 and # 2 in the Vernier Lab Pro box according to the convention above. Place the photogates symmetrically about the center of the track, leaving about 70 cm of open space between them.
- Place one of the calibrated flags on top of each glider. If a flat flag is used ensure that the plane of the flag is aligned PARALLEL to the centerline of the glider. Adjust height of photogates so that the flags will interrupt the beams when the gliders pass through the photogates. (Test to see if photogate timers work properly – when the beam is blocked the Red LED will light up.)
PART 2: Inelastic Collision
Figure 4: Inelastic at launch
- Rotate the gliders by 180o^ so that the straight pin and a clay cup will be facing each other. Remove the safety cork from the straight pin.
- Weigh both gliders and enter the data in Table 2. Ensure that the masses are the same to within 1.0 gram. If necessary add a couple 1.0 gram disks to the lighter glider.
- Place Glider #1 between the two gates, and bring it to rest. Start the timer by clicking on the Collect button, and launch Glider #2 toward Glider #1.
- Go to step #3 and Repeat that Procedure.
- You have finished taking data. In Part 3, for the Kinetic Energy calculations, you will use the data that was taken in Part 1 and Part 2.
PART 3: Energy Calculations
- In the elastic cases the value of the total kinetic energy should be the same after the collision as it was before the collision.
- Compare the kinetic energies in each of your elastic trials. KE = (1/2) m v^2
- For the elastic case: KEf = KEi
- Express the % difference between them. ( KEf - KEi )*100/ KEi
- In the completely inelastic cases , where the objects stick together after the collision, a substantial amount of kinetic energy is "lost" in the collision.
- Measure the change in kinetic energy observed in the inelastic cases. Compare the measured differences between before and after to the anticipated differences.
- For the inelastic case: KEfCalc^ should be (m 2 /(m 1 + m 2 ))KEi
- Express the % difference between them. ( KEf - KEfCalc^ )*100/ KEfCalc
Lab Report
Your report should follow the instructions in the document “Format for Formal Lab Reports.”
11d-Conservation of Momentum
Data Tables
Flag Length 1_____________(m)
Flag Length 2_____________(m)
(4 significant figures)
Table 1A - Energy Calculations - Elastic
Trial
KE
1B
KE
2B
KE
Total B
KE
1A
KE
2A
KE
Total A
% Diff
Table 2
INELASTIC
COLLISION
Before Collision
After Collision
Trial
m
1
m
2
v^1
v^2
p 1
p 2
p tot
(m
+m 1
v^1
’; v
(v
’+v 1
p tot
’^
% Diff
Table 2A - Energy Calculations - Inelastic
Trial
KE
1B
KE
2B
KE
Total B
KE
Total A
% Difference
Table 1
ELASTIC
COLLISION
Before Collision
After Collision
Trial
m
1
m
2
v^1
v^2
p 1
p 2
ptot
v^1
’^
v^2
’^
p^1
’^
p
p tot
’^
